Mathematics Grade 4: Volume 2 9798628219782, 9781678030827

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Copyright © 2020, March 19, by Hassan A. M. Shoukr All rights reserved. This book or any portion thereof may not be reproduced or used in any manner whatsoever without the express written permission of the author except for the use of brief quotations in a book review. ASIN: B08641T1VH ISBN: 979-8-62821-978-2 ISBN: 978-1-67803-082-7 ISBN: 979-8-64036-895-6

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Dear parent, teacher, and student, The series of Mathematics Grade for primary stage is based on several principles: 1-

Mathematics is the queen of other sciences, i.e. all science has a certain amount of mathematics.

2-

Therefore, it must be accessible to all students and with different abilities, attitudes and inclinations...

Based on the previous principles, we did all of the following: 1) The mathematics grade series for primary

stage explains in details each topic of the book in simple, new and easy ways with solved examples followed by graduated exercises. Our strategy is analysis then construction, we analyze the mathematics topic into its initial blocks (small lessons); then we build every two blocks then every three and so on until the topic is finally built in a pyramid form from all its apparent aspects.

2) The mathematics grade series is built on using

the colors well to help the reader to understand quickly every part.

3) In addition to, the dictionary of new terms and

words in the course at the end of the book. We did it in English-Arabic

4) In the end of the book, there are five self-tests

as a bank of problems to measure the abilities of self-analysis and self-assessment.

5) After self-Test, there are ten Exam Style

Papers to ensure the capabilities of using the different skills in the books.

Mathematics Grade Primary Volume 8 has the topics: fractions, its operations, and its application in our life; decimals, its operations, and its applications; the data representation (the bar chart, bar line graph, and broken line graph). We are pleased to know your opinion and observations about the book with our correspondence Hassan A. Shoukr

Contents Subject

Page

Arithmetic I-Fractions

1

2

Reading fractions

2

Equality of two or more fractions

3

Mixed number and improper fractions

8

Comparing two fractions

9

Arrangement of fractions

12

Addition of fractions

15

Subtraction of fractions

20

Multiplication of fractions

22

Division of fractions

26

II- Applications on Fractions

29

Different Types Of Problems

29

Word Problems

35

III- Decimals

45

Decimal Form

45

Reading Decimals

45

Numeral Decimals

46

Place Value

49

Equivalence of two or more Decimals

51

Comparing Decimals

52

Arrangement of Decimals

52

Addition of Decimals

56

Subtraction of Decimals

59

Multiplication of Decimals by 10, 100, 1000, …

60

Division of Decimals by 10, 100, 1000, …

63

IV- Applications on Decimals

67

Different types of problems

67

Word problems

78

Data Representations

84

V-Bar chart, Bar line graph and broken line graph

85

Self-Tests

97

Examinations

117

Answers of self-tests and examinations

133

Terms

143

Mathematics will be making you very

intelligent, so you must study it hard

Fractions

The fraction is a part (or parts) of a whole number (or a quantity)

Reading Fractions Example 1: 2 can be read as “ 2- Thirds” or “ Two over Three” 3 3 can be read as” 3- fifths” or “ Three over five” 5

Exercise 1: Show how to read the following: i)

6 7

ii)

5 9

iii)

7 10

iv)

7 12

v)

9 11

vi)

4 13

vii)

1

2 3

viii)

3

ix)

3

7 12

x)

10

5 8 7 10

Equality of Two or More Fractions Note: Value of a fraction is unchanged by multiplying or dividing both top and the bottom figures by the same number ×8 Example2: You can ×4 multiply in 3 5

×2

6 12 = = 10 20

= ×2

×4

Exercise 2:

24 40

any number, also you can multiply the new fraction to get the next

×8

Complete i)

1    = = = 2   

ii)

2    = = = 5   

iii)

3    = = = 7   

iv)

4    = = = 5   

v)

5    = = = 8   

vi)

3    = = = 4   

vii)

3    = = = 9   

viii)

4    = = = 11   

ix)

1    = = = 6   

x)

2    = = = 9   

xi)

3    = = = 10   

xii)

4    = = = 9   

•

If you want to simplify a fraction

Example 3: 8 12

÷2

= ÷2

Also Exercise 3:

10 5 = = 20 10

÷2

4 6 1 2

2 3

= ÷2

Simplify, then complete:

You can simplify a fraction by dividing both the top and the bottom by the same number

i)

8    = = = 16   

ii)

4  = 10 

iii)

10    = = = 30   

iv)

16    = = = 32   

v)

40    = = = 80   

vi)

14  = 49 

vii)

15    = = = 20   

viii)

36    = = = 48   

ix)

16    = = = 20   

x)

50   = = 100  

xi)

32    = = = 64   

xii)

9    = = = 27   

♦ If we want to reduce a fraction into its simplest form, we divide the top and the bottom by the greatest number that they are divisible by it. Example 4: Put the following fractions in lowest terms or “simplest form”. i)

8 16

ii)

18 24

8 16

÷ ..

=

Solution ... ...

Ask your self: are 8 and 16 divisible by 8? Where 8 is the greatest number that are they divisible by it

÷ .. 8 16 8 16

÷8

= ÷8

=

... ... ..1. ..2.

÷ ..

18 24

=

... ...

Ask your self: are 18 and 24 divisible by 6? Where 6 is the greatest number that they are divisible by it

÷ ..

÷6

18 24 18 24

=

... ...

÷6 ..3. = ..4.

Exercise 4: A-Reduce these fractions into their lowest terms i)

4 8

ii)

4 6

iii)

4 12

iv)

4 10

v)

3 6

vi)

3 9

vii)

3 12

viii)

3 18

ix)

5 10

x)

5 15

xi)

5 25

xii)

5 30

xiii)

8 16

xiv)

8 12

xv)

8 24

xvi)

8 32

xvii)

6 12

xviii)

6 18

xix)

6 30

xx)

6 36

xxi)

12 24

xxii)

9 27

xxiii)

12 30

xxiv)

15 60

xxv)

24 48

xxvi)

27 54

xxvii)

18 90

xxviii)

72 84

B- Join equal fractions i)

5 10

8 16 1 5

ii)

24 48

iii)

1 4

3 4 12 18

15 3

1 3

8 24 15 20

4. 6 12 16

9 12

2 5

iv)

6 30 4 16

8 32 3 6

27 54

3 7

4 10 20 50

21 49

If you have the following problems

•

Example 5: Complete: 4 ... = 5 10

i)

Solution

40

÷ 4 5

ans

1 6 = ... 12

ii)

= =8

2= 6 1 = 12 ...

... 10

8 4 ... = 5 10

ans

÷ 12

6 1 = 2 ... 12

Exercise 5: Complete Ai)

4  = 8 4

ii)

8  = 12 6

iii)

8  = 10 5

iv)

3 1 = 6 

v)

1 3 =  12

vi)

3 6 =  8

vii)

2  = 5 15

viii)

 3 = 20 5

ix)

 1 = 20 4

x)

1  = 2 24

xi)

3  = 4 28

xii)

3 9 =  24

xiii)

... 10 = 3 30

xiv)

2 16 = ... 32

xv)

25 ... = 35 7

xvi)

36 9 = 88 ...

xvii)

... 10 = 5 25

xviii)

4 40 = ... 80

Mixed Number and Improper Fraction •

If we want to convert an improper fraction into mixed number Example 6: Put the following in “mixed number form” 3 2

i)

ii)

5 3

Solution Ask yourself “How many 2 are in 3?

3 ... =… 2 2 ... =1 1

5 ... =… 3 3

Ask yourself “How many 3 are in 5?

... =1 2

2

and what‘s the remainder over 2”?

3

and what‘s the remainder over 3”?

Exercise 6: Convert the following into “mixed number” i)

10 4

ii)

11 5

iii)

6 5

iv)

10 7

v)

12 5

vi)

13 4

vii)

15 10

viii)

20 3

ix)

39 11

x)

40 3

xi)

53 12

xii)

19 4

Example 7: Put the following in “ improper form” +

2 17 3 = 5 × 5

+

3 31 = 7 × 7

4

We multiply the bottom ‘5’ by the whole number ‘3’, then we add on the product the top ‘2’ all over the bottom ‘5’

Exercise 7: Convert the following in to “ improper fraction “ i)

3

v) 10 ix)

1 4

ii)

3 5

1

10 11

5

3 4

3 5

iv)

5

3 5

3 10

viii)

1

5 7

5 11

xii)

8

iii)

2

vi)

4

2 9

vii)

1

x)

3

2 9

xi)

4

6 11

Comparing Two Fractions •

If we want to compare two fractions

Example 8: Put the suitable sign < , > or =: i)

4 5

...

3 7

Solution 15

28

4 5

...

3 7

We will use the arrow method as you see

28

>

15

4 5

...

3 7

4 5

... >

3 7

Exercise 8: Put the suitable sign < , > or =: i)

3 5  8 11

ii)

3 4  4 5

iii)

6 9  7 10

iv)

2 3  5 3

v)

3 4  10 7

vi)

3 9  5 11

vii)

5 6  11 7

viii)

3 9  9 27

ix)

8 1  16 2

x)

6 1  3 18

xi)

9 3  20 9

xii)

9 5  11 7

If we have two mixed numbers

•

Example 9: Complete using > , < or = : i)

4 4

4 4

>

3 4 … 3 4 5 3

3 4 … 3 4 5 3 4 … 3 > 4 5

ii)

2

1 2 … 2 3 5

Solution You noticed, the two whole numbers are different and 4 >3

1 3

>

2 5

2

1 2 … 2 3 5

2

2 1 … 2 > 3 5

You noticed, the two whole numbers are the same, we compare the two fractions as the previous

Exercise 9: Complete using > , < or = :

•

i)

4

5 3 … 3 7 4

ii)

3

1 3 …3 5 2

iii)

4

2 1 …5 3 2

iv)

7

2 4 …7 4 8

v)

3

1 3 …5 2 4

vi)

2

5 4 …2 7 8

vii)

10

4

2 3 …4 7 3

ix)

4

3 2 … 5 viii) 3 5

3 9 …6 5 15

If we have an improper fraction and mixed number Example 10: Complete using > , < or = : 2

11 3 … 5 4

Solution Convert the mixed number into improper fraction

2

11 3 … 4 5

11 11 … 4 5

Use the method

11 11 … > 4 5

arrow

Exercise 10: i) iv)

11 2 … 3 3 14 …2 7

2

ii) v)

15 2 …3 4 3 23 2 5 … 7 3

iii) vi)

14 1 …4 5 2 3 27 6 … 4 6

vii)

1

13 3 … 2 4

viii)

5…

16 5

ix)

2

5 20 … 5 7

Arrangement of Fractions If we want to arrange improper fractions

•

Example 11: Arrange each of the following groups of fractions in ascending order: 3 1 2 i) , , 10 4 5 Solution 20÷10

1 4

,

,

1 ×5 20

,

2× 4 20

6 20

,

5 20

,

8 20

1 4

,

3 10

,

2 5

3 10

,

3×2 20

Exercise 11:

2 5

20÷4 20÷5

Remember ascending order

10 = 2 × 5 4 =2×-×2 5 =- ×5

.

C.D=2 × 5 × 2 = 20 C.D means common denominator

A- Arrange each of the following groups of fractions in ascending order: 3 1 7 3 1 5 i) ii) , , , , 5 2 10 4 2 8

iii)

3 1 7 , , 8 4 16

iv)

2 1 4 , , 3 2 9

v)

3 2 8 , , 5 3 15

vi)

2 1 5 , , 9 3 18

vii)

23 3 13 , , 32 4 16

viii)

5 29 7 , , 6 36 9

ix)

13 7 19 , , 20 10 30

x)

2 5 7 , , 3 6 9

xi)

5 11 8 , , 6 12 9

xii)

2 5 7 , , 3 6 9

xiii)

13 7 19 , , 20 10 30

xiv)

1 2 5 , , 3 7 21

B- Arrange each of the following groups of fractions in descending order: i)

2 3 5 1 , , , 3 5 6 2

ii)

4 11 23 1 , , , 5 15 30 3

iii)

3 7 5 1 , , , 4 8 6 3

iv)

5 2 1 5 , , , 9 3 2 6

v)

5 3 7 1 , , , 6 4 9 2

vi)

7 5 11 3 , , , 8 6 12 4

vii)

4 7 17 1 , , , 5 8 20 2

viii)

5 7 22 1 , , , 6 9 7 3

ix)

4 13 7 1 , , , 11 33 22 3

x)

9 17 13 1 , , , 10 20 15 2

xi)

3 8 5 1 , , , 5 15 9 3

xii)

5 17 11 1 , , , 6 20 12 3

•

If we have an improper fraction , mixed number and a fraction If the whole Example 12:

numbers are different, then arrange them but if the whole numbers are the same, then arrange the fractions as the previous

Arrange the following in ascending order: i)

17 13 1 , ,1 20 5 2

Solution 13 5

17 20

,

17 20

,

23

17 20

,

11

5

2

,

1 2

,

1

,

11 2

23 5

Convert the improper fraction into mixed number Remember ascending order

Exercise 12: A- Arrange the following in ascending order: i)

2 12 5 1 , ,1 3 9 18

ii)

21 1 4 ,1 , 2 3 2 9

iii)

3 2 18 ,1 , 5 3 15

iv)

2 15 7 2 , ,1 3 6 9

v)

5 39 7 1 , ,2 6 36 9

vi)

23 7 19 ,1 , 20 10 30

vii)

13 1 17 ,2 , 8 4 16

viii)

3 1 15 1 ,2 , 4 2 8

ix)

15 1 8 ,1 , 2 6 12 9

x)

2 17 7 2 , ,2 3 6 9

1 12 5 2 , ,1 3 7 21

xi)

xii)

23 7 19 ,1 ,1 20 10 30

B- Arrange the following in descending order: i)

15 1 ,1 , 2 6 2

ii)

5 1 3, 2 , 2 9 2

iii)

7 15 1 , ,2 8 6

iv)

2

v)

27 13 ,1, 20 15

vi)

1

vii)

10 14 , 2, 3 11

viii)

17 13 , 3, 9 4

ix)

15 11 , ,4 6 3

x)

17 5 ,3 , 2 8 6

xi)

15 1 ,2 , 3 9 3

xii)

2 3 2 ,1 ,1 3 4

Addition of Fractions Proper fractions

•

Example 13: Add: i)

5 7 + 6 12

5 17 , 3, 6 9

17 23 ,2 , 20 12

Solution 5 6

12÷ 6

+

5 ×2 = 12

=

10

7 12

6

12 ÷12

7× 1 + 12

12 = 2 × 3 × 2 .

C.D = 2 × 3 × 2 = 12

7

+ 12

Convert the improper fraction into mixed number

17 12

=

=2×3

1 12 11 4 3 ii) + + 20 15 5

= 2

+ 4 + 3 20 15 5 11

60 ÷20

= = =

Solution

11 × 3 60 33

+

25 25 =1 = 1 60 60 5 =1 12

4 × 4 3 × 12 + 60 60

+ 16 + 60

85 60

60 ÷15

5 12

60 ÷ 5

20

=2×2×5

×- ×5×3 5 =- ×- ×5 C.D = 2 × 2 × 5 × 3 15

=-

= 60

36 Convert the improper fraction into mixed number You must put the fraction in the simplest form

.

Exercise 13: Find the result: i)

1 1 + 3 4

ii)

1 1 + 4 5

iii)

2 3 + 3 4

iv)

1 2 + 3 5

v)

1 3 + 3 5

vi)

1 3 + 2 4

vii)

1 1 + 2 8

viii)

1 1 + 4 8

ix)

1 2 + 2 5

x)

1 1 + 5 8

xi)

3 1 + 4 6

xii)

4 2 + 3 9

xiii)

4 3 + 5 10

xiv)

4 2 + 5 15

xv)

1 1 1 + + 2 3 4

xvi)

1 1 3 + + 2 3 4

xvii)

1 1 1 + + 3 4 6

xviii)

2 1 1 + + 3 4 6

xix)

2 3 5 + + 3 4 6

xx)

1 3 3 + + 4 8 16

xxi)

3 3 3 + + 4 8 16

xxii)

3 1 5 + + 8 6 12

xxv)

1 1 8 + + 4 6 9

•

xxvi)

7 9 13 + + 11 22 33 3 1 5 + + 8 4 12

xxiv)

11 7 5 + + 15 20 6

xxvii)

1 3 5 + + 4 8 16

Improper fractions and mixed number

Example 14: Add i)

xxiii)

5 1 +2 3 2

Solution

Convert into mixed number

5 3

1 2

+ 2

3

1 + 2 2

2 =1 3

12÷ 6

12 ÷12

1 ×3 2 × 2 =1 +2 6 6 4

= (1 + 2) 1

7 6

=3

7

1 = 4 6

ii) 2

60 ÷20

=5

=1

13 11 4 + + 20 15 5

5 =

6

11 20

+

11 + 5 20 11 × 3 60

= (5 + 2)

33

+

2 =-

×2

.C.D= 2 × 3

=6

3

+ 6

=3×-

Convert the improper fraction into mixed number

1 6

Solution

4 15

+

4 15

3 +2 5

13 5

60 ÷15 60 ÷ 5

4× 4 3 × 12 +2 60 60 + 16 + 60

36

20

=2×2×5

15

=- ×- ×5×3

5

=- ×- ×5

.C.D = 2 × 2 × 5 × 3 = 60

1

=7

Convert the improper fraction into mixed number

85 60

25 25 =8 =8 60 60

5 12

You must put the fraction in the simplest form

5 =8 12

Exercise 14: Find the result i)

1 2 3 1 +1 + 2 4 2 3

ii)

1 3 3 1 +1 + 3 6 4 8

iii)

2 4 1 + 3 5

iv)

15 +5 7

v)

3 7 5 3 + +1 4 16 8

vi)

1 1 8 2 +1 + 5 10 15

vii)

2 1 3 2 + 2 +1 9 3 4

viii)

1 1 7 4 +1 + 5 4 15

ix)

2+3

x)

4

xi)

5 5 5 + 2 +1 8 12 6

xii)

1 1 7 +1 + 5 4 15

xiii)

1 1 2 +1 + 2 2 4

xiv)

1 1 1 +3+ 2 3 6

xv)

5+2

2 3

xvi)

2+1

xvii)

7+2

1 2

xviii)

1 4 +5 3

1 2

3 2 +2 4 7

1 +3 6

Subtraction of Fractions •

Proper fractions

Example 15: Subtract

3 1 − 4 2

i)

3 4

4÷ 4

3 ×1 = 4

= =

3

-

1 2

-

1× 2 4

− 4

Solution 4 ÷2

2

=2×-

4 =2×2 C.D = 2 × 2 =4

2

1 4

Exercise 15: Subtract: i)

1 1 − 2 4

ii)

1 1 − 2 3

iii)

1 1 − 2 5

iv)

1 1 − 3 4

v)

1 1 − 3 4

vi)

1 1 − 4 5

vii)

2 1 − 3 2

viii)

2 1 − 3 4

ix)

2 2 − 3 5

x)

3 1 − 4 3

xi)

3 2 − 4 3

xii)

2 1 − 5 3

xiii)

1 1 − 2 8

xiv)

1 1 − 4 8

xv)

1 1 − 3 8

xvi)

5 3 − 8 5

xvii)

7 2 − 8 5

xviii)

1 1 − 3 6

xix)

7 5 − 12 9

xx)

7 5 − 8 6

xxi)

3 8 − 4 15

xxii)

7 9 − 15 20

xxiii)

19 5 − 20 6

xxiv)

9 13 − 22 33

xxv)

5 4 − 8 7

xxvi)

13 5 − 15 6

xxvii)

7 31 − 8 36

Improper fractions and mixed numbers

•

Example 16: i)

Convert into improper fraction

Subtract: 3 5 3 −1 4 8 3 3 4

=

15 4

=

15 × 2 8

=

30

5 - 1 8 13 8

− 8

13 × 1 8 13

Solution 4

=2×2

8 =2×2×2 .C.D= 2 × 2 × 2 =8

17 8

=

1 8 Exercise 16 : =2

Subtract i)

3 2 3 −1 4 3

ii)

7 2 −1 2 5

iii)

1 1 3 −1 5 6

iv)

25 3 −1 12 8

v)

13 3 −1 4 6

vi)

3

vii)

2

viii)

7 5 4 −3 9 12

ix)

1 4 3 −2 6 9

x)

5 7 4 −3 9 12

xi)

2

xii)

1 23 3 − 8 12

xiii)

2 10 3 −1 3 11

xiv)

1

xv)

3

5 11 −1 8 12

11 5 −1 12 18

7 14 − 20 15

Multiplication of Fractions •

Proper fractions

Example 17: i)

Multiply: 1 1 × 2 3

8 3 −1 15 10

3 8 −1 15 10

1 2

×

Solution

1 3

We multiply the top by the top and the bottom by the bottom

1 1 × 1 = 6 2 × 3

=

Exercise 17: Multiply i)

1 3 × 2 4

ii)

1 3 × 2 5

iii)

1 1 × 2 5

iv)

1 1 × 3 4

v)

1 2 × 3 5

vi)

1 4 × 3 5

vii)

2 5 × 3 7

viii)

1 1 1 × × 2 3 4

ix)

2 2 1 × × 3 5 3

x)

3 1 5 × × 4 2 7

xi)

2 1 1 × × 7 3 4

xii)

3 1 3 × × 5 2 4

xiii)

4 1 2 × × 5 7 9

xiv)

3 3 6 × × 4 5 7

xv)

4 1 1 × × 7 3 2

Example 18: i)

You must simplify before multiplication

3 2 × 4 6 1 2

= =

3 4

1 2

Solution

1

×

×

2 6

2

1 2

1 1 × 1 = 6 2 × 2

We multiply the top by the top and the bottom by the bottom

Exercise 18: Multiply: i)

1 ×8 2

ii)

1 ×9 3

iii)

1 ×8 4

iv)

1 × 10 5

v)

2 ×3 3

vi)

3 ×4 4

vii)

4 × 10 5

viii)

2 3 × 3 5

ix)

2 5 × 3 8

x)

3 4 × 4 5

xi)

2 3 × 3 4

xii)

3 8 × 4 9

xiii)

2 5 × 5 8

xiv)

5 3 × 6 8

xv)

5 9 3 × × 6 10 4

xvi)

2 5 3 × × 3 8 10

xvii)

3 5 4 × × 4 6 5

xviii)

5 3 4 × × 8 5 9

xix)

5 6 14 × × 9 7 15

xx)

5 3 7 × × 7 10 12

xxi)

9 5 4 × × 10 6 5

Improper fractions and mixed numbers

♦

Example 19: Multiply i)

4 3 ×3 4 3

=

4 3

×

4 3

×

3 3 4 15 4

Solution Before, you must convert the mixed into improper

1

4 = 3

×

1 1

×

1

= =

1 1

× 5 × 1

15 4

5 Remember: You must simplify before multiplication

1

5 1

=

5 =5 1

Exercise 19: Multiply: i)

2 1 ×1 3 2

ii)

3 1 ×1 4 3

iii)

2 1 ×2 5 2

iv)

3 1 × 5 3

v)

2 5 1 × 5 7

vi)

5 1 ×3 8 5

vii)

3 4 1 × 4 7

viii)

1 1 1 ×1 2 3

ix)

2 1 1 ×1 3 5

x)

3 1 1 ×1 4 7

xi)

3 1 1 ×1 5 4

xii)

3 1 1 ×1 5 4

xiii)

1 2 2 ×2 4 3

xiv)

1 3 3 ×1 4 13

xv)

1 1 3 1 ×1 × 2 7 11 3

xvi)

3 3 3 4 3 3 1 ×1 ×1 4 5 7 xvii) 1 × 2 × 1 13 11 8

xviii)

14 4 4 ×1 × 2 39 9 7

xix)

1 1 5 2 × 3 × 2 xx) 7 5 8

7 7 4 × 1 × xxi) 11 9 24

1

5 27 5 3 × ×1 6 46 9

Division of Fractions Proper fractions

♦

Example 20: Divide 3 3 i) ÷ 4 5 3 4

÷

Solution

3 5

15 5 × 3 = 12 3 × 4

= 5

We will use the arrow method of division as you see, where you must put the product at the head of the arrow

15

= 12 4

=

5 1 =1 4 4

Exercise 20: Divide i)

1 2 ÷ 2 3

ii)

2 3 ÷ 3 4

iii)

3 4 ÷ 4 5

iv)

2 3 ÷ 5 7

v)

3 1 ÷ 5 2

vi)

3 2 ÷ 4 3

vii)

5 2 ÷ 8 9

viii)

6 2 ÷ 7 5

ix)

7 3 ÷ 8 5

9 3 ÷ 10 8

x)

xi)

4 2 ÷ 5 3

xii)

5 2 ÷ 7 7

Improper fractions and mixed numbers

♦

Example 21: Divide: 1 1 i) 1 ÷ 2 2 3 3 1 2

= = =

÷

7 2

Solution

3 2 3

÷

13 3

You must convert the mixed numbers into improper fractions, then use the arrow method of division as you see and don’t forget put the product at the head of the arrow

3 × 7 13 × 2 21 26

Exercise 21: Divide i) iv) vii) x) xiii)

1 1 2 ÷1 2 3 1 2 4 ÷2 5 3 2 2 3 ÷4 3 5 3 2 ÷1 5 5 2 1 1 ÷3 3 2

ii) v) viii) xi) xiv)

1 1 1 ÷2 2 4 1 3 2 ÷1 2 4 2 1 4 ÷5 3 4 1 13 6 ÷ 7 5 3 2 1 ÷3 7 5

iii) vi) ix) xii) xv)

1 3 3 ÷1 2 4 1 1 2 ÷3 3 5 3 1 11 ÷ 2 7 5 13 1 ÷2 4 3 1 5 3 ÷1 8 9

Applications on Fractions Different Types of Problems ♦

Using >, or = : 3 3 1 2 i) +  × 5 10 5 3 Solution 3 3 1 2 +  × You must calculate the R.H.S 5 10 5 3 and L.H.S before using the 9 2  10 15 135 > 20

arrow method of or =.

9 2  10 15 Thus

9 2 > 10 15

Exercise 22: Put the suitable sign or =: i)

3 2 3 2 +  ÷ 7 5 8 5

ii)

3 3 2 3 1 + 1 − 3 5 4 8

iii)

2 5 3 ... + 3 6 5

iv)

5 2 5 − ... 7 5 9

v)

3 2 5 5 ×  − 9 5 7 14

vi)

2 3 3 3 1 × 1 ÷ 1 5 5 4 4

vii)

5 3 5 ... × 7 4 6

viii)

5 3 4 ÷ ... 6 5 9

ix)

1 1 1 1 1 + 2 3 ÷ 3 6 4 2

x)

3 3 2 3 2 − 1 ÷ 5 10 3 5

xi)

2 3 +3 9

xii)

15 5 2 − 1 ... 6 7

xiii)

1 3 1 1 3 − 1 1 × 2 2 4 2 3

xiv)

1 4 1 1 3 −  2 × 1 5 5 2 3

... 6

1 3

Problems of Completing

♦

♦ Addition Example 23: Complete: 1 1 i) 2 +  = 3 5 3 1 - 2 5

1 3 3 10 = 3

= =

-

10 × 5 15 50

11 5

− 15

-

11 × 3 15 33

Solution Here the space comes first or second the sign “+”always convert into “-“, but you must subtract the smallest from the greatest

=

17 15

2 15 Therefore =1

2

1 5

+ 1

2 15

= 3

1 3

Exercise 23 Complete ii)

5 4 +  = 7 5

1 1 1 +  = 2 3 3

iv)

1 1  + 1 = 3 4 2

v)

1 3  + 3 = 3 5 4

vi)

3 2 1 +  = 2 4 3

vii)

1 1 1 +  = 2 5 10

viii)

3 1  + 1 = 3 8 2

i)

 +

iii)

3 1 =1 4 2

Subtraction

♦

Here if the space in the first, the sign “-“convert into “+”, add the second and the last

Example 23: Complete i)

1 1 3 −  = 2 5 3

1 1 -2 3 5 3 10 11 = 5 3

1 3  − 1 = 2 8 4

ii) Solution

Here if the space in the second, the sign “-“ stills as it and subtract the last from the first

=1 =1

3 4 ×

+

2

+2

1 8 ×

= = =

10 × 5 15 50

-

− 15

11 × 3 15 33

1 3

6

1

+ 8

7 8

=3

7 8 Therefore

17 15

= 3

2 =1 15 Therefore 3

= (1 + 2)

3

- 1 2

15

7 8

-1 3 4

= 2

1 8

= 2 1 5

Exercise 23: Complete i)

1 3  − 2 = 1 3 4

ii)

3 1 1 −  = 4 2

iii)

1 2 3 −  = 1 5 3

iv)

3 3  − 2 = 1 5 10

v)

3 1  − 1 = 4 8 3

vi)

3 3 4 −  = 1 7 5

vii)

1 1 5 −  = 1 2 3

viii)

 −

♦

Multiplication

Example 24: Complete

i)

3 3 1 ×  = 1 4 5

4 1 =1 7 2

Here the space comes first or second the sign “ × ”always convert into “ ÷ ”, but you must divide the last by the first or the second3 1 1 2

8

8

1 =

3 5

÷

8 5 4 7

=

32 35

Therefore 1

3 4

×

Remember you must convert the mixed into improper before dividing

7 4

÷

=

Solution

3 1 4

× 8 × 5

32 35

= 1

3 5

Exercise 24: Complete ii)

1 3 ×  = 2 5

3 1 1 ×  = 4 2

iv)

1 5  × 1 = 3 7

v)

2 1  × 2 = 1 3 3

vi)

1 3 2 ×  = 1 3 4

vii)

4 ×  = 1

viii)

 × 3 = 2

ix)

3  × 1 = 4 4

x)

1 2 ×  = 1 3

i)

 ×

iii)

3 1 = 4 3

3 4

1 3

Division

♦

Example 25: Complete 1 1 3 ÷  = 2 4

i) 3

1 1 ÷ 4 2

= = =

7 2

÷

4 1

1 4

× 7 × 2

28 = 14 2

3

1 2

÷

14

Solution

Here if the space in the second, the sign “ ÷ ” stills as it “ ÷ ”, divide the first by the last

Therefore =

1 1  ÷ 2 = 3 5

ii)

1 4

1 5

2

×

1 3

=

1 5

×

7 3

=

1 5

×

7 3

=

1 5

× 7 × 3

=

Therefore 7 15

Exercise 25:

÷2

Here if the space in the first, the sign “÷” convert into “ × ” the second by the last

7 15 1 3

=

Complete

3 1 = 4 2

i)

 ÷

iii)

3 4 1 ÷  = 4 7

v)

 ÷

vii)

3 2 = 10 7 1 5 5 ÷  = 6 8

ii)

4 2 ÷  = 1 7 3

iv)

3 1  ÷ 1 = 2 5 5

vi) viii)

1 1 1 ÷  = 3 2 4 3 1 1 ÷  = 2 3 10

1 5

Word Problems on Fractions ♦ Addition Example 26: Ahmed bought three pencils for L.E 1 L.E

3 and two pens for 4

5 Find the total cost for the three pencils and two 7

pens?

Solution The total cost for the three pencils and two pens = 28÷ 7

5 7

+ 1

3 4

3 ×7 5× 4 +1 28 28

=

= (1) 1

=1

20

+ 28

28 ÷4

21

41 28

= L.E 2

4

=2×2

×-×7 C.D= 2 × 2 × 7 7 =-

= 28

Convert the improper fraction into mixed number

13 28

Exercise 26: i)

Hany bought two pencils for L.E

3 and two rulers for L.E 4

1 1 . Find the total cost for the two pencils and two rulers? 2

ii)

Mohamed bought two books for L.E 1 1 3

3 and two pens for 5

L.E 2 . Find the total cost for the two notebooks and two pens? iii)

1 2

Amr bought three coloured balls, the red one 1 gm weight, the green one 5

3 3 gm weight and the yellow 7 5 10

gm weight. Find the total weight of Amr’s balls? iv)

Bassem has got three toy coloured cars, the red one 5 cm long, the yellow one 10

1 2

3 cm long and the blue one 6 4

cm long. Find the total length of Bassem’s cars? v)

Mona bought three coloured satin ribbons , a red ribbon m long , a green ribbon 1

vi)

3 4

1 m long and the blue ribbon 2

3 m long. Find the total length of Mona’s satin ribbons? 10

Nadia has got a bag for L.E 10 1 2

3 3 , shoes for L.E 50 and 4 8

stokes for L.E 5 . Find the total cost of Nadia’s things? vii) Samia bought some chocolate for L.E 1 for 2

3 , two notebooks 5

1 3 pounds and a pen for L.E . Find the cost for the 10 4

chocolate, two notebooks and a pen?

viii) Ramy has trousers for L.E 30 35

3 and a smart jacket for 8

2 pound. Find the total cost of Ramy’s uniform? 5

Subtraction

♦

Example 27:

3 4

Nabila has got L.E 1 . She bought a ruler and a pencil for 5 remainder. . How much money was left? greater …….. than 8

L.E

Solution

The left = 1

3 4

=

7 4

=

7 ×2 8

=

5 8

5 8

− 8

14

5× 1 8 5

less …….. than difference left increase decrease more …….. than and so on. All these words denote to subtraction. 4

=2×2

8 =2×2×2 .C.D= 2 × 2 × 2 =8

= 9 8

= L.E 1

1 8

Exercise 27: i)

Bassem has got 2 1 4

1 pounds. He bought a chocolate and a 2

pen for L.E 1 . How much money was left?

ii)

Ahmed has got two containers. the first one weighs 1 , and the second one weighs 3

1 kg 3

1 kg . What is the 6

difference between the two Ahmed’s containers? iii)

Ramy’s length is

3 1 m and Mohammed’s length is 1 m. 2 4

How much is Mohammed’s length greater than Ramy’s length by? iv)

Abd El Rahman’s Weight is 10 is 15

3 kg , and Magdy’s weight 5

1 kg. How much is Abd. El Rahman’s Weight less 10

than Magdy’s weight? v)

Amr has got 3

1 1 kilograms of Oranges. He ate 2 3 6

kilograms of it. What is the remainder? vi)

Mona has got L.E 4

3 3 and her brother has got L.E 5 . 10 5

How much is what her brother has more than what Mona has? vii) Ahmed bought a ruler for L.E

3 3 and a pen for L.E . 5 10

How much do the price of ruler increase the price of pen?

Example 28: Heba Has got L.E 3 3 8

1 3 . She bought a pen for L.E and a pencil 2 4

for L.E 1 . How much money was left? Solution

The price of pen and the pencil = The price of pen

3 3 +1 8 4

3× 2 3 ×1 +1 8 1 6+3 3 6 = +1 =1 8 8 8 9 1 = 1 = 2 pounds 8 8 1 1 The left money = 3 − 2 2 8 What Heba has

=

= = = = =

This type of problem firstly, we add, then we subtract.

7 17 − 2 8 7 × 4 17 × 1 − 8 8 28 17 − 8 8 28 − 17 8 11 3 = 1 pounds 8 8

The price of pencil

What Heba spent.

Exercise 28: i)

12 1 kilograms of sweets. She gave kg 3 3 2 for her brother and 1 kg for her sister. How much 9

Rasha has got 4

sweets was left? ii)

1 from his father. He bought a 2 3 3 and a notebook for L.E 1 . What is chocolate for L.E 4 4

Nagy had taken L.E 3

the remainder?

iii)

2 3

Walaa had taken L.E 4 . She bought a book for L.E 1 a notebook for L.E

2 5

3 3 and a pencil for L.E 1 . How 10 4

much money was left? iv)

Ahmed’s mother has got a cake. She gave Ahmed his sister

v)

1 . How much cake was left? 4

1 and 3

3 meters of cloth. He gave Nadia 4 1 3 3 meters and her sister 2 meters. How much cloth 2 4

Nadia’s father has got 7

was left?

♦

Multiplication

Example 29:

1 2

Ahmed bought 2 kilograms of oranges, the price of onekilogram L.E

3 . How much did he pay? 4

Solution

The paying money

3 4

= The price of one kilo

= = =

Exercise 29: i)

3 4

3 4

×

×

1 2 5 2

The number of kilos

5 3 × 2 4 7 × 5 15 = = L.E 1 8 × 2 8

Mohammed has got 3 metre L.E

2

1 meters of cloth, the price of one 3

3 . What’s the total price? 5

3 kilograms of coffee, the price of the 5 1 kilogram L.E 15 . How much did he pay? 2

ii)

Ahmed bought

iii)

Mona’s dress was 3

1 meters, the price of one meter L.E 4

3 1 . What’s the total price of the dress? 7

iv)

3 4

Nadir bought a kilogram of apples for L.E 5 . What’s the price of 3

v)

1 kilograms? 2

Hoda has got 5 1 4

1 bars of chocolate, the price of a bar was 3

LE 1 . How much did she pay? ♦

Division

Example 30: Bassem bought 4

1 3 kilograms of butter for L.E 5 . 3 4

What’s the price of each one-kilogram? Solution The price of each one kilogram = 5 The total price

23 = 4

÷ ÷

4

1 3

13 3

The number of kilos

3 × 23 13 × 4

= =

3 4

69 17 = L.E 1 52 52

Exercise 30: i)

3 metre of cloth for making a suit, the price 4 1 of total cloth was L.E 9 . Find the price of total each one 2

Amr bought 5

metre of this cloth?

ii)

Layla has got 3

3 1 kilograms of a cake , she paid L.E 4 . 5 4

What’s the price of each one kilo? iii)

iv)

3 kilograms of butter, the price of 4 4 the kilogram was L.E . Find the price of butter? 5

Mohammed bought 5

Samira bought 5

3 1 bars of chocolate for 6 pounds. Find 4 2

the price of each bar of chocolate? v)

Bassem bought 9

5 2 kilos of oranges for 2 pounds. Find 5 9

the price of each kilo of oranges?

0

1

2

3

4

5

6

7

8

9

10

11

The decimal is a part (or parts) of whole numbers 10, 100, 1000, … and so on

Defn: Decimals are fractions that have denominators 10, 100, 1000, … and so on.

Decimal Form Well dear pupil comes to know the form of the decimals and its fractional form. 3 can be written in the form 0.3 10 6 can be written in the form 0.06 100 7 can be written in the form 0.007 1000

Thus the dot “.” is called “the decimal point” and 0.3, 0.06, 0.007, … are called “decimals”.

Reading Decimals Well dear pupil comes to learn how to read a decimal, we can read the decimals as follows:

Example 31: i)

0.5 can be read as “Zero point five”

ii) 1.65 can be read as “One point six five” iii) 23.053 can be read as “Twenty-three point zero five three” Exercise 31: Show how to read the following: i)

4.36

ii)

0.003

iii)

v)

413.6

vi)

40.31

vii) 14.362

1.001

iv)

0.043

viii) 133.005

Numeral Decimals Look at:

413.056 Whole number

Decimal

Numeral Decimal

Defn: Numeral Decimal (or mixed number) is a whole number and a decimal

♦ Converting from fractional form into decimal form Example 32: Put the following fractions in the decimal form: i)

5 10

Since 10 has 1zero, then insert “.” after 1-digit form the right.

51 100

ii) Solution 5 = 0.5 10

6 = 0.06 100

Since 100 has 2- zeros, then insert “.” after 2-digit from the right.

Exercise 32: Convert from the fraction form into the decimal form: 2 10

iv)

9 100

viii)

136 1000

xii)

3 1000

xvi)

i)

7 10

ii)

3 10

iii)

v)

4 100

vi)

7 100

vii)

ix)

23 1000

x)

15 100

xi)

xiii)

31 100

xiv)

5 10000

xv)

5 10 3 100

45 10000 3191 10000

Example 33: Convert the following into decimal form: 436 100

i)

6 43 1000

ii) Solution

Since 100 has 2Zero Then insert the “.” after 2digits from the right

436 = 4.36 100

43

Since 1000 has 3-Zeros Then insert the “.” after 3-digits from the right

43006 6 = = 43.006 1000 1000

Exercise 33: Put the following in the decimal form: i)

563 10

v)

11

♦

3 100

ii)

563 100

vi)

4

36 1000

iii)

1536 1000

vii) 46

7 10

iv)

15381 100

viii) 361

4 1000

Converting the decimal form into fractional form

Example 34: Put the following decimals in the fractional form: i) 0.03 ii) 0.015

There are 2digits after “.” To the right, then the denominator

Solution 0.03 =

003 100

There are 3digits after “.” to the right, then the denominator is 1000

0015 1000

0.015 =

Exercise 34:

Convert from the decimal form into the fraction form: i)

0.1

ii)

0.03

iii)

0.13

iv)

0.001

v)

0.05

vi)

0.007

vii)

0.0002

viii)

0.36

ix)

0.315

x)

0.013

xi)

0.0315

xii)

0.103

xiii)

0.1003

xiv)

0.0101

xv)

0.300

xvi)

0.400

Example 35: Convert from the decimal form into the fraction form: i) 41.3 ii) 5.36 There is 1-digit after the “.” to the right then the denominator is 10

Solution 41.3 = 41 3

10

5.36 = 5

36 100

=5

9 25

There is 2-digits after the “.” to the right then the denominator is 100

Exercise 35:

Put the following in the fractional form: i)

3.56

ii)

41.03

iii)

v)

4.301

vi)

45.001

vii) 136.038

viii) 5.006

ix)

12.5

x)

125.06

xi)

xii) 6.0002

xiii) 1.0025

xiv) 10.2314

153.4 2.008

xv) 1254.9

iv)

45.36

xvi) 123.1

Place Value

Look at: ..Thousands Hundreds Tens Units

To the right of the point

4361.381

To the left of the point

Tenth

Example 36:

hundredth thousandth ..

Show the place value of “ 8 “ in the following: i) 486.314 ii) 513.816 Solution 486.314

513.816

8 is tens

8 is tenth

Exercise 36: A-Show the place value of “5” in each of the following: i)

1.051

ii)

v)

543.186 vi)

25.38

iii)

163.005

vii) 5619.1

34.035

iv)

31.560

viii) 3413.5

B-Complete: i)

The place value of “3” in the number 4.328 is …….

ii) The place value of “6” in the number 1638.41 is ……. iii) The place value of “7” in the number 4.367 is ……. iv) The place value of “9” in the number 139.4 is ……. v) The place value of “2” in the number 14.32 is ……. Note:

After you have known the place value of a digit, we are going to show “another read” for the numeral decimals.

Example 37: i)

5.06 is “five and 6-hundredths”

ii)

25.46 is “twenty-five and 46-hundredths”

iii)

1.306is “one and 306-thousandths”

Exercise 37: Show how to read the following: “Write in letters” i)

1.05

ii)

22.003

iii)

0.033

iv)

1.08

v)

155.2

vi)

510.07

vii)

1.3

viii)

41.025

Example 38: Write in digits: i) One and hundredths

ii) Twenty-two and 3tenths

2-

Solution One and 2-hundredths

Twenty-two and 3-tenth

1.02

22.3

Remember: 2-hundredths = 2 = .02 100

Remember: 3-tenths = 3 = .3 10

Exercise 38: Write in digits: i)

3-thousandths.

ii)

Four and fifty-one hundredths.

iii)

Sixty-one and 9-thousandths.

iv)

3-hundreds, one and thirty-five thousandths.

v)

Seventy and 6-tenths.

Equivalence of Two or More Decimals Look at: As you have known:

3 = 30 = 300 = … 10 100 1000

Therefore 0.3 = 0.30 = 0.300 =… i.e. 3-tenth = 30-hundredths = 300-thousandths = … Note: The decimal doesn’t change by adding “Zeroes” to the right or by canceling “Zeroes” from the right. Example 39: i)

Complete adding zeros or canceling zeros: 5.3 = … ii) 1.4600 = … Solution 5.3 = 5.30 = … By adding the “Zeroes”

1.4600 = 1.460 = 1.46 By canceling the “Zeroes”

Exercise 39: Complete adding zeros or canceling zeros: i)

66.2 = …

ii)

1.4100 = …

iii)

6.431 = …

iv)

1.500 = …

v)

12.6 = …

vi)

4.3000 = …

vii)

17.46000 = …

viii)

9.000 = …

ix)

12.3000 = …

Example 40:

Don’t forget: 0.3 = 0.30 = 0.300 = ...

Complete: i)

3-tenths = … -hundredths = … -thousandths Solution 3-tenths = 30-hundredths = 300-thousandths

Exercise 40: Complete: i) 5-tenths = ……… hundredths = ………. thousands ii) 9-tenths = ……… hundredths = ………. Thousands iii) 20-hundredths = …….. thousandths = …….. tenths iv) 100-thousandths = ……… hundredths = …….. tenths v) 60-hundredths = …….. tenths = …….. thousandths

Comparing Decimals Well dear pupil comes to understand how to compare two decimals or decimal and a fraction Don’t forget, we compare from the left

Example 41: Complete using < , > or = : i) 32.4 … 7.65 i)

4.35

…

4.29

Solution 32.4

…

7.65

4.35

2-digits > 1-digit Therefore: 32.4

… = >

4.29

Therefore: >

7.65

4.35

>

4.29

Exercise 41: Put the suitable sign < , > or = : i) 46.3 …… 9.78

ii) 41.03 …… 561.6

iii) 5.061 ……. 22.3

iv) 96.1 ……. 8.91

v) 55.38 ……. 56.18

vi) 6.08 …….. 6.80

vii) 5.60 ……. 5.6

viii) 56.36 …….. 56.360

ix) 5.6 …….. 5 xi) 6

3 5

x) 3

1 …….. 6.25 3

2 ……… 32.4 5

xii) 3.46 ……… 3

3 4

Arrangement of Decimals ♦ All decimals Example 42:

i)

Arrange each of the following groups of decimals in ascending order: Add “0” to the left to make the whole number 2-digits in all

7.25 , 72.5 , 0.725

Solution

First digit to the left in all

17.25

,

72.5

,

17.25

,

72.5

, 09.725

09.725

0

7

1

,

9.725

17.25

,

72.5

Don’t for get: In ascending order

Exercise 42: A- Arrange each of the following groups of decimals in ascending order: i)

5.31 , 53.1 , 41.5

ii)

0.43 , 39.61 , 19.4

iii)

9.61 , 17.3 , 71.2

iv)

143.4 , 46.31 , 201.4

v)

1.35 , 13.5 , 0.135

vi)

9.38 , 93.8 , 0.938

vii) 44.61 , 446.1 , 4.461

viii) 66.31 , 663.1 , 6.631

B- Arrange each of the following groups of decimals in descending order: ix)

9.43 , 94.3 , 19.32

x)

xi)

19.04 , 19.40 , 19.41

xii) 65.32 , 65.12 , 65.42

13.5 , 1.35 , 23.06

Decimals and fractions. The whole numbers are different

♦

Example 43: Re-arrange the following in ascending order: i)

9.3 , 3

1 , 5.25 2

Solution

9.3 Remember: In ascending order

,

9

3

3

1

2

5.25

,

3

1 2

,

You note that: the whole number are different, then we descend them.

5

5.25

,

9.3

Exercise 43: A- Arrange each of the following groups in ascending order: i)

12.7 , 6.6 , 9

1 5

ii)

7.25 , 5.65 , 8

1 3

1 , 3.5 , 5.15 5

iii)

9

v)

2.75 , 3

vii) 3

iv) 4.35 , 6

1 , 1.9 3

vi)

2 , 4.9 , 1.81 5

6

1 , 5.1 4

1 , 2.8 , 5.3 5

viii) 4.32 , 5

1 , 3.11 2

B- Arrange each of the following in descending order: ix) 4.9 , 2 xi) 5

3 , 1.08 4

1 , 7.9 , 12.01 3 4 xii) 4.3 , 5 , 1.98 5

x) 9

3 , 1.13 , 6.1 4

Decimals and fractions. The whole numbers are the same

♦

Example 44: Arrange each of the following in ascending order: i)

4.5 , 4

1 , 4.4 3

Solution

4.5

,

4 1

,

4.4

.5

,

1 3

,

.4

3

5 10

,

1 3

,

4 10

5 ×3 30

,

1 × 10 30

,

4 ×3 30

You note that: whole numbers are equal, then we descend the fractions and decimals

10 = 2 × 5 3

= -- × -- × 3

10 = 2 × 5

C.D = 2 × 5 × 3 = 30

15 30

10 30

,

4 1

,

3

4.4

,

12 30

,

4.5

Don’t forget: In ascending order

Exercise 44:

A- Arrange each of the following groups in ascending order: i)

3.4 , 3

iii) v)

4 , 3.09 5

3 , 4.75 , 4.18 4 3 6.3 , 6.03 , 6 5 4

1 , 5.1 , 5.93 2

ii)

5

iv)

2.7 . 2.17 , 2

vi)

9.2 , 9

1 3

3 , 9.12 5

B- Arrange each of the following groups in descending order: 1 , 1.3 2

viii)

vii)

1.25 , 1

ix)

7

xi)

5.120 , 5.210 , 5

3 , 7.18 , 7.81 7

Example 45: Add: i)

3.361 + 96.8

x) 3 4

1

3 , 1.05 , 1.5 4

3.153 , 4

xii)

Addition of Decimals

3

3 , 4.71 5

1 , 3.4 , 3.81 2

Add “0” to become whole number in the above of 2-digits like the under

Solution 03.361 + 96.800

Add “00” to become the decimals in the under of 3-digits like the above

Now, the problem becomes: 03.361 Put “.” under the above + 96.800 . Exercise 45:

1 1

03.361 + 96.800 100.161

Add the problem as normal addition

Add i)

1.36 + 93.563

ii)

iii)

96.4 + 8.63

iv)

3.461 + 31. 3

v)

1.563 + 65.7

vi)

10.5 +13.006

0.638 +63.181

viii)

563.01 + 4.938

ix)

9.363 +91.29

0.6.38 + 93.986

xi)

1.008 + 23.919

xii)

xiii)

36.4 +29.69

xiv)

4.36 +315.48

xv)

938.3 + 1.98

xvi)

96.456 + 9.39

xvii)

4.369 +39.84

xviii)

4.638 +89.19

.

vii) x)

♦

.

Horizontally:

Example 46: Add: i) 36.4 + 365.381

+

361.3 9.638

.

.

.

9.867 + 68.39 .

.

Solution

1 1

36.4 + 365.381 = 401.781 You can solve the problem by putting it vertically in the draft then solve

036.400 + 365.381 401.781

Exercise 46: Add: i)

0.361 + 36.4

ii)

963.43 + 9.363

iii)

9.386 + 368.4

iv)

5.463 + 563.46

v)

363.4 + 5.486

vi)

561.36 + 36.586

vii)

96.36 + 1.361

viii)

9.368 + 563.3

ix)

31.38 + 39.49

x)

0.003 + 933.4

Whole number and a decimal

♦

Add “.” and “000” to 365 to become like the under, then carry out the addition

Example 47: Add i) 365 + 4.631

Solution

365. 000 + 004.631 369.631

365 + 4.631 = 369.631 Exercise 47: Add: i)

46 + 9.463

ii)

4.36 + 563

iii)

363 + 1.36

iv)

586 + 0.008

v)

4.363 + 500

vi)

0.038 + 36

vii)

600 + 0.046

viii) 156 + 3.481

Subtraction of Decimals Note: Subtraction of decimals looks like addition in the previous types, where we will make the number of digits in the above equals the number of digits in the under before and after the point, then display normal subtraction. Example 48: Subtract: i) 46.3 - 8.463 46.3 - 8.463

Add the zeroes

Descend the point

46.3 - 8.463 .

1

Exercise 48:

Display as a normal subtraction

3 15 12 9 10 5 2 10

Solution 2

46.300 - 08.463 .

3

4 6 .3 0 0 - 0 8 .4 6 3 3 7 .8 3 7

A-Subtract: i)

46.3 - 21.46

ii)

19.38 - 0.968

iii)

39.4 - 3.509

iv)

363.1 - 15.986

v)

406.05 - 39.981

vi)

56.93 - 9.863

400.5 54.86

ix)

50.03 - 8.964

506.09 9.698

xii)

vii) x)

.

189.3 - 19.68

viii)

46.03 - 9.693

xi)

-

363.4 - 79.93

.

.

B- Subtract i)

14.3

– 9.32

ii)

56.4

– 6.983

iii)

63.1

– 1.608

iv)

5.38

– 0.988

v)

93.5

– 10.98

vi)

99.1

– 4.908

vii)

36.1

– 1.819

viii)

36.4

– 9.009

ix)

461.4

– 16.96

x)

463.3

– 19.381

xi)

563.1

– 73.568

xii)

386.1

– 56.563

xiii)

593.2

– 96.693

xiv)

406.9

– 56.381

xv)

638.5

– 17.906

xvi)

406.5

– 99.463

xvii) 15

– 0.561

xviii)

19

– 0.361

xix)

65

– 9.098

xx)

18

– 9.361

xxi)

75

– 20.506

xxii)

99

– 5.888

xxiii) 86

– 5.986

xxiv)

78

– 4.361

xxv)

– 3.056

xxvi)

200

– 46.36

xxvii) 300

– 14.361

xxviii) 400

– 56.36

xxix) 800

– 9.639

xxx)

500

– 1.981

xxxi) 600

– 1.989

xxxii) 900

– 5.309

100

Multiplication of Decimals by 10, 100, 1000, … Vertically

♦

Example 49: Multiply: i) 0.56 × 10

Solution

ii) 1.438 × 100

10 has one zero, then we walk with “.” To the right 1-step

0.56 × 10 = 05.6 = 5.6

1.438 × 100 = 143.8 100 has two zero, then we walk with “.” To the right 2-step

Don’t forget: Zeros on the lift has no meaning

Exercise 49: A- Multiply: i)

0.063 × 10

ii)

0.045 ×100

iii)

0.069 ×100

iv)

1.36 ×10

v)

36.43 ×10

vi)

36.461 × 100

vii)

1.3613 × 1000

viii)

0.9381 × 10000

B- Multiply: ix)

10

x)

× 9.006

xii)

100

× 0.6381

xiii)

× 5.381

xv)

100

xi)

100

× 0.3631

xiv)

10 × 4.361

xvi)

× 563.511

1000 100 × 36.361

xvii)

1000 × 0.3619

1000 × 0.0386

Horizontally

♦

Example 50: i)

Multiply 3.5 × 10

Don’t forget: Walking with “.” one step because 10 has 1-zero

3.5 × 10 = 35. = 35

ii) Solution

31.3 × 100

You note: 100 has 2-zeros, then you must walk 2-steps to the right but there is 1-digit after the “.” So, we “0” to become 2-digits

31.3 × 100 = 3130. = 3130

When the “.” is the last, then we can cancel it

Don’t forget: if the “.” is the last, you can cancel it

Exercise 50: Multiply: i)

10 × 356.1

ii)

100 × 3.3

iii)

1000 × 0.361

iv)

0.36 × 1000

v)

1.36 × 100

vi)

361.3 × 1000

ix)

56.31 × 10000

vii) 3.5 × 100

viii) 561.1 × 1000

x)

10000 × 0.36

xi)

1000 × 5.3

xii) 935.1 × 100

xiii) 100 × 23.5

xiv) 10 × 231

xv) 10000 × 12.3

xvi) 2.3 × 100

xvii) 0.01 × 1000

xviii)0.001 × 10000

xix) 1.002 × 10

xx) 23.01 × 100

xxi) 1000 × 2.33

xxii) 1000 × 12.02

xxiii)100 × 112

xxiv) 0.003 × 10000

Division of Decimals by 10, 100, 1000, … Note :

Just we will take dividing a decimal or a numeral decimal by 10, 100, 1000, ……

Example 51: Divide i) 55.5 ÷ 10

ii) Solution

10 has one zero, then we walk with the “.” 1-step to the left

55.5 ÷ 10 = 5.55

361.3 ÷ 100

100 has 2- zero, then we walk with the “.” 2-steps to the left

361.3 ÷ 100 = 3.613

Exercise 52: Divide i)

453.1 ÷ 10

ii)

56.3 ÷ 10

iv)

631.3 ÷ 100

v)

6356.1 ÷ 1000 vi)

vii) 538.1 ÷ 100 x)

463.361 ÷ 10

iii)

viii) 361.361 ÷ 100 ix) xi)

43.43 ÷ 10

631.3 ÷ 100 5631.3 ÷ 100 563.36 ÷ 10

xii) 563.319 ÷ 100

xiii) 300.005 ÷ 100 xiv) 361.3 ÷ 100

xv) 199.36 ÷ 10

xvi) 46.38 ÷ 10

xviii)14.361 ÷ 10

xvii) 136.3 ÷ 100

Example 52: Divide i) 13.15 ÷ 100

1.36 ÷ 1000

ii) Solution

Don’t forget: walking with the “.” 2-steps to the left because 100 has 2-zeros

13.15 ÷ 100 = .1315 = 0.1315

You note: 1000 has 3-zeros then, you must walk with the “.” to the left 3-steps but there is 1-digit before the “.” So add “00” to become 3-digits

1.36 ÷ 1000 = .00136 = 0.00136

If the “.” is first add “0” to the left of it

Don’t forget: If the “.” is the first, you can add “0” to the left of it.

Exercise 52: Divide i)

ii)

2.36 ÷ 100

iii) 1.361 ÷ 1000

iv) 43.5 ÷ 100

v)

36.48 ÷ 1000

vi) 361.3 ÷ 100

vii) 1.63 ÷ 1000

viii) 5.631 ÷ 100

ix) 23.5 ÷ 10

x)

xi)

0.2 ÷ 100

xii) 0.02 ÷ 1000

xiii) 235.6 ÷ 100

xiv) 6 ÷ 1000

xv) 0.007 ÷ 100

xvi) 78.154 ÷ 1000

xvii) 213 ÷ 10

xviii)231.5 ÷ 10

xix) 654 ÷ 10

xx)

xxi) 2134 ÷ 1000

xxii) 21 ÷ 1000

xxiii) 0.8 ÷ 100

xxiv)451 ÷ 10

xxv) 854.1 ÷ 100

xxvi) 7 ÷ 10

xxvii0.004 ÷ 100

1.3 ÷ 10

0.221 ÷ 10

0.547 ÷ 1000

Applications of Decimals Different type of Problems Example 53: Rewrite the following in digital from. i)

ii)

5-hundredths

7-tens

Solution

Convert it into fraction then convert the fraction into decimal as the previous

5 100 = 5.

7-tens = 7 × 10 = 70

5-hundredths = You note: hundredths has “ths” so we divide by “100”

You note: tens has “s” so, we multiply “10”

= .05 = 0.05

Exercise 53: Rewrite the following in decimal from: i)

4- thousandths ii)

iv)

7-tens

v)

5-tenths

iii) 5-hundredths

6-thousandths vi)

7-thousandths

vii) 9-thousands

viii) 8-tens

ix)

x)

xi)

xii) 6-tens

12-hundredth

7-hundreds

4-hundreds

Example 54: Rewrite each of the following in digital form, then find the result: i) 5-tens + 6-hundredths 5-tens + 6-hundredths 50.06

Change it into digital form

Solution 50. 2 + 0.06

1

50.00 + 00.06

5-tens =5×10 = 50 6-hundredths = 6 100

= .06 = 0.06

Make all digits equal in the above and the under by adding zeroes

Exercise 54:

Rewrite each of the following in digital from, then find the result: i) 3-hundredths + 4-tenths iv) 7-thousands - 5-tenths

ii)

5-tenths - 4-thousands

v) 6-thousandths + 7-hundredths

vii) 3-tenths + 5-hundreds

iii)

6-hundreds + 3-tens

.

vi) 7-tens - 5-thousandths

viii) 9-hundreds – 5-hundredths

ix) 4-hundredths – 4-thousandths

x) 5-tens + 6-thousandths

Come to understand the following type

♦

Example 55: A- Write the decimal that B- Write the decimal that come after each of the comes before each of the following: following: i)

3.7 , …

ii)

… , 4.26

Look at the last digit, then ask your self: what’s the number after “7”? It’s “8”

3.7 ,

3.8

Solution

Look at the last digit, then ask your self: what’s the number before “6”? It’s “5”

4.25 , 4.26 1-

+1

Exercise 55 : A- Write the decimal that comes before each of the following. i)

… , 1.3

ii)

… , 1.36

iii)

… , 5.201

iv)

… , 2.06

v)

… , 3.001

vi)

… , 1.312

vii)

… , 0.07

viii)

… , 1.008

ix)

… , 2.003

B- Write the decimal that comes after each of the following. xiii)

1.004 , …

xiv)

2.6 , …

xvi)

5.07 , …

xvii) 3.00 , …

xix)

1.315 , …

xx)

2.12 , …

xv)

1.72 , …

xviii) 2.005 , … xxi)

0.006 , …

Come to see the following type

♦

Example 56: A-Write the decimal that B-Write the decimal that comes between each of come between each of the the following two decimals following two decimals i)

3.36 , … , 3.38

ii)

4.015 < … < 4.017

Look at the last two digits in the given two number then; Ask your self, what’s the number between 6, 8 ? It’s 7

Solution

3.36 , 3.37 , 3.38 +1

Or

Look at the last two digits in the given two number then; Ask your self, what’s the number between 5, 7 ? It’s 6

4.015 < 4.016 < 4.017

1-

+1

or

1-

Exercise 56 A- Complete the decimal that comes between each of the following two decimals: i)

4.3 < … < 4.5

ii)

1.31 < … < 1.33

iii)

1.03 > … > 1.01

iv)

4.031 > … > 4.029

v)

4.36 < … < 4.38

vi)

5.007 < … < 5.009

vii)

6.041 > … > 6.039

viii)

2.21 > … > 2.19

B- Write the decimal that comes between each of the following two decimals: ix) xi) xiii) xv) ♦

4.021, …, 4.019 6.051 , … , 6.049 7.001, …, 7.003 6.18, …, 6.2

5.31, …, 5.29 5.32, …, 5.34 0.091, …, 0.089 1.03, …, 1.028

Come to see the empty squares (addition)

Example 54: Complete the missing digits: i)

x) xii) xiv) xvi)

5. 4 + 3 . 3 1 96. 1 29

Solution 5. 4 + 3 . 3 1 96. 1 29

Remember in case of addition, ask your self I want to reach the under number I have “1” and I want to reach “9” It’s “8”

5. 4 8 + 3 . 3 1 96. 1 29 1

I have “4” and I want to reach “2”. impossible because 4 >2. Then consider “2” as “12” and carry up above the following and again I have and I want to reach “12”. It’s “8”

1

1 + 3 = 4, I have “4” and I want to reach “1”. It’s impossible then “1” become “11”, again I have “4” and I want to reach “11”. It’s “7”

5. 4 8 + 3 . 38 1 96. 1 29

1

5. 7 4 8 + 3 . 38 1 96. 1 29 1

1

1

1 7

It’s we “1” “4”

1 + 5 = 6, I have “6” and I want to reach “6”. It’s “0”.

5. 7 4 8 + 30. 38 1 96. 1 29

I have “3” and I want to reach “9”. It’s “6”.

5. 4 8 + 30. 38 1 96. 1 29 Exercise 58: 6

Complete the missing digits: i) 5 . 3 5 + 3. 1 91. 12 9

ii)

3

.3 +4 2. 4 9 1 6. 1 6

iii)

3

.3 1 + 2. 2 86. 215

.

iv) 3. 5 + 3 .1 2 9 2. 0 9 1

v)

3. 5 + 2 .2 8 8 2 .9 1

viii)

43 5.36 + . 896.81

4

vii)

. + 391.38 680.81

x)

……

xi)

53.386 + …… = 71.103

xii)

……

xiii)

3.436 + …… = 9.103

xiv)

…… + 4.006 = 7.863

xv)

53.481 + …… = 90.013

xvi)

…… + 5.406 = 7.105

vi)

ix)

3 .3 +5 2. 4 920.11 . + 65.81 80.19

+ 356.28 = 921.31 + 531.46 = 931.401

xvii) 15.306 + …… = 19.101 xviii) …… + 363.28 = 472.13 ♦

Come to see the empty squares (subtraction)

Example 59 Complete the missing digits: i)

3. 2 -3 .2 1 54.813 3. 24 -3 .2 1 54.813

Don’t forget, in case of subtraction, look the square, if it’s above, we add and if it’s under, we subtract

Solution is above, then we add: 1+3 = 4

3. 24 -3 .21 1 54.813

is under, subtract 2-1 = 1

3.024 -3 .21 1 5 41 . 8 1 3

is above, add 2+8=10, we can’t write 10 in but, we write 0 and carry down “1” under the following.

3.024 -3 8 .21 1 1 5 41. 8 1 3

1 + 4 =5, is under, subtract; 3 - 5 is impossible, then “3” becomes “13” and carry down “1” under the following, again is under, subtract 13 – 5 = 8

93.024 -3 8 .21 1 1

1 + 5 = 6,

is above, add 6 + 3 = 9

5 41. 8 1 3

Exercise 59: Complete the missing digits: i) 3 2 . 1 - 2 .3 1 3 1. 21

ii)

3. 2 - 2 .1 2 25.231

iv) 3 . 8 -5 3.2 1 8 4. 31

v) -

5 6. .63 15.12

vi)

vii)

viii) 6 8 2 . 1 3 . 1 87 .51

ix)

. -68. 893 16. 293

ix)

…… - 35.361 = 11.186

x)

563.108 - …… = 138.619

xi)

…… - 4.386 = 36.381

iii) 2 . 3 1 2. 2 . 15.323 3

2. 1 - 2 .32 683.21 .367 –3 67. . 1 62.173

xii)

14.386 - ……

= 0.419

xiii)

…… - 431

= 361.43

xiv)

365 - ……

xv)

…… - 53.006 = 111.111

xvi)

555.33 - ……

= 131.486

xvii) …… - 4.007

= 222.22 = 15.001

Come to see multiplication in the following form

♦

Example 60: Complete i)

…… × 13.478 = 1347.8 ii) Solution

Ask your self: How many steps did the “.” walk? It’s “2” then put “00” and I means “100”

100 × 13.478 = 1347.8 Exercise 60: i)

…… × 1000 = 4361.2 Ask your self: where is the “.” before multiplying by 1000?

4.3612 × 1000 = 4361.2 Don’t forget: multiplying by “1000” means walking with the “.” to the right 3 steps

…… × 4.361 = 43.61

ii) 56.313 × …… = 56313

iii) 5.3618 × …… = 5361.8

iv) …… × 4.3 = 430

v) …… × 1.36 = 1360

vi) 153.3 × …… = 153300

vii) 43.56 × …… = 43560

viii)

ix) 100 × …… = 43.5

x) 1000 × …… = 163.4

…… × 4.36 = 436

xi) …… × 10 = 36.4 xiii)

xii) …… × 100 = 1.4

1000 × …… = 43.6

xiv) 10 × …… = 0.361

xv) …… × 100 = 0.13

xvi) …… × 1000 = 0.003

Come to see division in the following form

♦

Example 61: Complete 36.17 ÷ …… = 0.03617 ii)

i)

Ask your self: How many steps did the “.” Walk to the left? It’s “3” then put “000” and I means “1000”

…… ÷ 100 = 1.361

Solution

36.17 ÷ 1000 = 0.03617

Ask your self: where is the “.” before dividing by 100?

136.1 ÷ 100 = 1.361 Don’t forget: dividing by “100” means walking with the “.” to the left 2-steps

Exercise 61: Complete the missing: i)

43.38 ÷ …… = 4.338

ii)

iii)

36.4 ÷ …… = 0.0364

iv)

4.36

v)

43.3 ÷ …… = 0.433

vi)

3.436 ÷ …… = 0.3436

vii)

36.3 ÷ …… = 0.0363

viii)

ix)

…… ÷ 100 = 4.361

x)

…… ÷ 1000 = 0.0361

xi)

…… ÷ 10

xii)

…… ÷ 10

= 0.36

xiv)

…… ÷ 100

= 0.361

= 0.4

xiii) …… ÷ 1000 = 0.03

436.31 ÷ …… = 4.3631

4.3

÷ …… = 0.00436

÷ …… = 0.0043

…… ÷ 100 = 0.5

xv)

xvi)

…… ÷ 1000 = 3.6

Come to see how to complete as the pattern

♦

Example 62: Complete as the pattern: i) 36.22, 36.26, 36.30, ……, ……, ……, …… Solution Firstly: note is the problem in ascending order or descending order? It’s in ascending

Secondly: Ask yourself, how did he add in each one time ? by subtracting, it’s “0.04”

36.22 , 36.26 , 36.30 , 36.34 , 36.38 , 36.42 , 36.46 Note that: if the biggest came after the smallest. Then it is in ascending order and vice versa.

In the draft calculate each one. For example 36.30 + 0.04 36.34

Exercise 62: Complete as the pattern: i)

4.36, 4.41, ……, ……, ……, ……

ii)

36.431, 36.437, ……, ……, ……, ……

iii)

32.4, 32.51, ……, ……, ……, ……

iv)

361.5, 361.62, ……, ……, ……, ……

v)

51.31, 51.321, ……, ……, ……, ……

vi)

63.46, 63.38, ……, ……, ……, ……

vii)

713.5, 713.42, ……, ……, ……, ……

viii)

9.813, 9.8, ……, ……, ……, ……

36.34 + 0.04 36.38

ix)

11.361, 11.35, ……, ……, ……, ……

x)

56.38, 56.31, ……, ……, ……, …… Using or =

♦

Example 63: Put the suitable sign < , > or = : i) 36.36 + 25.7 ……100 × 6.36 Solution 36.36 + 25.7 ……10 × 6.36 36.36 + 25.70 …… 63.6 62.06 ……63.6 Don’t forget all of Calculate it in the draft 62.06 ……63.6 these steps on your mind = < Thus; 36.36 + 25.7 < 10 × 6.36 Exercise 63: Put the suitable sign < , > or = : i)

361.3

ii) iii)

÷ 100

325.25 21.2

iv)

+ 125.3

254.2

………

3.613

………

3.2525 × 100

………

231.5

………

5248.2 - 210.523 78.3

v)

36.38

+ 4.9

………

vi)

12.54

÷ 100

………

vii)

0.0023

× 100

………

- 6.06

1.20546 12.3

÷ 1000

viii) 46.38

× 10

………

73.63

+ 238.3

ix)

437.8

- 13.006

………

736.3

÷ 100

x)

436.1

÷ 1000

………

1000

× 0.4361

xi)

36.38

× 100

………

36.38

÷ 100

xii) 431.3

+ 7.36

………

963.1

- 13.486

xiii) 43.5

+ 73.15

………

11.31

× 10

xiv) 56.38

× 1000

………

5631.4 + 13.481

xv) 5.36

÷ 100

………

5.3

♦

Addition

- 4.361

Word Problems

Example 64: Mohamed bought two kilos of oranges for L.E 3.75 and three kilos of apples for L.E 17.5. Calculate the total cost of oranges and apples. Solution The total cost of oranges and apples = 3.75 + 17.5 = L.E 21.25 Exercise 64: i)

You can calculate it in the draft

03.75 + 17.50 21.25

Nadia has got a stock for L.E 1.35 and shoes for L.E 85.3. Calculate the total cost for what Nadia has.

ii) Ramy bought a pencil for L.E 3.25 and two pen for L.E10.5. Find the total cost for what Ramy buy.

iii) If Bassem has got 2.65 metres of material for making a trousers and 3.5 metres for making a jacket. Then what are the total metres for making the suit? iv) If Abd El Rahman bought three kilos of rice for L.E 5.75 and two kilos of butter for L.E 15. Then calculate the total cost that he paid. v) Amr paid three pounds for 3.25 kilos of banana and two pounds for 1.5 kilos of watermelon. Calculate the total kilos that he bought. vi) Marwa bought three notebooks for L.E 5.5, two pencils for L.E 2.75 and three pens for L.E 6.35. Find the total cost of what she buy. vii) Mohamed has got three coloured cars, the green one 3.75m long, the yellow one 2.5m long and the blue one 3m long. Find the total length of Mohamed’s cars. ♦

Subtraction

Example 65: Mohamed has got two containers, the first weighs 2.75 kg and the second one weighs 12.3kg. Calculate the difference between the weight of the two containers. Solution The difference = 12.3 - 2.75 = 9.55 kg

12.30 Remember the previous words that denote to the subtraction problem

- 02.75 09.55

Exercise 65: i) Nabila has got 3.35 metres of cloth for making a dress and 2.5 metres for making a blouse. Calculate the different between the cloth of the dress and that of the blouse.

ii) Ramy’s tall is 1.75 metres and Amr’s tall is 2.01 metres. How much is Amr’s tall greater than Ramy’s tall? iii) If Bassem’s house height is 43.46 metres and Ahmed’s house height is 50 metres. Then how much is Bassem’s house height less than Ahmed’s house height? iv) If Madiha has got 134.5 pounds and her brother has got 93.75 pounds. How much did they have together? v) Marwa has got a tree whose height is 50.36 metres and Mona has another one whose height is 131.5 metres. How much does Mona’ tree increase Marwa’s tree? vi) If Abd El Rahman has got L.E. 15.25, he bought three kilos of apples for L.E 12.6. How much money was left? vii) If Mohamed has got L.E 56.3 and his sister has got L.E 35.65. How much did Mohamed has more than his sister? viii) Donia has bought 3.25 kilos of banana and 13.5 kilos of potatoes. How much did the banana decrease the potatoes? ♦

Addition and Subtraction to gather

Example 66: i)

Doaa has got L.E 20.2, she bought three kilos of banana for L.E 5.75 and two kilos of apples for L.E 12.3. How much money was left? Solution The cost of banana and apples = 5.75 + 12.3 = L.E 18.05 The left money = 20.2 – 18.05 = L.E 2.15

Carry out it in the draft

05.75 +12.30 18.05 20.20 -18.05 2.15

Exercise 66: i)

Basma has got L.E 5.3, she bought a pencil for L.E 1.25 and a pen for L.E 2.7. How much money was left?

ii) If Omr has got 5 kilos of banana, he gave Hany 2.5 kilos and Mona 1.25 kilos. How many bananas were left? iii) Abd El Rahman has took 9.35 metres of cloth from his father, he made a trousers by 3.3 metres and a jacket by 4.65 metres. How much metre was left? iv) Marwa’s mother has got a cake, she gave Marwa 0.25 and her brother 0.5. What’s the remainder from the cake? v) Mahmoud has took L.E 3.25 from his father and L.E 2.7 from his mother, he bought a pencil for L.E 0.5. How much money was left? vi) Nagy has took 1.25 kilos of sweets from his father and 2.3 kilos from his mother, he gave his brother 1.75 kilos. How much sweet was left with him? vii) Magda has took 3.5 metres of cloth from her brother and 1.35 metres from her sister, she made a dress by 2.75 metres. How much cloth was left? viii) Mohamed has took L.E 5.35 from his father and L.E 3.2 from his mother, he bought a pencil for L.E 2.3 and a pen L.E 3.75. How much money was left? ♦

Multiplication

Example 67: i)

If Mohamed has bought 100 kilos of rice for L.E 1.75 each. What’s the total cost?

The total cost = 100 × 1.75 = 175. = L.E 175

Solution Remember, in multiplication, walk with the point to the right

Exercise 67: i)

Maged has got 10 metres of material for L.E 0.75 each. What’s the total cost of the material?

ii) What’s the total cost of 1000 kilos of banana, if you knew the price of one kilo L.E 1.3? iii) Mohamed has bought a pencil for L.E 2.75. What’s the price of 10 pencils? iv) If you knew the price of a metre of cloth L.E 0.3. Then can you calculate the total price of 1000 metres? v) Mona has got 5.3 kilos of sweets, the price of a kilo L.E10. What’s the total cost? ♦

Division

Example 68: i)

Mohamed has got 10 kilos of watermelon for L.E 17.5. What the price of one kilo? Solution The price of one kilo = 17.5 ÷ 10 = 1.75 pounds

Remember, in the division, walk with the “.”to the left

Exercise 68: i)

How many 100s are there in 35.36?

ii) How many 100s are there in 1.35? iii) How many thousand are there in 361.3? iv) How many hundreds are there in 1.36? v) If Ahmed has got 100 metres of cloth for L.E 563.4. then What’s the price of each metre? vi) Mona bought 10 kilograms of apples for L.E 30.5. What is the price of each one?

vii) Hoda bought 1000 metres of a certain material for making a balloon, she paid L.E 361.3, what’s the price of each kilo? viii) Ramy has got 100 toy cars for L.E 136.5. What is the price of each one?

100 80 60 40 20 0 Ahmed

Aiya

Bassem

Mona

In each natural science, there is a certain quantity of mathematics. Cant

Bar chart, Bar-Line Graph and Broken Line Graph ♦

Come to understand how to draw each of them

Example 69: The following table shows the marks obtained by Waleed in each of five subjects. Subject

Math’s.

English

Arabic

Science

Art

Mark

2

10

6

9

8

Use the information from the table to draw: a bar chart. a bar-line graph. a Line graph or “broken line graph” Solution We will show the steps of drawing : 1- Bring a lattice, then draw the vertical axis and the horizontal axis. It is called the vertical axis

Put “0” at the intersection point of the two axis

0

It is called “origin”

It is called the horizontal axis

2- Put the first row in the table on the horizontal axis:

Make the distance between each two equal the previous and so on

Art

Science

English

Math’ s

Arabic

Subjects 0

3- Put that the second and the third rows represent in the table on the vertical axis: Marks 11 10 9 8 7 6 5 4 3 2

Famous scales: 1,2,3,… 2,4,6,8,… 5,10,15,20,… For example: From (1). You can add “0” for all, then you’ll get a new one: 10,20,30,… or add “00”, you’ll get: 100,200,300,… and so on

Subjects Art

Science

Arabic

0

English

1

Math’ s

You note; we took 1,2,3,… because the greatest mark is “10” that means if you took 1,2,3,… the vertical axis is sufficiently

Note: Pay Attention to the following: i) ii)

If you want to use the scale: 1,2,3,…. Then. Each one in the data = 10-small squares. 10÷1 =10 If you want to use the scale: 2,4,6,…. Then. Each one in the data = 5-small squares.

10÷2 = 5

iii)

If you want to use the scale: 5,10,15,…. Then. Each one in the data = 2-small squares. 10÷5 = 2

iv)

If you want to use the scale: 10,20,30,…. Then. Each one in the data = 1-small squares. 10÷10 =1

4- Determine the ends of columns: Marks 11 10 9 8 7 6 5 4 3 2

Subjects Art

Science

Arabic

English

0

Math’ s

1

5- Now, draw the graph: a) bar chart: Marks 11 10 9 8 7 6 5 4 3 2

Subjects Art

Science

Arabic

Math’ s

0

English

1

b) a bar-line graph Marks 11 10 9 8 7 6 5 4 3 2

Subjects Art

Science

Arabic

English

0

Math’ s

1

3- Broken line graph or a line graph Marks 11 10 9 8 7 6 5 4 3 2

Subjects

Exercise 69:

Art

Arabic

English

Math’ s

0

Science

1

A-Group: The following tables show the marks obtained by children in each of six subjects. Use the information in each table to draw: 1a bar charts. 2a bar line graph. 3a line-graph. Then show the greatest and the smallest mark and their subjects. i)

Ahmed’s marks:

Subject

Math’s

English

Science

Arabic

Art

History

Marks

6

3

9

8

2

7

ii) Subject Marks

Heba’s marks: English 8

iii) Subject Marks

History 6

Art 2

Math’s 9

Science 5

Arabic 4

Math’s 2

Arabic 7

History 9

Art 5

English 9

Math’s 8

Science History 3 6

Waleed’s marks: Science English 6 8

iv)

Marwa’s marks:

Subject Marks

Art 6

Arabic 5

B- Group: The following tables show the temperatures obtained in a week in many cities. Use the information in each table to draw: 1- a bar charts. 2- a line-graph. 3- a broken-line graph. Then show the greatest and smallest temperatures and their days in each city. v)

Cairo temperatures:

Day

Sat. 10

Temperature

vi)

Day

Temperature

Mon. 16

Tue. 28

Wed. 18

Thu. 23

Fri. 12

Wed. 22

Thu. 11

Fri. 18

Sat. 26

Thu. 18

Fri. 20

Sat. 28

Sun. 25

Alex. Temperatures:

Day Temperature

vii)

Sun. 20

Sun. 12

Mon. 28

Tue. 16

Tanta temperatures: Mon. 22

Tue. 26

Wed. 14

viii) Day

Assuit’s temperatures:

Temperature

Tue. 23

Wed. 28

Th. 20

Fri. 12

Sat. 18

Sun. 26

Mon. 20

C- Group: In the following tables show the number of famous players obtained in each activity many clubs. Use the information in each table to draw: 1- a bar charts. 2- a broken-line graph. 3- A line-graph. Then; show the greatest and smallest number of players and their activities in each club. ix)

Ahlly club:

Activity

Foot ball

Hand ball

No. of plays

Basket ball

Volleyball

Table tennis

40

25

30

20

7

x)

Zamalik club:

Activity

Foot ball

Hand ball

No. of plays

Basket ball

Volleyball

Table tennis

30

40

25

5

22

xi)

Ismaely club:

Activity

Foot ball

Hand ball

No. of plays

Basket ball

Volleyball

Table tennis

15

35

25

30

6

xii)

Mansoura club:

Activity

Foot ball

Hand ball

No. of plays

Basket ball

Volleyball

Table tennis

4

15

25

40

30

D- Group: In each of the following tables show the weights of pupils in kilograms. Use the information in each table to draw: 1- a broken-line graph. 2- a bar charts. 3- A bar-line graph. Then; show the heaviest and lightest pupil and their weight; then find the difference between them. xiii)

First group

Name

Ahmed

Waleed

Maged

Marwa

Hind

Heba

Weight in kg

150

135

100

75

80

53

xiv)

Second group

Name

Mona

Aiya

Donia

Nagy

Nabil

Ramy

Weight in kg

123

105

150

85

50

100

xv)

Third group

Name

Mohamed

Akram

Amr

Magda

Walaa

Doaa

Weight in kg

135

145

120

83

70

65

xvi)

Fourth group

Name Weight in kg

Bassma Nadia 65

95

Nabila Bassem 150

55

Abd El Mahmoud Rahman 105

73

E- Group: In each of the following tables show the tall of pupils in meter. Use the information in each table to draw: 1- a line graph. 2- a bar-line graph. 3- a bar graph. Then; show the tallest and shortest pupil and their weight; then find the difference between them. xvii) First group Name

Tall in m

Ahmed 1

Hoda 1.8

Nabil 3

Amal 2.7

Waleed 105

Mona 2.1

Nabila 0.9

Ramy 1

Amany Bassem 1.7 3

Abd El Rahman 2.5

Doaa 1.3

1

3

Ayman 1.5

Karima 0.8

Samir

Nagwa 1.6

xviii) Second group Name

Tall in m

xix)

Name

Tall in m

xx) Name Tall in m

Magda 2.3

Amr 1.7

Third group Mohamed

Aiya

2

1.7

Mahmoud Walaa

Fourth group Adel 3

Marwa 2

2.5

F- Group: The following tables show the heights of trees in Ahmed’s garden in metres. Use the information in each table to carryout the under required. xxi)

First group

Tree name A-tree B-tree C-tree D-tree E-tree F-tree G-tree 80.5 90 100 70.7 65.8 120.3 60.4

Height in m

Draw a line-graph, then find the highest and the shortest and difference between the highest and shortest one. xxii) Second group Tree name H-tree I-tree 50.7 100.8

Height in m

J-tree K-tree L-tree M-tree N-tree 80.2 95.7 70.7 60 110.3

Draw a bar chart, then find the difference between the highest and the shortest. xxiii) Third group Tree name O-tree P-tree Q-tree R-tree S-tree T-tree U-tree 120 110.3 40.7 75.3 80.5 60.5 90.9

Height in m

Draw a bar-line graph, then find the highest and the shortest tree, the difference between the highest and the shortest. xxiv) Fourth group Tree name V-tree W-tree X-tree Y-tree Z-tree 120 110.3 40.7 75.3 80.5

Height in m

ζ-tree

60.5

ξ-tree 90.9

Draw a broken line graph, then show the highest and the shortest tree and the difference between them. G- Group: The following tables show the population in many of governorates in Egypt. Use the information in each table to carry out the under required. xxv) First group Governerate Population in thousands

Ismaelia

Port-said

513684

600000

El Suize Domiatta Dakahlia 486193

681931

938138

Draw the bar-graph, then show the biggest and the smallest governorate and find the difference between them in population.

xxvi) Second group Governorate Population in thousands

Sharkia

Assiut

Aswan

Monofia

Kalubia

456381

513831

200000

731932

638153

Draw the bar-line graph, then show the biggest and the smallest governorate in population, also find the difference between them. xxv) Third group

governorate

Population in thousands

Gharbia

Menia Beni-Sueif Behera Kafr El sheik

738631

538138

4000000

235631

353638

Draw the line graph, then show the biggest and the smallest governorate in population, also find the difference between them. xxvi) Fourth group Governerate Population in thousands

Kena

Sohage

Red sea

Fayoum

El-Wady

138386

300000

538134

638193

238153

Draw the broken line, then show the biggest and the smallest governorate, also find the difference between them.

Please… Dear pupil… Review all syllabuses before solving each self-test and each exam, determine for your-self the time of exam and solve each exam more than once. Hassan A. Shoukr

Self-Tests Self–Test I Complete: 1)

5    = = = 8   

2)

36    = = = 48   

3)

3  = 9 3

4)

2 16 =  64

5)

3 36 =3  11

6)

 50 =  4

7)

83 2 = 9 9

8) 11 =

9)

13  3

3 5

 5

11)

1 3

5 8

24)

45 39 33 , , ,,, 73 69 65

1 2 + = 3 5

26)

3 3 1 + = 4 8

27)

3 1 2 +3 = 4 8

28)

29)

1

31)

1 3 + = 8 2

23)

> 2

25)

33)

3 8

1 3 3 +2 + = 5 4 10

3 7 +1 = 4 3

3 2 1 + + = 8 5 2 3 8 = 5 9

30)

+

32)

1 3 1 + = 3 5 4

34)

1 3 1 1 + + = 5 4 8 2

35)

3 2 2 ++1 = 5 4 9 3

36)

37)

3 3 1 − = 4 8

38)

3 1 = 8 4

40)

5 5 − = 9 18

5 1 − = 6 3 5 5 4 −4 = 7 14

39)

−

41)

3 3 1 − = 8 4

42)

− 2

43)

3 18 × = 9 21

44)

2 3 ×1 =  5 4

45)

3 3 3 4 ×1 × =  5 4 7

46)

×

47)

4 5 × = 9 8

48)

3 5 1 × = 4 8

49)

× 3

50)

3 2 ÷ = 4 5

1 7 = 4 10

3 3 =1 10 5

3 4 = 5 8

51)

3 3 1 ÷ = 4 5

52)

÷

3 4 = 5 9

53)

3 4 ÷ = 1 5 10

54)

3 4 1 ÷ = 5 7

55)

3 1 ÷ 4 = 2 5 2

56)

÷

57)

0.06 =

 

58)

5.003 = 

59)

64 = 1000

60)

1

5 5 = 9 3  

3 = 100

61)

1.005 can be read as: ………………

62)

463.06 can be read as: ………………

63)

The place value of “6” in the number 4.316 is ………

64)

The place value of “5” in the number 53.41 is ………

65)

The place value of “3” in the number 14.319 is ………

66)

The place value of “0” in the number 413.306 is ……

67)

6-hundredths

= …………….

68)

5- tens

= …………….

69)

7- thousands

= ……………..

70)

100- thousandths = …………….

71)

507- hundredths = 

72)

6003- thousandths = 

73)

43.361, 43.370, ……, ……, ……,

74)

96.406, 96.4, ……, ……, ……,

 

 

75)

46.361 < …………

76)

………. < 563.3

77)

43.461 < ………< 43.463

78)

531.4 > ……… > 531.38

79)

4.367 + 463.4 = ………

80)

……… + 56.38 = 136.4

81)

56.381 + ……… = 936.5

82)

5-tens + 6-hundredths = ………

83)

5- thousandths + ……… = 4- hundreds.

84)

……… - 9-tens = 4- thousands.

85)

563.4 – 35.438 = ………

86)

……… - 4.389 = 463.5

87)

563.5 - ……… = 46.531

88)

4-tens – 6- hundredths = ………

89)

……… - 5-tenths = 43.45

90)

363.3 ÷ 100 = ………

91)

4.631 × 1000 = ………

92)

……… ÷ 100 = 0.003

93)

456.3 ÷ ……… = 0.04563

94)

……… × 1000 = 1563

95)

4361.3 × ……… = 43613

96)

7-hundredths × 100 = ………

97)

4-tenths × 1000 = ………

98)

9-thousandths × ……… = 9

99)

7-tens ÷ 100 = ………

100)

9- hundredths ÷ 10 = ………

101)

103 – tenths ÷ ……… = 103

102)

………, 43.361

103)

4638.43, ………

104) 431.3, ……, 431.32 106)= 3.4 +5 . 3 4 91. 8 3 1

105) 107)

463.4, ……, 463.38

108)

109)

.3 6 1 - 3 1 5. .. 1 4 1. 6 1 7

4. 3 1 -2 3 . 2 . 5 11 .015 4 6 3. 2 + .. 1 3 9 9 1.231

B- Complete Using < , > or = : 3 4

110)  3 4

5 7

112) 4 3 3 4

3 8

3 6

111) 1  3 4

4 5

113) 5 5

2 9

114) −  + 3 2 5 4

3 5

1 3

116) 1 ×  + 1 3 7

118) + 1

7 3

2 5

115) 1 + 3 10

2 1 3 1 ÷ 2 5 10 14

120)4.831 …… 53.43

5 6

3 1 1  2 − 1 10 2 4

2 3

3 4

3 8

117) 1 ÷ 2 1 − 3 1 4 4

3 8

119) 4 × 1 ÷

1 4

121)63.31 …… 63.41

1 4

122)3.5 …… 4

1 4

123)603.60 …… 603.06

2 5

124) 6  6.4

125)3-tenths …… 5-tens

126)

9- thousandths …… 4-hundredths

127)

100-thousandths …… 10-hundredths

128)

600-hundredths …… 6-tenths

129)

1000-thousandths ……1

130)

60 …… 600-tenths

Self-Test II Put the answer either “True” or “False”: 5 8

1) =

3 4

1 4

7 4

3 5

8 5

3 5

4) 1
3 5) 0.05 = 7)

3 4

2) 1 =

30 = 0.003 1000

8) 1

9)7-hundredths = 700 11)538-tenths = 53

8 10

157 1000

3 = 1.3 10

10) 40-thousandths = 0.04 12)46.38 < 46.39

13) 361.4 < 36.14 < 361.42 14) 43.06 can be read as: “forty three point six”. 15)

3-tenths + 4-hundredths = 0.34

16) 17)

5-tenths – 3-thousandths = 0.497 7-hundredths × 10 = 0.7

18)

100 × 4-tenths = 0.4

19)

5-thousands ÷ 100 = 5

20)

3-tenths ÷ 10 = 3-hundredths

21)

3.438 × 100 = 0.03438

22)

3.438 ÷ 100 = 343.8

23)

436 + 3.46 = 7.82

24)

536 – 48.93 = 43.43

25)

The place value of “5” in the number “4.315” is “thousands”

26)

The place value of “9” in the number “391.381” is “tenths”

27)

3 2 6 ×1 = 1 5 4 20

28)

3 3 2 1 ÷ =2 5 4 15

29)

1 4 3 +3 =3 15 5 10

30)

3 1 2 5 − =5 4 2 4

31)

5 1 3 3 1 +2 + =4 8 2 8 4

32)

3 2 1 4 −1 = 3 7 14 14

33)

5-tenths = 50-hundredths = 500-thousandths

34)

25.46 is “twenty-five and forty-six hundredths”

35)

Sixty-one and 9-thousandths is 61.09

36)

0.725, 17.25, 72.5 are in descending order.

37)

17 1 13 are in ascending order. ,1 , 20 2 5

38)

4.381 kg > 4381 gm.

39)

4.381 m2 > 4381 cm2.

Self-Test III Choose the correct answer: 1)

4  = 12 3

[ 8 , 4 , 1 , 2 ]

2)

 4 = 25 5

[ 20 , 5 , 4 , 25 ]

3)

3 9 = 7 

[ 3 , 63 , 21 , 27 ]

4)

 27 =3 8 8

[ 3 , 8 , 7 , 27 ]

5)

3  4 = 5 5

[ 12 , 20 , 23 , 15 ]

6)

13  9

 28 29 30 31 , , ,  9 9 9   9 

10)

3.46, …

 47 45 44 43  3 100 , 3 100 , 3 100 , 3 100 

11)

,

361 100

[3.6, 3.62, 3.63, 3.46]

12)

3 4 +1 =  5 8

8 6 7  7 2 40 , 2 40 , 2 40 ,1 40 

13)

1 3 4 +1 + 2 =  2 4 8

3 3 18   1 4 ,3 , 4 ,  4 4 4  4 

14)

1 3 1 + = 3 8 4

3 3  4 2 1 8 ,1 8 , 2 8 ,1 8 

15)

3 3 1 ++1 = 5 5 4 2

5  3 63  4 3 20 , 3 20 , 20 , 3 20   

16)

3 3 3 +1 + 2 = 9 8 4 4

 3 2 4 5 5 8 , 5 8 , 5 8 , 5 8 

17)

3 3 2 − = 8 4

13 14 4 3   8 , 8 , 1 8 , 1 8 

18)

4 3 1 − = 5 10

3 4 5 6 , , ,  2 2 2 2 

19)

− 3

1 3 = 4 16

5 7 6  8 3 , 3 , 3 , 3  16 16 16 16   

20)

4 3 ×1 =  9 8

 8 9 10 11  , , ,  18 18 18 18  

21)

3 1 1 × = 3 4 8

 11 10 9 8  114 ,114 ,114 ,114 

22)

× 2

3 4 =1 9 8

 7 8 9 10  , , ,  14 14 14 14  

23)

1 3 4 ÷ = 5 8

 55 56 57 54   5 , 5 , 5 , 5 

24)

÷

3 5 = 4 8

 13 14 15 16   32 , 32 , 32 , 32 

 9 10 11 13   22 , 22 , 22 , 22 

1 3 ÷ = 2 5 10

25)

1

26)

51.03

27)

6- hundredths = …

[600, 0.006, 0.06, 0.6]

28)

30-tens

=…

[ 30 , 300 , 3 , 0.3 ]

29)

32 = 100

30)

103-tenths = …

31)

The place value of “3” in “431.415” is …

=

 100

[ 5103 , 510.3 , 5.103]

[32-hundredths, 32-hundreds, 3.2] 30   3 03 30 10 10 ,1 10 ,1 10 ,10 10  

[tenths, tens, hundredths, hundreds] 32)

96.406, 96.3, …

[96.194, 96.506, 96.206, 96.106]

33)

4.381, … , 4.379

[4.382, 4.38, 4.383, 3.378]

34)

536.41 > … > 536.39 [536.38, 536.39, 536.4, 536.41]

35)

46.381 + 4.9 = …

36)

… + 361 = 461.386

[53.281, 52.281, 51.281, 50.281]

[100.486, 100.386, 100.281, 100.181] 37)

463 - … = 4.386 [456.614, 457.614, 458.614, 459.614]

38)

435.386 ÷ 100 = … [4.35386, 43538.6, 435.386, 435386]

39)

541.438 ÷ … = 0.514138

[100, 10, 1000, 10000]

40)

100 × 563.198 = … [5.63198, 56319.8, 563.198, 563198]

41)

… × 534.039 = 5340.39

[ 10, 100, 1000, 10000 ]

42)

6- hundredths ÷ 10 = …

[ 0.6 , 0.06 , 0.006 , 6 ]

43)

100 × 30-thousandths = …

[ 0.03 , 0.003 , 0.3 , 3]

44)

300-tenths ÷ … = 3

[ 10, 100, 1000, 10000 ]

45)

… × 20-tens = 200

[ 1 , 100 , 1000, 10000 ]

46)

100 of 4-tenths = …

[ 4 , 40 , 400 , 4000 ]

Self-Test IV Word Problems: 1)Samiha bought some chocolate for L.E

3 and two notebooks 5

3 . Find the total cost for the chocolate and two 5

for L.E

notebooks in pounds?

2)Amina bought three coloured satin ribbons. A red 3 4

ribbons metres long, a green one yellow one

4 metres long and 5

1 metres long. Find the total length of Amina’s 2

satin ribbons.

3)Hazem had one pound. He bought biscuits for L.E ruler for L.E

3 . How much money was left? 4

1 and a 5

4 from his father. He bought a protractor 5 3 and set-square for L.E . How much money was left? 4

4)Hossam took L.E

5)Amal bought 4 metres of cloth to make a dress but it shrunk by

1 metres after washing. How much cloth did she have 5

left?

6)Ramy is

6 1 metres tall and his brother Amr is metres 5 4

shorter. How tall is Amr?

7)Samira bought a pen for L.E magazine for L.E

1 1 , a cola drink for L.E and a 5 4

5 . How much money did Samira spend? 8

8)Wafaa bought three strips of coloured decorations the length

3 1 metres, the length of the second was 8 4 1 metres. Find the metres and the length of the third was 2

of the first was

total length of the three strips. 9)Hany needs

5 kg of sugar for one day. How much sugar does 8

he need for one week?

10)If the price of one kilogram of cheese is L.E 12. Then what is the price of

3 kilograms? 4

11)A grocer puts 36 kg of vegetables into bags, each bags holds 3 kg. How many bags are needed for the whole quantity? 4

12)The distance between Ahmed’s house and the school is

4 km. He covers this distance in 10 minutes. Find the 5

distance that Ahmed covers in one minute.

13)Bassem bought two bottles of sherbet. The first was rose flavoured weighing weighing

7 8

kg and the second flavoured

4 kg. Find the total weigh of the two bottles. 5

14)Mona bought

3 2 metres of cloth, each metre costs L.E . 4 5

How much did Mona pay in L.E? 1 5

15)Six boxes of biscuits cost L.E 1 . How much does one box cost?

16)How many books can you buy for L.E 4, if each book costs L.E

2 ? 5

17)In a house keeping section, the students made 5 kg of jam. They want to put them in jars that can hold

5 kg. How 8

many jars are needed for the whole quantity of jam.

18)How many bags are needed to hold 3 kg of rice if each bag holds

3 kg 4

19)Three cakes, each one is divided into 3-equal parts. How many parts are there?

20)Abd El-Rahman bought

2 kg of tea, the price of the 3

kilogram was L.E 12. How much did he pay? 21)A lady bought

3 kg of butter, the price of the kilograms 4

was L.E 6. How much did she pay?

22)A merchant has two pieces of cloth, the length of one is 54 metres and the length of the other is 45 metres. If he sold of the first and

3 4

3 of the second. How many metres did he 5

sell from each of the two pieces.

23)Mohamed has L.E 15. He bought fruits for L.E 3.42 and vegetables for L.E 2.86, as well as compass and a protractor for L.E 3.05. Calculate how much money he has left. 24)Nagwa has got a tree whose height is 50.36 metres and Mona has got another whose height is 131.5 metres. How much does Mona’s tree increase Nagwa’s tree? 25)Mohamed has took L.E 5.35 from his father and L.E 3.2 from his mother, he bought a pencil for L.E 2.3 and a pen for L.E 3.75. How much money was left?

Self-Test V Data Representation: i)

The following table shows the heights of some students

Name Mohamed Height in m 1.12

Nagy 0.98

Amr 0.83

Omr 1.2

Bassem 0.91

Draw the line graph, then answer: a)

What is the name of the tallest student?

b)

What is the name of the shortest student?

c)

Arrange the students from the shortest to the tallest.

ii)

The following table shows the value of petroleum and raw oil produced in Egypt in the period from 1973 to 1978.

Year Value in millio ns

1973

1974

1975

1976

1977

1978

178.4

263.9

385.7

574.6

696

794

Draw the bar chart, then answer: a)

Find the yearly increase in the value of petroleum and raw oil products in Egypt.

iii) In the following table shows the change in the number of pupils in “one class room schools” from the academic year 1982/83 to the academic year 1988/89. Academic year Number of pupils

1982/83 68358

1984/85 37599

1986/87 25781

1988/89 27023

Draw the broken line graph. iv) In the following table shows the prediction about maximum temperatures in some Egyptian towns and 3rd December 1995.

Town

Cairo

Temperatures in Co

30

Alex. Ismaeliya Assuit

26

25

Luxor

40

Kafr El Port Sheik Said

42

25

20

Represent these data by a line graph, then show: a) The hottest town b) coldest town c)

The difference between highest temperature and lowest one.

v)

The following table shows the number of ships which passed through the Seuz canal in the period 1985-1990. Year

Number of ships

1985

1986

1987

1988

1989

1990

17664 17628 18190 17541 18403 19791

Represent the previous data by bar line graph and the line graph. vi) The following table shows the number of different types of housing units built in the year 1988/1989. Type Egypt Number of 84789 units

Nigeria Algeria Kenya Zimbabwe Morocco 56043

17137

5633

26227

40328

Represent the data by bar-line graph and the line graph, then show: a)

The ascending order of types of these housing units.

b) The biggest state in the number of types of housing

units.

vii) The following table shows the quantities of needs in ardebs sold by a farmer during some months: Month

March

April

May

June

July

August

Quantity in ardebs

20

30

45

40

15

20

Represent the previous data by the bar-line graph and the line graph. viii) The following table shows the number of television colour sets sold in Egypt during the period 1970-75 Year Number of sets in thousands

1970

1971

1972

1973

1974

1975

77.2

84.0

91.3

114.6

130.9

142.5

Represent the data by bar-line graph and broken line. ix) The following table shows the production of grain on a certain from during the period from 1968-1973. Year Grain production in millions

1968

1969

1970

1971

1972

1973

395

410

495

560

420

515

Represent the data by the bar-line graph and a line graph, then show: a)

In which year is the greatest grain production.

b)

In which year is the smallest grain production.

c)

The difference between them.

x)

The following table shows the area of the various continents of the world.

Continent

Area in millions of square miles

Africa

Asia

Europe

N.America

30.3

26.9

4.9

24.3

S.America Oceania

17.9

22.8

Represent the data by line graph and bar-line graph, then show: a)

Which is continent of the world the greatest?

b)

Which is continent of the world the smallest?

xi) The following table shows the sales of motor cars by a certain company in the period 1990-1995.

Year Sales

1990 2000

1991 2500

1992 3200

1993 2700

1994 3000

1995 2500

Represent the data by a bar-line graph and line graph. xii) The information below gives the production of tyres (in thousands) produced by a certain company for the first six months of 1998. Month January February March April Production 40 43 39 38

May 37

June 45

Represent the data by a bar-line graph and a broken line. Then show: a)

The month of the best production.

b)

The month of the lowest production.

c)

The difference between them.

Examinations Exam Style Paper I Answer the following questions: 1 a) Complete: i)

1 3 1 + = 3 5

ii)

− 2

iii)

21.35 + … = 118.13

iv)

365 – 32.51 = …

2 3 =4 10 10

b) Put the suitable sign (√) or (×). i)

15.31× 100 = 0.1531

ii)

81.313 ÷ 10 = 8131.3

iii)

1 2 2 3 × =3 3 7 21

iv)

3 1 9 ÷2 = 2 5 3 5

2 a) Choose the correct answer: i)

4  = 12 3

[ 8 , 4 , 1 ,

ii)

103-tenths = …

30   03 03 30 10 10 ,1 10 ,1 10 ,10 10 

iii)

32 = 100

2 ]

[32-hundredths, 32-hundreds, 32, 3.2]

b) Put the suitable sign < , > or = : i)

4 5  9 7

iii)

31.56 – 26 … 5

1 6

ii)

4.831 … 48.31

iv)

6

2 … 6.4 5

3

a) Arrange in ascending order : b) If there are 11

2 3 1 , , 5 10 4

1 3 cans of oil and each one contains kg 3 7

of oil. Then find the amount of oil in the cans.

4 The following table shows the marks of Nagy in different subject. Subject

Math’s

Arabic

Science

English

Mark

32

25

17

28

Social studies 19

Represent the data by a bar-line graph and a line graph, then show; a)

What is the best subject of Nagy?

b)

What is the bad subject of Nagy?

c)

What is the total mark of Nag?

Exam Style Paper II Answer the following questions: 1

2

Find the result: i)

3 4 1 × 5 5

ii)

5 2 1 1 +2 + 7 3 3

iii)

5.56 – 2.763

iv)

35.25 ÷ 100

a) Put the suitable sign “ + ” , “ - “ , “ × “ or “ ÷ “: i)

7 2 3 3 2 = 5 10 10 5

ii) 135.43 … 100 = 1.3543

10 … 43.36 = 433.6

iii)

3 2 17 1  = 8 3 24

iv)

b) There is a piece of land whose area is 3565.562m2. If we want to divide it on 10 brothers, Then what is the share of each one? 3 a) Complete i)

3 3 1 − = 8 4

iii)

0.4 ÷ = 1

3 5

3 = 100

ii)

1

iv)

56.381 + … = 936.5

b) Put the suitable sign (√) or (×) : 157 100

i)

5 3 = 8 4

iii)

The place value of “8” in 391.381 is tenth.

ii)

15.007 =

4 a) Put the suitable sign < , > or = : i)

3 3  3.57 4

ii)

3 2 1 −  5.3 ÷ 10 7 5

iii)

3 16 1  5 10

iv)

13.2 – 5.36 … 6

1 5

b) Arrange in ascending order: 1 2

5

,

0.05 ,

1 , 4

0.025

The following table shows the book types and its number of pages.

Book type Math’s English Number of pages

160

200

Science

Arabic

170

240

Social Religion studies 100

80

Represent the data by a bar-line graph and a broken line, then show: a) the big book b) the smallest book.

Exam Style Paper III Answer the following questions: 1 a) Put the suitable sign < , > or = : i)25.36 … 25

4 7

3 4

ii) 2 + 3

iii)15.31 × 10 …1.531 × 100

5 3 2 9 − 4 14 5 10

iv)5.3 – 2.35 … 1.15 + 2.6

b) Complete as the pattern: 3.2, 5.5, 7.8, …,… , …,… 2 a) Complete: 1 3 =2 6 5

i)

35 = 8

ii)

+

iii)

35.43 × … = 3543

iv)

53.5 - … = 25.31 1 4

b) Mohamed and his sister have L.E 11 . If his sister has 3 4

L.E 5 . Then find what Mohamed has? 3

Join in order: 3

1

3 2 −1 4 8

1 3 ×2 5 4 5

3

2 3 +1 3 6

3 2 −3 4 5

1

1

3 2 ÷1 7 5

3 1 ×1 5 4

4 a) Arrange in descending order: 6.2 , 6

1 4

, 6.3 , 6.35

b) Choose the correct answer: i)

13 : i)

42 2  49 5

iii) 2.4 × 10 … 0.24 × 100

ii)

0.25

1 8

iv) 1000-thousandths … 1

3 a) Find the result of each: i)

1 1 1 7 + 2 +1 4 6 3

ii)

0.85 + 2.013

iii)

9.79 ÷ 1000

iv)

2.015 – 1.278

b) Arrange in ascending order:

8007 2 , 0.7 , 0.08 , 0.0087 , 1000 24 3 each and a book for 8 L.E 4.75. If she had L.E 10 then find the money left with her.

4 a) Madiha bought 4-notebooks for L.E

b) Put the suitable sign (√) or (×) : i)

4.381 m2 = 43810 cm2

iii) 10-hundredths = 100-tenths 5

ii)

30 = 0.003 1000

iv)

3 8 1 < 5 5

The following table shows the number of housing units of different types built in the year 1998: Type

Economy

Intermediate

Above inter

Luxury

Number in thousands

85

56

17

6

Represent the data by a bar chart and a line graph.

Exam Style Paper VI Answer the following questions: 1

Find the result: i)

3546 × 100 = …

ii)

483 ÷ 1000 = …

iii)

5 5 1 +3 = 7 14

iv)

2 3 3 −1 =  5 3

35.31 – 1.356 = …

v)

vi)

63 + 31.56 = …

2 a) Complete: i)

356.35 × … = 3.5635

ii)

563 ÷ 10 = …

iii)

3  81 = = 5 15 

iv)

1 3 × = 12 4

b) How many hundreds are there in 35.36? 3 a) Put the suitable sign < , > or = : 35.3 … 35

i)

1 3

3 2 ii) 1 + 1.35 + 2.36 4 8

iii) 9-thousandths … 4-hundredths iv) 3.48 × 10 … 348 ÷ 10 b) Arrange the following in ascending order: 13.15 , 41 , 0.015 , 1.015 , 13.015 4 a) Complete:

 

i)

5-tenths = …

iii)

The place value of “4” in the number 1356.438 is …

ii)

3.005 = 

b) Find the perimetre of a rectangle and its area, if its length is 13 cm and its width is 5 cm. 5 The following table shows the population in millions in the period 1940-2000. Year

1940

1950

1960

1970

1980

1990

2000

Population in millions

8

15

20

27

40

55

65

Represent the data by a bar-line graph and a line graph.

Exam Style Paper VII Answer the following questions: 1

Complete: i)

3  11 = 5 

ii)

2 16  = =  64 8

iii)

0.005 =

 

iv)

7-thousandths = …

v)

431.29, …, 431.31

vi)

“6” in 41.426 is …

2 Choose the correct answer: i)

9-thousandths…4-hundredths

[ < , > , =]

ii)

27  =3 8 

 3 8 7 27   8 , 3 , 8 , 8 

iii)

 or = : i)

603.60 … 603.06

iii)

3 7 1  6 3

ii)

3.5 … 4

1 4

b) Complete as the pattern: 96.406 , 96.4 , … , … , … , … 5 a) Arrange in ascending order: 4 3 4.3 , 5 , 1.98 , 3 5 4 b) How many bags are needed to hold 3 kg of rice if each 3 bag holds kg? 4 6 In the following table the heights of some trees in Mona’s garden. Tree name Height in m

V-tree

W-tree

X-tree

Y-tree

Z-tree

ζ-tree

ξ-tree

55.6

80.5

60.4

115.3

110.4

70.6

60.7

Draw the bar chart and the broken line. Graph.

Exam Style Paper VIII Answer the following questions: 1 Put the suitable sign (√ ) or (X): 3 i) ii) 1 = 1.03 10

538-tenths =

4 5

iii)

536 – 48.93 = 43.43

iv)

v)

4.381 m2 > 4381 c m2

vi)

2 Choose the correct answer: 3  i) 4 = 5  2 ii) 3 > 9 4 3 1 iii) +1 + 2 =  8 4 2

2 1 3 4 −1 = 3 14 7 14 3 3 2 1 ÷ =2 5 4 15

12 20 23 15   5 , 5 , 5 , 5   28 29 30 31  9 , 9 , 9 , 9   1 3 3 18  4 4 ,3 4 ,4 4 , 4 

iv)

46.381+ 4.9 = …

v)

541.438 ÷ … = 0.541438

[53.281, 52,281, 51.281, 50,281] [10, 100, 1000, 10000]

3 Find the result: i)

3 4 +1 8 5

ii)

4 3 ×1 9 8

iii)

563 – 459.614

iv)

563.198 ÷ 1000

4 a) Arrange the following ascending order: 66.31, 663.1, 6.631, 0.6631 b) Complete the missing digits: i)

3

+4

.3 2.

5 4

9 1 6.16 1 5

ii)

.3 6 7 -3 67.

.

1 62. 1 73

The information below gives the production of tyres ( in thousands) produced by a certain company for the first six months of 1998.

Month Productio n

a)

January

February

March

April

May

June

40

43

39

38

37

45

Represent the table a bar line graph and a line graph, then show: The month of the best production. b) The month of the lowest production. c) The difference between them.

Exam Style Paper IX Answer the following questions: 1 a) Complete using < , > or = : 1 3 5 ii) 7.5 … 7 i) 5 5 2 4 6 3 1 3 1 iii) 4 × 4 ÷ iv) 0.345 × 100 … 345 ÷ 10 4 4 4 4 b) Arrange the following groups in ascending order:

1 3 3 , 3.3 , 3 , 3.25 2 4 2 a) Choose the correct answer: i)

300-tenths ÷ … = 3

[10, 100, 1000, 10000]

ii)

1 3 − 3 = 4 16

 8 7 6 5 3 16 ,3 16 ,3 16 ,3 16 

iii)

The place value of “5” in the number 431.365 is … [hundreds, hundredths, thousandths, thousands]

b) How many books can you buy for L.E 4, if each book 2 costs L.E ? 5

3

Complete: i)

… × 20-tens = 200 ii)

iii)

1 3 3 + = 4 4 8

iv)

3 1 ×1 = 2 8 4

v)

36.38 × …= 3638

vi)

÷

6-hundredths ÷ … = 0.006

3 5 = 4 8

4 a) Complete as the pattern:

1 5 9 , , ,,,, 2 4 6 b) Complete as the pattern: 2.5, 4.8, 7.1, … , … , … , … 5

The following table shows the change in the number of pupils in “one class room schools” from the academic year 1992/1993 to the academic year 2000/1. Academic year

1992/93

1994/95

1996/97

1998/99

2000/1

Number of pupils

68358

37599

25781

27023

53028

Represent the data by line graph.

Exam Style Paper X Answer the following questions: 1

Find the results: i)

3 3 1 1 + 3 +1 4 8 2

ii)

1 3 − 3.25 2

iii)

35.53 × 100

iv)

45.38 ÷ 10

2 a) Complete the missing digits: i) 4 5 . 3 +2 . 2 9 01.5 1

ii) 3 . 5 6 - 2.3 18.893

.

b) How many 100s are there in 4538? 3 a) Complete using < , > , = : i)

438.3 ÷ 10 … 4383

ii)

1 4 × 28 2

iii)

1 1 1 1 1 ÷ 1 × 4 4 4 4

iv)

3 7 3  8 2

b) Complete as the pattern: 49.3 , 52.8 , … , … , … , … 4 a) In a house keeping section, the students made 5 kg of jam. 5 They want to put them in jars that can hold kg. How 8 many jars are needed for the whole quantity of jam? b) Arrange the following in descending order:

56 1 2 3 , 9 , 4.35 , 10.75 , 10 2 3 5 Put the suitable sign (√) or (×): i)

1 3 1 = 2 2

ii)

1 104 =1 100 25

iii)

35.3 + 0.368 = 4.21

iv)

46 – 0.46 = 0

v)

2 3 2 ×3 = 6 3 2

vi)

1 1 1 ÷1 = 1 4 4

6

The following table shows the weights of pupils in kilograms. Use the information in the table to draw the line graph and bar line graph. Name

Bassem

Nadia

Nabila

Bassma

Ramy

Amr

Weight in kg

65

95

150

55

105

73

Please… Dear pupil… Try to solve the problems before looking these answers. Hassan A. Shoukr

i) ii) iii) v) vii) ix) xi) xii)

10, 16, 15, 24, 20, 32 18, 24, 9, 12, 3, 4 1 iv) 11 vi) 9 viii) 14, 5 x) one of the answers is 15 19 23 , , 12 14 16

8 12, 1, 2 58 19, 3 4

xiii) 16, 20, 12, 15, 8, xiv) 4, 5,8 , 10 10 xv) 15 xvi) 3 xvii) 13, 1 xviii) 5 xix) 21, 9 xx) 8 xxi) 6, 9 xxii) 6, 8 xxiii) one of the answers is 3 17 21 15 , , . 61 57 53 11 xxv) 15 7 xxvii) 5 8 1 xxix) 4 4 3 xxxi) 1 8 7 xxxiii) 12 31 xxxv) 3 36 3 xxxvii) 1 8 5 xxxix) 8 5 xli) 8 2 xliii) 7 9 xlv) 3 20

xxiv)

xxvi) 2

1 8

xxviii) 1 xxx)

13 32 14 xlix) 65 11 li) 2 12 1 liii) 4 1 lv) 11 2 3 lvii) 50

xlvii) 1

Self-Test I

13 45

11 40

9 20 7 xxxiv) 3 8 1 xxxvi) 2 5 xxxviii) 14 5 xl) 18 9 xlii) 3 10 7 xliv) 10 5 xlvi) 6

xxxii) 1

5 14 7 l) 1 8 4 lii) 15 4 liv) 2 5 25 lvi) 27

xlviii)

lviii) 5

3 1000

lix) 0.064 lx) 1.03 lxi) One point zero zero five lxii) 4-hundred and sixty-three point zer six. lxiii) thousandth lxiv) tens lxv) tenth lxvi) hundredth lxvii)0.06 lxviii)50 lxix) 7000 lxx) 0.1 lxxi) 5.07 lxxii)6.003 lxxiii)43.37, 43.388, 43.397 lxxiv)96.394, 96.388, 96.382 lxxv)46.362 lxxvi)563.29 lxxvii)43.462 lxxviii)531.49 lxxix)467.767 lxxx)80.02 lxxxi)880.119 lxxxii)50.006 lxxxiii)0.035 lxxxiv)130 lxxxv)527.962 lxxxvi)467.889 lxxxvii)516.969 lxxxviii)39.94 lxxxix)43.95 xc) 3.633 xci) 4631 xcii) 0.3 xciii)10000 xciv) 1.563 xcv) 10 xcvi) 0.7 xcvii)400 xcviii)1000 xcix) 0.7 c) 0.009 ci) 0.1 cii) 43.36 ciii) 4638.43 civ) 431.31 cv) 46339 cvi) 3, 8, 3, 9, 7 cvii) 7, 4, 3, 3, 4, 6 cviii)4,5,7,7,4,4 cix) 5, 2, 9, 1, 0, 9 cx) > cxi) < cxii) > cxiii)< cxiv) < cxv) > cxvi) < cxvii)< cxviii)>

cxix) < cxxi) < cxxiii) > cxxv) < cxxvii) = cxxix)
cxxx) =

Self-Test II

i) X iii) X v) X vii) X ix) X xi) √ xiii) X xv) √ xvii) √ xix) X xxi) X xxiii)X xxv) X xxvii) X xxix) X xxxi) √ xxxiii)√ xxxv) X xxxvii)√

ii) √ iv) X vi) X viii) √ x) √ xii) √ xiv) X xvi) √ xviii)X xx) √ xxii) X xxiv) X xxvi) X xxviii)√ xxx) √ xxxii) X xxxiv)√ xxxvi)X xxxviii)X Self-Test III

i) iii)

1 21

v)

23

vii)

3 5 28 9

ix) xi)

3.6

ii) iv) vi)

20 3

15 4 viii) 2 1 8 x) 3 47 100 xii) 2 7 40

xiii) 4 3

xiv) 1 3

4 xv) 3 3 20 13 xvii) 8 xix) 3 7 16 11 xxi) 1 14 xxiii) 56 5 13 xxv) 22

8 xvi) 5 5 8 xviii) 3 2 11 xx) 18 xxii) 9 14 xxiv) 15 32

xxvi) 5103

xxvii)0.06 xxviii)300 xxix)32-hundredths xxx) 10 3 10

xxxi)tens xxxiii)4.38 xxxv)51.281 xxxvii)458.614 xxxix)1000 xli) 10 xliii)0.3 xlv) 100

xxxii)96.194 xxxiv)536.4 xxxvi)100.386 xxxviii)4.35386 xl) 56319.8 xlii)0.006 xliv)10 xlvi)40

Self-Test IV

i)

1 1 5

The total = L.Eii) The total = L.E 2

1 20

iii)

The left = L.Eiv) The left = L.E

v)

The

1 20

3

4

5

1 20

m

left

=vi) Amr’s tall = 19 m 20

b) The shortest is Amr c) Amr, Bassem, Nagy, Mohamed, Omr.

vii) Samira spent L.E 1 3

40

viii)The total of three strips = 1 1 m

2)

8

3 8

ix)

For one week = 4 kg

x)

The price of

3 kg = L.E 9 4

xi) –The number of bags = 48 xii) The distance per one minute 2 km 25

=

1977

1978

80000

19 82 /8 3 19 84 /8 5 19 86 /8 7 19 88 /8 9 30 20 10

Nagwa’s

0 Cairo

5) 0.98

0.91

0.83

0.6 0.4 0.2 0

a) The tallest is Omr

1976

40

1.2

N

1975

4) 50

1.4

M

1974

0

Self-Test V

0.8

263.9

20000

2

tree = 81.14 m xxv)The left = L.E 2.5

1

178.4

40000

xxiii)The left = L.E 2.66 xxiv)Mona’s tree increases

1.12

574.6 385.7

60000

1 The cost of one box =L.E 5

1.2

794

The yearly increasing ~ 784 – 696 = 88

3)

xvi) The number of books = 10 xvii)The number of jars = 8 xviii)The number of bags = 4 xix) The number of parts = 9 xx) He paid = L.E 8 xxi) She paid = L.E 9 xxii)The number of metres = 67 1

1)

696

1973

xiii)The total = 1 27 kg 40 xiv) Mona paid = L.E 3 10 xv)

800 700 600 500 400 300 200 100 0

A

O

B

Ismaeliya

Luxor

Port Said

a) Hottest town is Luxor b) The coldest town is Port said c) The difference = 22o 20000 19500 19000 18500 18000 17500 17000 16500 16000 1985

1986

1987

1988

1989

1990

6) 100000

10) 30 35

80000

25

60000

20

40000

15

20000

10

0

5

O

ce an ia

er ic a m

ei ca

S. A

N .A m

a

a) The greatest is Africa b) The smallest is Europe

11)3500

50 45 40

3000

35 30

2500

25

2000

20

1500

15 10

1000

5

500

0 March

May

July

0 1990

8) 160

1991

1992

1993

1994

1995

12) 50

140

20 1971

1972

1973

1974

1975

Ja nu a

1970

ry

0

600

Ju ne

40

M ay

60

A pr il

80

M ar

100

ch

45 40 35 30 25 20 15 10 5 0

120

9)

Eu ro pe

A fr ic

a

a) The ascending order is : 5633 , 17137, 26227, 40328, 56043 , 84789 b) The biggest state is Egypt

Fe br ua ry

7)

0

Kenya

A si

Egypt

a) The best month is June b) The lowest month is May c) The difference is 8

500 400

Exam I

300 200

1)

100

a) Complete: i)

0 1968

1969

1970

1971

1972

a) The greatest in 1970 b) The smallest in 1968 c) The difference = 165

1973

1

14 15

ii)

6

1 2

iii) 96.78 iv) 332.49 b) Put the suitable sign (√) or (X): i)X ii)X

ii) 10

i)1

03 10

iii)32-hundredths b) Put the suitable sign or = i)< ii)< iii)> iv)=

b) In ascending order: 0.025, 0.05,

5) 300 200 150

17 b) The total amount in cans = 3 kg 21

100 50

53

4) 03 51

R el

tu di e

s

ig io n

bi c

lS

A ra

a) The big book is Arabic book b) The smallest is Religion book

01 5 0 Math's

cibarA

ecneicS

hsilgnE

laicoS seidutS

a) The best is Math’s b) The bad is Science c) The total mark is 121

Exam II Find the result: i) 1

7 25

ii) 4

5 7

iii)2.797 iv)0.3525 a) Put the suitable sign “+” , “-“ , “ × ” or “ ÷ ”. i)+ ii) ÷ iv)iii) × b) the share of each one = 356.5562 m2 3) a) Complete 5 8

Exam III

1)

a) Put the suitable sign or =: i)< ii)> iii)= iv)< b) Complete: 10.1 , 12.4 , 14.7 2) a) Complete i) 4

2)

i)

nc e

So ci a

02

h

M at h' s

0

52

1)

1 1 , . 4 2

250

1 3 2 , , 4 10 5

a)

a) Put the suitable sign or =: i)> ii)> iii)= iv)>

Sc ie

3)

4)

En gl is

2)

iii)X iv)X a) Choose the correct answer:

ii)1.03

iii)0.25 iv)880.119 b) Put the suitable sign (√) or (X): i)X ii)X iii)X

3 8

iii)100

ii) 1

17 30

iv)28.19

b) Mohammed has L.E 5

1 2

3)

Join

4)

a) In descending:6.35, 6.3, 6 , 6.2

1 4

b) Choose: i)

15 4

iii)10

ii) 3

47 100

iv)20

5) 80

Exam V

70

1)

60 50 40

i)

30 20 10

W af aa

H od a

r A m

y

m

R am

B as se

A hm

ed

0

a) The heaviest pupil is Amr b) The lightest pupil is Hoda c) The difference is 45.35 kg.

Exam IV 5 i) 3 12

6 ii) 7

iii)10

1 iv) 2 4

Choose: ii)

i)3.4

1 20

58 7

iii)7 iv)1000 v)30 2) a) Complete i)1000 ii)3200 iii)2485 iv)73024 b) Put the suitable sign or =: i)> ii)> iii)= iv)= 3) a) Find the result: 3 4

ii)2.863 iv)0.737

b) in ascending: 0.0087, 0.08,

2 , 0.7, 24

8007 1000

4)

a) The left = L.E 4

7 8

b) Put the suitable sign (√) or ( X): ii)X i)√ iii)X iv)X

5)

90 80 70 60 50

160

40

140

30

120

20

100

10

80

0

60

Economy

40 20

Inter mediate

Above inter

Exam VI

A

M us H ic ou se K gr e ep ic l tu in g ra lE du Ph ca ys ti o ic n al Ed uc at io n

0 rt

4) 5)

ii)

iii)0.00979

iii)0.02 iv)Tenth v)0.8005 vi)4000m2 Complete i)23.532 ii)0.354 iii)6.3 iv)7.45 v)10 vi)201.8 Problem ( xxv) in self test iv

A

3)

51 40

i) 10

s

2)

Find the result:

Sp or t

1)

Choose

1)

Find the result i)354600

ii)0.483

Luxury

iii) 5

2)

1 14

iv) 1

iii)X iv)X vi)X v)√ 4) a) Complete using or =: i)= ii)< iii)< b) Complete: 96.394, 96.388, 96.382, 96.376

2 5

v)33.954

vi)31.44

a) Complete i)100

ii)56.3

iii)9, 13

iv) 3

i)0.5

ii) 3

9 13

3

5) a) in ascending order: 1.98, 3 , 4.3, b) the number of 100s = 0.3536 4 3) a) Put the suitable sign < , > or =: 4 5 i)< ii)< 5 iii)< iv)= b) the number of bags = 4 b) in ascending: 0.015, 1.015, 13.015, 6) 140 13.15, 41 120 4) a) Complete

5)

iii)tenth

5 1000

100 80 60

70

40

60

20

50

0

40

V

30 20

0 1940

1950

1960

1970

1980

1990

2000

Exam VII

2)

Complete i)58, 5 iii)5, 1000 v)431.3 Choose

ii)8, 2 iv)0.007 vi) thousandth

i)
or =: i)< ii)= iii)> iv)>

120 100 80

1 2

3 4

1 2

iv) 1

b) Complete: 9.4, 11.7, 14, 16.3 5) Problem (III) in self-test V

Exam X 1) Find the result 5 8

ii)0.25

iii)3553 iv)4.538 2) a) Complete i) 6 , 5, 6, 2, 8 ii) 1, 1, 2, 6, 3 b) The number of 100s = 45.38 3) a) Complete using < , > or =: i)< ii)> iii)< iv)< b) Complete: 56.3, 59.8, 63.3, 66.8 4) a) problem (xvii) in self-test IV 2 3

b) In descending: 10.75, 9 , 1 3 . 2

20

56 , 4.35, 10

5) Put the suitable sign (√) or (X):

r

y

A m

a

R am

B as sm

N ab ila

m

7 11 15 vi) v)100 32 13 17 21 25 4) a) Complete: , , , 8 10 12 14

i) 6

40 0

7 16

iii)thousandth b) The number of books = 10 3) Complete i)100 ii)10 iii) 1

60

N ad ia

i)10

6)160

B as se

ii) 3

ii)√ iv)X vi)√

140

b) in ascending order: 3.25, 3.3, 3 , 3 2) a) Choose

i)√ iii)X v)X

Mathematical Terms addition angle measure area

A

ascending order arrangement breadth bottom bar chart

B

broken line graph comparing convert calculate common denominator

C

dimensions data representation decimal

‫ﻋرض اﻟﺷﻛل‬ ‫ ﻗﺎع‬/‫أﺳﻔل‬ ‫اﻻﻋﻣدة اﻟﺑﯾﺎﻧﯾﺔ‬ ‫رﺳم ﺧط ﻣﻧﻛﺳر‬ ‫ﺑﺎﺳﺗﺧدام اﻟﻣﺳطرة‬ ‫ﻗﺎرن‬ ‫ﺣول اﻟﻰ‬ ‫اﺣﺳب‬ ‫اﻟﻣﻘﺎم اﻟﻣﺷﺗرك‬

D

decillion 10 division operation determine drawing divisible by divisibility divisor dividend quotient division operation 15

‫ﻋﻣﻠﯾﺔ اﻟﺟﻣﻊ‬ ‫ﻗﯾﺎس اﻟزاوﯾﺔ‬ ‫ﻣﺳﺎﺣﺔ‬ ‫ﺗﺻﺎﻋدﯾﺎ )ﻣن اﻟﺻﻐﯾر‬ (‫اﻟﻰ اﻟﻛﺑﯾر‬ ‫ﺗرﺗﯾب‬

‫دﯾﺷﻠﯾون‬ ‫ﻋﻣﻠﯾﺔ اﻟﻘﺳﻣﺔ‬ ‫ﺣدد‬ ‫رﺳم‬ ‫ﯾﻘﺑل اﻟﻘﺳﻣﺔ ﻋﻠﻰ‬ ‫ﻗﺎﺑﻠﯾﺔ اﻟﻘﺳﻣﺔ‬ ‫ﻗﺎﺳم‬ ‫ﻣﻘﺳوم‬ ‫ﻧﺎﺗﺞ اﻟﻘﺳﻣﺔ‬ ‫ﻋﻣﻠﯾﺔ اﻟﻘﺳﻣﺔ‬ ‫اﺑﻌﺎد )اﻟﺷﻛل او‬ (‫اﻟﻣﺟﺳم‬ ‫ﺗﻣﺛﯾل اﻟﺑﯾﺎﻧﺎت‬ ‫ﻛﺳر ﻋﺷري‬

decimal form E

Equality

F

factor first multiple fraction

H

highest common factor (H.C.F) hundred-million digit horizontally

I

L

line graph length million milliard multiplication operation multiple measure of

‫ﺗﺳﺎوي‬ ‫ﻋﺎﻣل‬ ‫اﻟﻣﺿﺎﻋف اﻻول‬ ‫ﻛﺳر‬ ‫اﻟﻌﺎﻣل اﻟﻣﺷﺗرك‬ ‫اﻷﻋﻠﻰ‬ ‫رﻗم ﻣﺋﺎت اﻟﻣﻼﯾﯾن‬

infinite included angle improper fraction lowest common multiple long division

‫ﻓﻲ ﺻورة اﻟﻛﺳر‬ ‫اﻟﻌﺷري‬

M

‫اﻓﻘﯾﺎ‬ ‫ﻏﯾر ﻣﺣدد‬ ‫اﻟزاوﯾﺔ اﻟﻣﺣﺻورة‬ ‫ﻛﺳر ﻏﯾر ﻓﻌﻠﻲ‬ ‫اﻟﻣﺿﺎﻋف اﻟﻣﺷﺗرك‬ ‫اﻷدﻧﻰ‬ ‫اﻟﻘﺳﻣﺔ اﻟﻣطوﻟﺔ‬ ‫رﺳم ﺧط ﺑﺎﺳﺗﺧدام‬ ‫اﻟﯾد‬ ‫طول‬ ‫ﻣﻠﯾون‬ ‫ﻣﻠﯾﺎر‬ ‫ﻋﻣﻠﯾﺔ اﻟﺿرب‬

mixed number N

‫ﻣﺿﺎﻋف‬ ‫ﻗﯾﺎس ال‬ ‫ﻋدد وﻛﺳر )ﻋﺷري‬ (‫او اﻋﺗﯾﺎدي‬

numeral decimals place value prime number perimeter proper fraction remainder reduce side length simplify simplest form subtraction trillion

P

R S

T

3-digit number 2- third 3-fifth top 3thousandth total cost unit-million digit vertically

U V W

‫اﻷﻋداد اﻟﻌﺷرﯾﺔ‬ ‫اﻟﻘﯾﻣﺔ اﻟﻣﻛﺎﻧﯾﺔ ﻟﻠرﻗم‬ ‫اﻟﻌدد اﻻوﻟﻲ‬ ‫ﻣﺣﯾط‬ ‫ﻛﺳر ﻓﻌﻠﻲ‬ ‫ﺑﺎﻗﻲ‬ ‫اﺧﺗزل او ﺑﺳط‬ ‫طول اﻟﺿﻠﻊ‬ ‫ﺑﺳط‬ ‫اﺑﺳط ﺻورة‬ ‫ﻋﻣﻠﯾﺔ اﻟطرح‬ ‫ﺗرﯾﻠﯾون‬ ‫ﻋدد ﻣﻛون ﻣن ﺛﻼث‬ ‫ارﻗﺎم‬ ‫ﺛﻠﺛﯾن‬ ‫ﺛﻼث اﺧﻣﺎس‬ ‫ اﻋﻠﻰ‬/ ‫ﻗﻣﺔ‬ ‫ﺛﻼﺛﺔ ﻣن اﻷﻟف‬ ‫ﺗﻛﻠﻔﺔ ﻛﻠﯾﺔ‬ ‫اﺣﺎد اﻟﻣﻼﯾﯾن‬ ‫راﺳﯾﺎ‬

width zero multiple

Z

‫ﻋرش اﻟﺷﻛل‬ ‫اﻟﻣﺿﺎﻋف اﻟﺻﻔري‬

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