Chapter 3 Fractions

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Teacher’s Guide Sheet 3.1 Concept: Fractions Learning Outcomes: 1. Describe fractions as parts of a whole 2. Represent fractions with diagrams Teaching Aids: Biscuits, cakes, different sizes and shapes of paper, and strips of paper

Notes: 1. This lesson consists of three activities. 2. From activity (1) and (2), pupils will understand the concept of

fractions. 3. Pupils understanding of the concept of fractions will be tested in

Worksheet 3.1.

Activity 1

Approach Activity

Aim Pupils can represent fractions using papers.

Steps 1. Ask pupils to fold papers to represent: 21 , 4

1 , 81

2. Things to take note: All parts: (a) must be from one object. (b) must be smaller than the original object. (c) must be the same size.

3. Challenge the pupils to fold papers to represent: 31 , 5

1 , 61

4. Help show pupils the steps if needed. Folding Instructions 1. Fold the strip of paper into 3 equal parts.

2

2. Fold the strip of paper into 5 equal parts.

Activity 2

Approach Discussions

Aim 1. Pupils name and write the fractions given. 2. Pupils state the numerator and denominator of the fraction.

Steps 1. Pupils name fractions of the folded strips of paper.

2. Pupils state all the fractions that are drawn by the teacher like 32 , 4

3 .

3. Introduces the term ‘fractions’ by using 21 as an example.

Emphasise: The top number of the fraction is called the numerator. The bottom number is called the denominator.

Activity 3

Approach Individual exercise

Aim Pupils can write fractions

Steps 1. Pupils are given 10 minutes to answer questions in Worksheet 3.1. 2. Guide the pupils if needed. 3. Discuss Worksheet 3.1.

3

Worksheet 3.1 Write the fraction of the shaded part given in the space provided. 1. 2.

3. 4.

5. 6.

7. 8.

9. 10.

4

11. 12.

13.

5

Teacher’s Guide Sheet 3.2 Concept: Fractions Learning Outcomes: Write fractions of given diagrams Teaching Aids: Strips of paper, fractions flash card and fractions kit

Notes: 1. This lesson contains two activities. 2. In Activity 1, pupils will be able to understand how to represent the

number ‘1’ in fraction form through concrete materials. 3. Pupils will be able to represent fractions with diagrams in Activity 2. 4. Pupils do the exercise in Worksheet 3.2.

Activity 1

Approach Discussions and exercise

Aim 1. Pupils can rewrite the number ‘1’ in fraction form.

2. Pupils can write fractions for given diagrams.

Steps 1. Prepare strips of paper that represent 1 - 3 pieces

21 - 5 pieces

31 - 5 pieces

41 - 5 pieces

2. Pupils match two pieces of 21 with one strip of 1 unit.

Example:

6

3. Repeat (2) with the 31 and 4

1 strips.

Example:

4. Conclusions:

1 = 2 × ( 21 ) = 2

2 , 1 = 3 × ( 31 ) = 3

3 , 1 = 4 × ( 41 ) = 4

4

5. Pupils shade the part of the diagram that represents the following fractions :

41 , 6

1 and 52

6. Pupils answer question 1 in Worksheet 3.2. 7. Pupils draw the diagrams on the whiteboard. 8. Check pupils’ answer.

Activity 2

Approach Discussions and exercise

Aim Represent fractions with diagrams.

Steps 1. Ask pupils to draw any diagram to represent number 1.

2. Show the fraction flash card and ask pupils to shade the diagram to represent the fraction shown.

3. Ask 2 or 3 pupils to show their answers on the blackboard.

4. Repeat with for fraction flash cards 32 and 5

3 .

5. Pupils answer question 2 in Worksheet 3.2.

7

Worksheet 3.2 1. Shade the diagram below to represent the fractions given. (a) (b)

(c) (d)

(e) (f)

(g) (h)

8

(i) (j)

(k) (l)

2. Draw diagrams to represent the fractions given.

(a) 44 (b) 2

1

(c) 52 (d) 4

3

(e) 32 (f) 6

4

9

Teacher’s Guide Sheet 3.3 Concept: Fractions Learning Outcomes: To determine the position of a fraction on a number line. Teaching Aids: Fraction flash cards and number line chart.

Notes: 1. This lesson contains one activity only. 2. Help pupils to recall how to represent whole numbers on a number

line, and extend to the lesson on fractions. 3. A game will be introduced to test the pupils’ skills on arranging

fractions in order. 4. Pupils answer the questions on Worksheet 3.3.

Activity 1

Approach Demonstration and practice

Aim 1. Write fractions on a number line.

2. Mark the position of fractions on a number line.

Steps 1. Do revision to represent whole numbers on a number line. (a) Teacher shows the steps on how to draw a number line.

10

Pupils complete the box given

2. Explain how to label fractions on a number line. (a) 1

(b) 21

(c) 31

(d) 51

(e) 81

(f) 101

11

3. Explain the position of fractions on a number line for the following fractions: 5

3 , 32 , 8

5 .

4. Each pupil will be given a fraction card. When the teacher mentions any denominator, pupils who have that

number will come forward and arrange themselves in ascending order, like the examples below.

5. Pupils answer questions in Worksheet 3.3

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Worksheet 3.3 1. Fill in the blanks. (a)

(b)

(c)

2. Label the fractions given on the number lines. (a)

(b)

13

3. A Boeing 747 departs from Kuala Lumpur Interntional Airport. Write the missing fractions.

4. An ant climbs 10

1 of the height of the wall. Label the position of the ant on the number line.

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Teacher’s Guide Sheet 3.4 Concept: Equivalent fractions Learning Outcomes: 1. Find equivalent fractions for a given fraction.

2. Determine whether two given fractions are equivalent.

Teaching Aids: OHP, manila card, fractions kit

Notes: 1. This lesson contains two activities. 2. In Activity 1, the concept of equivalent fractions will be expanded

using diagrams. 3. Then, a method to find the equivalent fractions will be introduced in

Activity 2.

Activity 1

Approach Demonstration, discussions and exercises

Aim Finding equivalent fractions for a given fraction

Steps 1. Show some examples of equivalent fractions for 2

1 (see explanation note 1), using fractions kit. Compare the shaded parts.

2. Pupils answer questions in Worksheet 3.4.

Activity 2

Approach Explanations and exercises

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Aim Finding equivalent fractions by multiplying the numerator and the denominator with the same number.

Steps 1. Revise (a) multiplication table

(b) what is the value of 22 , 3

3 , 44 , 5

5 , etc.

2. Show how to find equivalent fractions using the following diagrams.

3. Introduce the algorithm method to find equivalent fractions.

52 = 5

2 × 1 = 52 × 2

2 = 2 52 2

×× = 10

4


Explanation Note 1 (a) Prepare a transparency. Draw a circle and colour 2

1 the circle.

(b) Prepare 3 pieces of transparencies, but shaded differently: 42 , 6

3 , 84 .

16

(c) Place the transparency with 42 on top of the transparency with 2

1 .

Ask the pupils if the coloured parts are the same size. (d) Formulate the expression

42 = 2

1

(e) Repeat steps (b) to (d) with other fractions like 63 and 8

4 .

17

Worksheet 3.4 1. Find the equivalent fractions and shade the diagrams to represent each fraction: (a) (b) (c) 2. Shade the diagrams below and state whether the following pairs of fractions are equivalent. (a)

18

(b)

19

Worksheet 3.5 1. Multiply the numerator and denominator of the fraction 5

2 with the given number.

Number Result of Multiplication

2 2 52 2 ×× = 10

4

3 3 53 2 ×× =

4

5

7

8

10

11

From the table, we can make a conclusion that,

52 = 10

4 = _____ = _____ = _____ = _____ = _____ = _____ = _____

All these are equivalent fractions. 2. Complete the blanks.

20

3. Determine whether the following pairs of fractions are equivalent.

(a) 53 , 15

10

(b) 129 , 4

3

(c) 64 , 18

8

(d) 168 , 4

2

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Teacher’s Guide Sheet 3.5 Concept: Equivalent fractions Learning Outcomes: 1. Compare the values of two given fractions.

2. Arrange fractions in order.

Teaching Aids: Fractions flash cards, chart

Notes: 1. This lesson consists of one activity only for one period of about 40

minutes. 2. Firstly, compare the two fractions that have a common denominator

using the diagrams. 3. Then ask pupils compare the two fractions using equivalent

fractions.

Activity 1

Approach Discussion, quiz and exercise.

Aim To compare the values of two given fractions.

Steps 1. Show diagrams of fractions with these common denominators :

(a) 62 and 6

3

(b) 31 and 3

2

(c) 53 and 5

2

Pupils will compare and identify which fraction has the greater value. 2. Explain how to compare two fractions with different denominators :

(a) 21 , 4

3 (the second denominator is a multiple of the first denominator)

(b) 21 , 3

1 (the second denominator is not a multiple of the first

denominator) (Refer to explanation notes) 3. Quiz using flash cards State the pair of fractions that have

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(a) common denominators (b) different denominators Ask pupils which fraction has the greater value. 4. Pupils do the exercise in Worksheet 3.6.

Explanation Notes 1. Teacher must take note, if the fractions do not have common denominators, find a common

denominator using equivalent fractions.

2. Place the flash cards and on the blackboard. Question (a) Which fraction has the greater value? (Take note: must find out a common denominator) What is the LCM of 2 and 3?

(b) Ask 2 pupils to change 21 and 3

1 to other equivalent fractions with the denominator 6, and place the answer on the blackboard using flash cards.

Question: Which fraction has the greater value? (c) Repeat the activity with other pairs of fractions.

3. Give more examples of fractions with the numerator 1 such as 21 and 3

1 , 51 and 8

1 . Guide pupils to conclude that, for fractions with number 1 as a numerator, the fraction with the largest denominator has the lowest value.

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Worksheet 3.6 1. State the denominator of the following fractions.

Fractions Denominator

85

92

1511

9340

229

2. Compare the following fractions and write the smallest and largest fractions in the space

provided.

Fractions Smallest fraction Largest fraction

(a) 53 , 5

4

(b) 74 , 7

1

(c) 94 , 9

2 , 96

(d) 1510 , 15

9 , 156

(e) 83 , 8

5 , 81 , 8

6

(f) 128 , 12

6 , 123 ,

1210

(g) 3310 , 33

12 , 3321 ,

338 , 33

9

(h) 206 , 20

9 , 2013 ,

203 , 20

16

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3. Compare the following fractions and write the smallest or largest fractions in the space provided.

Fractions LCM Denominator

Change into common denominator fraction

Smallest Fraction

Largest Fraction

Ex. 83 and 4

1 8 83 and 8

2 41 8

3

(a) 32 and 6

5

(b) 51 and 4

1

(c) 92 and 6

2

(d) 85 and 7

4

(e) 87 and 6

5

(f) 32 and 9

5

(g) 114 and 22

7

(h) 97 and 5

4

4. Circle the fraction with the greater value.

(a) 53 and 10

7

(b) 43 and 6

5

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Teacher’s Guide Sheet 3.6 Concept: Equivalent fractions Learning Outcomes: Simplify fractions to the lowest terms. Notes: 1. This lesson consists of 1 activity only. 2. The lowest fraction can be found using the division method.

Activity 1

Approach Explanations and exercises

Aim State the fractions in lowest terms.

Steps 1. Show how to find the lowest terms using the inverse process of finding equivalent fractions.

(a) To find equivalent fractions:

21 = 5 2

5 1 ×× = 10

5

(b) State in the lowest term:

105 = 5 10

5 5 ÷÷ = 2

1

2. Introduce the method of dividing the numerator and denominator with a common factor.

128 = 2 12

2 8 ÷÷ = 6

4 (common factor of 8 and 12 is 2)

64 = 2 6

2 4 ÷÷ = 3

2 (common factor of 4 and 6 is 2)

3. Then, use another method to simplify a fraction to the lowest term, divide both the numerator and denominator by their HCF.

128 = 4 12

4 8 ÷÷ = 3

2 (HCF of 8 and 12 is 4)

or

128 = 12

8 = 32

4. Pupils do the exercise in Worksheet 3.7. 5. For question 3 in Worksheet 3.7, pupils can use both methods, either

using HCF or repeated division.

2 3

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Worksheet 3.7 1. Fill in the blanks.

No. Fractions State all the common factors of both the numerator and denominator

Example 3624 2, 3, 4, 6, 12

(a) 1612

(b) 4515

(c) 3025

(d) 4818

(e) 276

2. Fill in the blanks and simplify the following fractions to the lowest terms.

Fractions Determine HCF of the numerator and denominator

Divide both numerator and denominator with HCF

Fractions in the lowest terms

Ex. 1812

6 186 12 ÷÷ = 3

2 32

(a) 108

(b) 158

(c) 249

27

Fractions Determine HCF of the numerator and denominator

Divide both numerator and denominator with HCF

Fractions in the lowest terms

(d) 3525

3. Change each of the following fractions into the lowest terms.

(a) 153 = (b) 20

8 =

(c) 2114 = (d) 30

18 =

(e) 156 = (f) 28

12 =

28

Teacher’s Guide Sheets 3.7 Concept: Mixed Numbers Learning Outcomes: 1. Represent mixed numbers with diagrams

2. Write mixed numbers based on given diagrams. 3. Compare and order mixed numbers on number lines.

Teaching Aids: Suitable concrete materials

Notes: 1. This lesson consists of one activity only. 2. Concrete materials, diagrams and number lines are used to explain

the concept of mixed numbers.

Activity 1

Approach Discussions and individual exercise

Aim 1. Write the mixed numbers represented by the diagrams.

2. Represent mixed numbers with diagrams. 3. Label the positions of mixed numbers on a number line.

Steps 1. Introduce the concept of mixed numbers using concrete materials such as pizza, biscuits and cakes.

2. Explain using diagrams:

Discuss with pupils other examples such as 4 3

1 , 2 61 , 2 5

2 .

3. Pupil activity: Ask pupils to draw a figure to represent the mixed numbers given.

4. Teacher activity: Pupils label the given number lines. Prepare the given number lines with:

(i) whole numbers only (ii) fractions only (iii) mixed numbers

29

5. Pupils mark the given mixed numbers on a number line. 6. Pupils answer Worksheet 3.8.

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Worksheet 3.8 1. State the following shaded parts.

Figure Answer

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

2. Shade the diagrams below to represent the mixed numbers. (a)

(b)

(c)

31

3. Draw a diagram to represent the following mixed numbers.

(a) 3 21

(b) 1 61

(c) 4 43

(d) 7 52

(e) 2 31

4. On the following number lines, write the mixed numbers for A. (a)

(b)

32

(c)

5. On the following number lines, label and write the mixed number given. (a)

(b)

(c)

(d)

6. Label the following mixed numbers on number lines.

Mixed numbers Draw and label on number lines

1 43

2 31

7. Didi cycles to school. After cycling for about 5 kilometres, the tyre punctures. He then has to

walk about 21 kilometre to school. What is the distance between Didi’s house and his

school?

33

8. In a marathon competition, when Ali was at the 9th kilometre, Ahmad was 41 kilometres

behind him. Label and show Ahmad’s position on a number line.

34

Teacher’s Guide Sheet 3.8 Concept: Proper fractions and improper fractions. Learning Outcomes: 1. Recognize proper and improper fractions from given fractions. 2. Change mixed numbers into improper fractions. Teaching Aids: Chart

Notes: 1. This lesson consists of one activity. 2. In this activity, a diagram is used to expand the concept of proper

fractions, improper fractions and mixed numbers. 3. The steps to change mixed numbers into improper fractions are also

shown.

Activity 1

Approach Discussions, group activity, and individual exercise.

Aim 1. Pupils can recognize proper and improper fractions.

2. Change whole numbers and mixed numbers into improper fractions.

Steps 1. Introduce the concept of proper and improper fractions using the following diagrams:

(a) (b)

(c)

35

2. Repeat step (1) using the following number line:

3. Group activity: Each group will be given cards with few proper and

improper fractions and pupils in the group will classify the fractions. At the end of the activity, a representative from each group will make a report.

4. Use diagrams to explain the following:

1 = 33

Repeat with other whole numbers like

2 = 24 and others.

Test your pupils’ knowledge orally with these questions:

(a) 2 = 8

(b) 4 = 3

5. Use the diagrams to explain:

6. Without using diagrams, explain the following examples:

(a) 3 = 13 = 6 1

6 3×× = 6

18

(b) 2 31 = 2 + 3

1

= 3 13 2

×× + 3

1

= 36 + 3

1

= 37

The following algorithm can be introduced after the pupils have understood Step 6 (b).

Example: 2 31 = 3

1 3) (2 +×

= 31 6 +

= 37

36

Test pupils’ understanding by using the following examples.

(a) 2 = 4

(b) 3 43 = 4

(c) 4 21 =

7. Pupils do exercise in Worksheet 3.9.

37

Worksheet 3.9 1. Classify each of the following fractions.

21 , 9

11 , 517 , 7

3 , 315 , 6

6 , 119 , 11

17 , 103 , 3

8

2. Change each of the following numbers into improper fractions. (a) 3 = 9

(b) 6 = 5

(c) 9 = 4

3. Change each of the following mixed numbers into improper fractions.

(a) 3 41 = (b) 5 10

3 =

(c) 7 75 (d) 10 5

3 =

(e) 8 65 = (f) 9 8

3 =

38

Teacher’s Guide Sheet 3.9 Concept: Proper and improper fractions Learning Outcomes: Change improper fractions into mixed numbers. Teaching Aids: Chart

Notes: 1. This lesson involves one activity only. 2. The method of changing improper fractions into mixed numbers will

be explained using diagrams first. 3. Exercises using the calculation method are given in Worksheet 3.10.

Activity 1

Approach Discussions and exercises.

Aim 1. Change improper fractions into whole or mixed numbers. 2. Change improper fractions into equivalent fractions.

Steps 1. Discuss using diagrams of improper fractions and mixed numbers.

4

9 = 48 + 4

1

= 2 + 41

= 2 41

2. Discuss the method of changing improper fractions into whole or mixed numbers.

Example: (a)

39

(b)

3. Discuss the steps of changing fractions into equivalent fractions. Example:

(a) 21 = 2 2

2 1×× = 4

2

(b) 26 = 3 2

3 6×× = 6

18

(c) 38 = 4 3

4 8×× = 12

32

(d) 1824 = 3 18

3 24÷÷ = 6

8

4. Evaluate pupils’ understanding using the following examples:

56 = 15

= 30

38 = 27

=


40

Worksheet 3.10 1. Write the value of the missing numbers on the number lines in the form of (a) improper fractions and (b) mixed numbers.

Number lines Improper fractions

Mixed numbers

(a)

(b)

(c)

(d)

2. Change each of the following into whole or mixed numbers.

(a) 227 (b) 7

30

(c) 835 (d) 4

23

(e) 981 (f) 5

62

3. Complete the following to find equivalent fractions.

(a) 21 = 6

= 5

41

(b) 23 = 6

= 21

(c) 35 = 35 = 9

(d) 418 = 9 = 8

(e) 1535 = 7 = 24

4. Find two equivalent fractions for each of the following:

(a) 32 = =

(b) 614 = =

(c) 45 = =

(d) 710 = =

5. Determine whether the following pairs of fractions are equivalent.

(a) 21 , 18

9

42

(b) 35 , 12

15

(c) 1421 , 7

3

(d) 58 , 25

40

43

Test 3.1 Name: _____________________________________________________________

Class: _____________________________________________________________

1. Name the fractions for the shaded parts in the space provided.

2. Shade the diagram below to represent the fraction 83 .

3. Complete the number line.

4. Mark “ ” on the diagram which has the same value as the fraction shown in the diagram on

the left.

44

5. Give two equivalent fractions of 31 .

31 = =

6. Place a tick “ ” into the box which is beside the fraction with the greater value.

(a) 43 (b) 5

2

87 3

1

7. Change the following fractions into the lowest terms.

(a) 159 =

(b) 7230 =

8. State the value of A on the following number line.

9. Label and mark 3 43 on the number line.

10. Fill in the missing numbers in the following boxes. (a) 5 = 7

(b) 2 81 = 8

(c) 6 31 = 19

45

11. Change the following numbers into improper fractions. (a) 2 =

(b) 4 52 =

12. Change each of the following improper fractions into whole numbers or mixed numbers.

(a) 832 =

(b) 649 =

13. Match the fraction on the left with its equivalent fractions on the right.

14. Two cakes are divided equally among six pupils. What fraction of the cakes does each pupil

get? Answer: ______________ 15. A class has 30 pupils. 18 of them are girls. Write the fraction that represents the number of

girls in the class. Answer: ______________

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Teacher’s Guide Sheet 3.10 Concept: Addition of fractions Learning Outcomes: Perform addition involving: (a) fractions with common denominators. (b) fractions with different denominators. (c) whole numbers and fractions. Teaching Aids: OHP, transparency, manila card and fractions chart kit.

Notes: 1. This lesson consists of one activity. 2. The lesson is divided into two parts. In the first part teacher gives

the explanation and in the second part pupils work in groups and answer questions in the worksheet.

Activity 1

Approach Group activity and exercises

Aim 1. Perform addition involving fractions with common denominators.

2. Perform addition involving fractions with different denominators. 3. Perform additions with whole numbers and fractions.

Steps 1. Show the diagrams and explain how to add two fractions with the same denominators.

Example: 2. Pupils find the sum of the fractions by shading the diagrams.

47

Example: 3. Explain the addition of fractions with different denominators. Example:

Repeat with other examples:

(a) 31 + 9

1

(b) 41 + 8

3

4. Group activity: Pupils answer the questions in Worksheet 3.11 in groups. 5. Conclusion: Addition of fractions, For fractions with different denominators, change the fractions into their

equivalent forms with common denominators. Then add their numerators. 6. Use the following example and give the answer in the simplest form:

41 + 12

5 = 123 + 12

5

= 128

= 32

7. Continue with the other examples.

(a) 2 + 52 = 2 5

2

(b) 71 + 4 = 4 7

1

8. Pupils answer the questions in Worksheet 3.12.

48

Worksheet 3.11 1. Find the sum of the fractions by shading the diagrams. (a)

(b)

(c)

(d)

2. In the diagrams below, shade and label the given fractions and solve the questions. (a)

49

(b)

(c)

(d)

50

Worksheet 3.12 1. Solve the questions below and state your answers in the simplest form.

(a) 61 + 6

4 (b) 83 + 8

1

(c) 72 + 7

4 (d) 91 + 9

3

(e) 103 + 10

5 (f) 123 + 12

4

(g) 95 + 9

1 (h) 41 + 4

3

(i) 31 + 3

2 (j) 126 + 12

3

(k) 121 + 12

3 + 125 (l) 10

2 + 103 + 10

3

(m) 91 + 9

2 + 93 (n) 8

1 + 83 + 8

2

2. (a) 21 + 6

1 = (b) 32 + 6

1 =

(c) 52 + 10

3 = (d) 101 + 20

7 =

51

3. (a) 3 + 53 = (b) 2 + 9

2 =

(c) 32 + 5 = (d) 1 + 11

6 =

(e) 73 + 4 =

52

Teacher’s Guide Sheet 3.11 Concept: Addition of fractions Learning Outcomes: Perform addition involving: (a) fractions and mixed numbers (b) mixed numbers Teaching Aids: Strips of paper

Notes: 1. This lesson consists of one activity. 2. At the beginning of the lesson, the concept of addition of fractions

can be introduced to pupils using concrete examples (folded strips of paper).

3. Revise on how to find LCM before teaching the addition of fractions and mixed numbers.

Activity 1

Approach Demonstration, discussions and exercises

Aim 1. Addition of fractions using the LCM method.

2. Perform addition involving mixed numbers.

Steps 1. Show addition of fractions by using folded paper.(Refer to Explanation Notes 1)

2. Relate the process of folding paper with the calculation method.

53

21 + 5

1 = ( 21 × 5

5 ) + ( 51 × 2

2 )

= 105 + 10

2

= 107

3. Show addition of fractions by using the LCM method.

(a) 61 + 8

3 = 244 + 24

9

= 2413

(b) 51 + 8

1 + 125 = 120

24 + 12015 + 120

50

= 12089

4. Pupils answer the questions in Worksheet 3.13. 5. Explain these examples.

(a) 2 72 + 3 2

1 = 2 + 72 + 3 + 2

1

= (2 + 3) + 72 + 2

1

= 5 + ( 144 + 14

7 )

= 5 + 1411

= 5 1411

(b) 211 + 4

21 = 23 + 4

9

= 46 + 4

9

= 415

= 3 43


54

Explanation Notes 1 Paper can be folded in this way. 1. Prepare 2 pieces of paper.

2. Fold the first paper into two equal parts. Shade 21 of the paper.

3. Next, fold each half of the paper into 5 equal parts. (Refer to Teacher’s Guide Sheet 3.1) 4. Now open the folded paper.

5. Fold the second paper into 5 equal parts. (Refer to Teacher’s Guide Sheet 3.1). Shade 51

of the paper.

6. Next, fold each folded section into two equal parts. 7. Now open the folded paper.

55

Worksheet 3.13 (1 period) 1. 3

1 + 51 = 15

+ 15 2. 2

1 + 61 = 6

+ 6

= =

3. 21 + 10

3 = 4. 41 + 5

2 =

= =

5. 31 + 12

5

6. 31 + 4

1 + 51 LCM of 3, 4 and 5:

7. 21 + 5

2 + 71 =

8. 31 + 8

3 + 61

56

Worksheet 3.14 (1 period) 1. 3 + 7

2 = 2. 5 + 107 =

3. 2 21 + 3 4

1 = 4. 3 31 + 2 6

1 =

5. 5 83 + 4 2

1 = 6. 10 74 + 3 3

2 =

7. 1 41 + 2 3

1 + 1 125 =

8. 1 51 + 3 10

3 + 2 154 =

9. 2 31 + 1 6

5 + 3 127 =

10. 1 21 + 2 4

1 + 2 83 =

57

Teacher’s Guide Sheet 3.12 Concept: Addition of fractions Learning Outcome: Solve problems involving addition of fractions.

Note: Guide pupils in using Polya’s 4 steps in solving problems.

Activity 1

Approach Discussion

Aim Solve problems involving operation of addition of fractions

Steps 1. Explain using a problem on how to add fractions. Example:

En. Bakar spends his salary as follows: 51 for house rental, 3

1 for food

and 101 for his children’s school fees. How many parts of his salary are

spent for the three purposes? Suggested solution:

Expenses = 51 + 3

1 + 101

= 303 10 6 ++

= 3019

2. Guide pupils to solve a problem using Polya method. Solve another problem through “Questions & Answers” (Q&A) and ask a

pupil to show the solution on the blackboard. Example:

Ismail spends 21 hour to do his homework, 1 3

1 hours to study and

1 41 hours to watch television. Find the total time used to do all the

activities. 3. Pupils answer Worksheet 3.15.

58

Worksheet 3.15 1. To reach his school, Bala walks about 3

2 km from his house and then travels by bus for

3 21 km. What is the distance between Bala’s house and his school?

2. Rokiah bought 2kg of watermelon, 1 21 kg of papaya and 5

4 kg of mangoes. What is the total mass of the fruits?

3. Ramesh arranges 3 pieces of wood with lengths 1 21 m, 2 3

2 m and 1 43 m one after the

other to form a straight line. What is the length of the straight line?

59

Teacher’s Guide Sheet 3.13 Concept: Subtraction of fractions Learning Outcomes: Perform subtraction involving: (a) fractions with common denominators (b) whole numbers and fractions Teaching Aids: Strips of paper

Notes: 1. In this lesson, we suggest you use the concept of subtraction of

fractions as the difference between fractions. However, the concept of subtraction of fractions as finding the remainder can be used.

2. In this lesson, strips of paper will be used to introduce the concept of subtraction of fractions before explaining the calculation method.

Activity 1

Approach Demonstration

Aim 1. Find the difference between 2 fractions with common denominators.

2. Find the difference between whole numbers and proper fractions.

Steps 1. Guide pupils to find the difference between 2 fractions by comparing fractions using strips of folded paper.

(Refer to explanation notes) 2. Repeat with several examples. 3. Pupils answer questions in Worksheet 3.16. 4. Teacher guides pupils in finding the difference between whole numbers

and proper fractions using strips of folded paper.

60

5. Pupils answer these questions using mental calculations.

(a) 1 – 43 = (b) 1 – 8

5 =

(c) 1 – 74 = (d) 1 – 9

7 =

6. Teacher uses another example to conclude the lesson.

2 – 31 = 3

6 – 31

= 35


Explanation notes Another method of solving subtractions between 2 fractions involves finding the remainder as shown below.

Example: 54 – 5

1 = ?

61

Worksheet 3.16 Solve:

1. 75 – 7

3 = 2. 85 – 8

3 =

3. 139 – 13

5 = 4. 1512 – 15

4 =

5. 107 – 10

4 = 6. 74 – 7

2 =

7. 87 – 8

2 = 8. 159 – 15

3 =

9. 178 –

175

62

Worksheet 3.17 1. Fill in the blanks.

(a) 33 – 3

1 = 3 (b) 1 – 5

2 = – 52

= 5

(c) – 73 = 7

7 – 73 (d) 1 – 6

2 =

=

(e) 1 – 83 =

2. Solve

(a) 1 – 43 (b) 2 – 5

3

(c) 3 – 72 (d) 4 – 8

3

(e) 5 – 109

3. I have 3 cakes, if 85 of a cake was eaten, how many cakes are still left?

63

Teacher’s Guide Sheet 3.14 Concept: Subtraction of fractions Learning Outcome: Perform subtraction involving fractions with different denominators. Teaching Aids: Strips of paper

Notes: 1. This lesson contains three activities. 2. In the first activity use the figure to explain the subtraction method

.Start from figure state, shows pupils calculations method in subtractions of fractions in second activity.

Further the calculation method to subtract mixed numbers in the third activity.

Activity 1


Aim Subtraction fractions by writing the fractions in their equivalent forms with

common denominators including the use of LCM

Steps 1. Revise the concept of equivalent fractions using diagrams. Example: Complete the equivalent fractions below. (a)

(b)

64

(c)

2. Explain subtraction of fractions using diagrams.

21 – 4

1 =

Difference of the shaded regions = 2

1 – 41

= 42 – 4

1

= 41

Discuss a few examples without using diagrams. 3. Pupils answer Worksheet 3.18.

Activity 2

Approach Discussion

Aim Subtract one fraction from another fraction by finding the LCM of the

denominators.

Steps 1. Teacher use LCM method to show subtraction of fractions.

(a) 21 – 3

1 = 63 – 6

2

= 61

(b) 65 – 8

3 = 2420 – 24

9

= 2411

(c) Repeat with other examples. 2. Pupils answer Worksheet 3.19.

65

Activity 3

Approach Discussion

Aim Subtract a:

(a) whole number from a mixed number (b) fraction from a mixed number (c) mixed number from a whole number (d) mixed number from a mixed number

Steps 1. Show the subtractions below:

(a) 3 32 – 1 =

(b) 3 43 – 4

1 =

(c) 4 21 – 4

3 =

(d) 5 – 3 31 =

(e) 4 43 – 2 4

1 =

(f) 5 31 – 2 3

2 =

(g) 8 51 – 4 10

1 =

(h) 10 31 – 3 2

1 =

Repeat with other examples. 2. Pupils answer Worksheet 3.20.

66

Worksheet 3.18 Solve 1.

2.

3.

4.

5.

67

Worksheet 3.19 Solve

1. 31 – 5

1 = 2. 43 – 5

2 =

3. 97 – 6

1 = 4. 65 – 15

2 =

5. 87 – 12

1 =

68

Worksheet 3.20 Find the value of each of the following and write your answer in the lowest form.

1. (a) 2 21 – 1 = (b) 8 6

5 – 4 =

(c) 12 91 – 7 =

2. (a) 3 83 – 8

1 = (b) 9 52 – 10

1 =

(c) 5 41 – 4

3 =

3. (a) 6 – 3 95 = (b) 5 – 2 2

1 =

(c) 8 – 4 32 =

69

4. (a) 1 54 – 1 5

2 = (b) 2 87 – 1 8

3 =

(c) 3 75 – 1 7

2 =

5. (a) 3 54 – 1 10

3 = (b) 3 54 – 2 3

2 =

(c) 7 43 – 4 6

1 = (d) 6 41 – 2 4

3 =

(e) 4 51 – 2 3

1 =

70

Teacher’s Guide Sheet 3.15 Concept: Subtraction of fractions Learning Outcome: Solve problems involving combined operations of addition and subtraction of fractions. Teaching Aids: Questions card

Notes: 1. This lesson contains one activity. 2. Pupils are encouraged to solve the questions actively. The activity

promotes discussions between teacher and pupils, team work and individual exercise.

3. Teacher guide pupils in using the four-step problem solving procedure.

Activity 1

Approach Discussions, individual exercise and group activity.

Aim Solve problems involving subtraction of fractions.

Steps 1. Pose problems using daily situations. Example:

Ali’s house is 5 km from the school. On the way home from school, he stopped at a shop which is 3 2

1 km from school. How far does Ali has to walk to reach his house?

71

2. Conduct a questioning and answering session where applying the Polya method.

3. Guide pupils to check their answers using the addition operation. 4. Group activity Give each group a different question cards. At the end of the activity,

representatives from each group will explain their answers on the blackboard.

5. Pupils answer Worksheet 3.21.

72

Worksheet 3.21

1. Pn. Mariam bought a container filled with 43 litre of orange juice. She drank 5

1 litre of the juice. How many litres of orange juice is left?

2. En. Sudir picked 7 21 kg rambutan. He sold 4 4

3 kg of the rambutan. How many kilograms rambutan are not sold yet?

3. The area of En. Hashim’s orchard is about 3 51 hectares. 2 10

3 hectares are used to plant fruits and the rest are planted with vegetables. What is the area used to plant vegetables?

4. Mr. Chan spends 85 of his salary. What fraction of his salary is left?

73

Teacher’s Guide Sheet 3.16 Concept: Subtractions of fractions Learning Outcomes: Perform addition and subtraction involves:

(i) three fractions with common denominators; (ii) three fractions by using the LCM of the denominators; (iii) three mixed numbers.

Teaching Aids: Fraction cards with denominators 10, 15 and others, 3 fraction cubes.

Notes: 1. This lesson contains 3 activities. 2. All activities been plan to encourage pupils to learn actively and

enjoyable. Pupils are encouraged to build their own questions, solve the questions and answer the worksheet individually.

Activity 1

Approach Demonstration, activities and exercises

Aim Add and subtract 3 fractions by using their LCM.

Steps 1. Ask pupils to select 3 fractions cards with same denominator from a beg. Then, ask pupils to write the fractions on the blackboard, while teacher determines the operations to be carried out. Pupils solve the questions.

2. Repeat for other (a) pupils; (b) fractions cards with other denominators. 3. Pupils answer Worksheet 3.22.

74

Activity 2

Approach Games

Aim Add and subtract 3 fractions with common denominator.

Steps 1. Play a game with pupils using the fractions cubes. (Refer to Explanation notes.)

Example:

32 + 8

3 – 125

= 2416 + 24

9 – 2410

= 2410 - 9 16 +

= 2415

= 85

2. Repeat with other pupils. 3. Pupils answer Worksheet 3.23.

Activity 3


Aim Add and subtract 3 mixed numbers.

Steps 1. Give several examples.

(a) 3 41 – 1 4

3 + 2 41 = 4

13 – 47 + 4

9

= 415

= 3 43

(b) 4 61 – 3 6

5 + 2 31 = 6

25 – 623 + 3

7

75

= 625 – 6

23 + 614

= 616

= 2 64

= 2 32

Emphasise that calculations involving addition and subtraction is done from left to right.


Explanation notes Games with fractions cube 1. Prepare three cubes of different colours. (a) White – to represent the first fractions (b) Blue – to represent the addition operation (c) Red – to represent the subtraction operation 2. Write fractions on each surface of the cube. 3. Make sure that

so that we won’t get a negative number. Suggestions:

White cube: 32 , 6

5 , 61 , 3

1 , 43 , 8

3

Blue cube: 65 , 4

1 , 32 , 3

1 , 83 , 2

1

Red cube: 241 , 4

1 , 125 , 8

1 , 245 , 6

1

4. Pupils throw the three cubes and write the fractions shown on the blackboard. Discuss the questions and answer it. Start from the fractions shown on the white cube; follow by blue/red cube and red/blue cube.

76

Worksheet 3.22 Solve the following.

1. 32 – 3

1 + 31 =

2. 54 – 5

2 + 51 =

3. 52 + 5

4 – 53 =

4. 76 – 7

3 + 71 =

5. 115 + 11

2 – 113 =

77


1. 21 + 4

3 – 81 = 2. 8

3 + 52 – 10

4 =

3. 74 – 3

1 + 212 = 4. 8

3 – 91 + 6

5 =

5. 97 – 15

9 + 4521 =

78


1. 5 91 – 4 9

8 + 1 94 = 2. 6 8

1 – 5 85 + 2 8

7 =

3. 2 41 – 1 6

5 + 3 61 = 4. 3 2

1 + 1 83 – 3 4

3 =

5. 4 31 + 2 5

2 – 5 54 =

79

Teacher’s Guide Sheet 3.17 Concept: Subtraction of fractions Learning Outcome: Solve problems involving combined operations of addition and subtraction of fractions.

Notes: 1. This learning contains 1 activity. 2. Guide pupils to use the steps in problem solving.

Activity 1


Aim Solve problems involving combined operations of addition and subtraction of

fractions.

Steps 1. Guide pupils to solve the questions using the steps of problem solving by Polya. Example 1:

“Ishak has 9 21 litres of pesticide. He used 6 5

3 litres at the oil palm plantation. If he buys another 5 litres, how much pesticide has he now?

2. Example 2:

The mass of a tin of biscuit is 3 21 kg.

The mass of the empty tin is 43 kg.

The mass of a plastic beg is 51 kg.

What is the mass of all the biscuits in the plastic beg? After answer the questions, guide the pupils to check their solution. 3. Pupils answer Worksheet 3.25.

80

Worksheet 3.25 1. En. Rahim spends 10

3 of his salary to pay the house rent, and 72 of his salary for other

expenses. Calculate the fraction of his salary that he keeps.

2. Mr. Baskaran bought 5 kg of star fruits from a distributor and another 2 43 kg from another

distributor. If he sold 4 21 kg of the star fruits, calculate the fraction of star fruits that has not

been sold.

3. Pn. Sofiah has 6 21 litres lime juice in a container. She sold 4 7

1 litres of the juice. If she add

another 3 51 litres of lime juice into the container, calculate the volume of lime juice in the

container now.

81

Test 3.2 Name: _____________________________________________________________

Class: _____________________________________________________________

1. Complete:

97 = 27

2. Write in the simplest fraction:

3012 =

3. Change the improper fractions to mixed numbers:

(a) 617 =

(b) 426 =

4. Change the mixed numbers to improper fractions.

2 74 =

5. Circle the greatest fraction.

53 , 10

7 , 158

6. Solve the following.

(a) 1 + 172 = (b) 7

2 + 145 =

(c) 32 + 4

1 = (d) 87 + 4

1 + 83 =

82

(e) 4 51 + 2 10

7 = (f) 21 + 3

1 + 41 =


(a) 1711 – 17

9 = (b) 98 – 3

2 =

(c) 73 – 6

1 = (d) 7 32 – 4 6

1 =

(e) 5 – 3 31 = (f) 9 5

1 – 2 53 =


(a) 139 + 13

2 – 137 = (b) 21

17 – 74 + 3

2 =

(c) 98 – 5

2 + 31 =

83

9. Yahya, Wahid and Zainal shared a pizza. Yahya ate 83 and Wahid ate 4

1 of the pizza. What fraction of the pizza did Zainal eat?

10. En. Ali collected 14 21 litres of milk while his son collected 13 8

3 litres of milk. They sold 26 41

litres of the milk. Calculate the fraction of the milk left.

84

Teacher’s Guide Sheet 3.18 Concept: Multiplication of fractions Learning Outcomes: - Teaching Aids: Fraction strips papers

Notes: 1. This lesson contains one activity. 2. Multiplication concept of fraction is expanded through the folded

strip papers modelling (concrete approach), and then is extended to an algorithm.

Activity 1

Approach Demonstration, group activities, discussions.

Aim 1. Multiplication of whole numbers and fractions as repeated addition of the

fractions. 2. Multiply whole number with the numerator of fraction to obtain the product

of multiplying a whole number and a fraction.

Steps 1. Group activities: Pupils determine the product of a whole number and a fraction by folding

strips of paper.

Pupils groups solve a few examples and show their work on the

blackboard. 2. Lead pupils to conclude that multiplying a whole number and a fraction is

85

the same as repeated addition of fractions. Example:

5 × 31 = 3

1 + 31 + 3

1 + 31 + 3

1

= 35

= 1 32

3. Pupils answer Worksheet 3.26. 4. Teacher shows an example as shown:

7 × 31 = 3

1 7 ×

= 37

= 2 31


86

Worksheet 3.26 1. Solve these questions.

2. 3. 4. Draw figure for multiplications of these fractions.

Figure Answer

3 × 51

4 × 61

87

5. 7 × 91 = 6. 3 × 11

1

7. 4 × 52 8. 4 × 7

4

9. 5 × 65 10. 7 × 13

4

88

Worksheet 3.27 1. Find the answers for the questions below.

(a) 4 × 71 (b) 4 × 5

3

(c) 9 × 112 (d) 11 × 13

2

(e) 7 × 165 (f) 8 × 7

4

(g) 6 × 31 (h) 21 × 7

2

(i) 30 × 65

89

Teacher’s Guide Sheet 3.19 Concept: Multiplication of Fractions Learning Outcomes: 1. Multiply a fraction by a whole number. 2. Multiply a fraction by a fraction. Teaching Aids: Discrete concrete materials: marbles, empty box. Continuous concrete materials: paper

Notes: 1. This lesson consist one activity. 2. Concrete materials are used to expand the concept to find the

fraction from a group of things. Pupils’ understandings are measured by the way they manipulate concrete materials to get the answers.

3. Pupils’ understandings are reinforced when they answer Worksheet 3.28.

Activity 1

Approach Group activity, discussion and exercise.

Aim 1. Find the fraction from a group of things.

2. Find the fraction from a fraction. 3. Change the word “from” to multiplication symbol “×”.

Steps 1. Group Activities Each group is given discrete concrete materials and continuous concrete

materials. Guide pupils to find: (a) Product of a fraction and a whole number by material groupings.

90

(b) Product of a fraction and a fraction by paper folding. Example:

61 × 3

2

i. Fold a piece of paper vertically, into 3 parts and shade two parts of them.

ii. Fold the same paper horizontally, into 6 parts and shade one part

of them. iii. Shaded parts are intersected.

61 × 3

2 = 182

All groups are given chance to use the both concrete materials 2. Explain the meaning of “from” through the following examples.

(a) 32 from 6 = 3

2 × 6

= 4

(b) 52 from 3

1 = 52 × 3

1

= 152


91

Worksheet 3.28 Find answers to the following.

1. 2.

41 × 8 = 6

1 × 18 =

3. 4.

53 × 10 = 7

2 × 14 =

5. 6.

41 × 6 = 3

2 × 9 =

7. 8.

41 × 2

1 = 41 × 2

2 =

9. 10.

32 × 2

1 = 65 × 3

1 =

92

11.

72 × 4

1 =

12. 21 from 10

2 13. 32 from 5

4

14. 75 from 2

1 15. 81 from 3

2

93

Teacher’s Guide Sheet 3.20 Concept: Multiplication of Fractions Learning Outcome: Multiply a fraction by a fraction.

Teaching Aids: Strips of paper

Notes: 1. This lesson consists of two activities. 2. In Activity 1, algorithms for product of 2 fractions have been

abstracted after the discussion of some examples. 3. A game is conducted in Activity 2 to reinforce the skill learned.

Activity 1


Aim 1. Find the product of 2 fractions by multiplying the numerator by numerator and denominator by denominator.

Steps 1. Explain using the following example: Ah Kow is a farmer. He owns a piece of land.

32 of the land is planted with vegetables

31 of the land is being used to rare chicken

52 of the land that is used to plant vegetables, is planted with water spinach.

Explain using diagrams.

Vegetables = 32

Rare chicken = 31

94

Calculations:

52 from 3

2 = 52 × 3

2

= 3 52 2

××

= 154


Activity 2

Approach Discussion, game and exercise

Aim 1. Find the product of a fractions and a whole number by simplification. 2. Find the product of 2 fractions by simplification.

Steps 1. Teacher revises skill “Multiply a fraction by a whole number” with following example:

2. Teacher introduces simplification method.

In simplest way,

Repeat with different examples. 3. Teacher expands the simplification method to multiply 2 fractions.

95

Example:

In simplest way,

4. Carry out mathematics game (refer note 1). 5. Pupils answer Worksheet 3.30.

Explanation Notes Mathematics Game: Pupils are divided into 4 groups. A pupil from first group chooses a card and writes the question on the writing board. Other 3 groups try to answer it, 2 marks are given to the group which can answer correctly and show the correct working. If the given answer is wrong, the question is open to 2 remaining groups. 3 marks are given if they answer correctly. The group that obtain the higher marks is a winner.

96

Worksheet 3.29 1. Solve following questions:

(a)

(b) (c)

(d)

2. 21 × 3

1 = 3. 32 × 9

1 =

52 × 4

3 =

91 × 3

2 =

76 × 2

1 =

43 × 5

1 =

97

4. 23 × 3

7 = 5. 75 × 10

7 = 6. 11

7 × 43 =

98

73 × 15

14 =

81 × 13

12 =

95 × 5

2 =

75 × 35

15 =

2621 × 14

13 =

32 × 12 =

134 × 26 =

20 × 43 =

109 × 25 =

1211 × 18 =

Worksheet 3.30

99

Teacher’s Guide Sheet 3.21 Concept: Multiplication of Fractions Learning Outcome: Multiply a whole number by a fraction or mixed number. Teaching Aids: Cards with questions

Notes: 1. This lesson consists of 2 activities. 2. Calculation of multiplication of fractions learned in previous lesson is

expanded to multiplication of 2 or 3 mixed numbers. 3. Pupil’s skill in calculations reinforced through a mathematics game.

Activity 1

Approach Group activity, discussion and exercise.

Aim Find the product of 2 numbers involving a mixed number by converting the mixed number into improper fraction.

Steps 1. Explain using daily life example.

A piece of cloth with length 1 41 m is needed to cover a table. How many

metres of the cloth is needed to cover 8 tables that are joined together?

1 41 × 8 = 4

5 × 8

= 10 m Explain using different examples:

(a) 2 41 × 10

9 = 49 × 10

9

= 4081

= 2 401

(b) 1 51 × 2 4

3 = 56 × 4

11

= 1033

= 3 103

2

3

100

2. Group activity Pupils answer Worksheet 3.31 in group. Guide pupils in solving the

problems. Pupils check the answers among the groups.

Activity 2

Approach Game

Aim Perform multiplication of 3 fractions involving mixed numbers.

Steps 1. Ask a few pupils to solve the questions on the blackboard. Examples:

(a) 32 × 11

6 × 83 = 22

3

(b) 1 31 × 2 8

1 × 2 52 = 3

4 × 817 × 5

12

= 534

= 6 54

Note: Show other methods of problem solving. 2. Mathematics game (Refer Explanation notes) Pupils need to record the answers in Worksheet 3.32. 3. After the game, pupils answer question 2 in Worksheet 3.32.

Explanation notes Mathematics Game 1. Prepare cards with questions to solve by pupils. Examples of questions that can be written

on the cards:

(a) 76 × 10

7 × 125 = (b) 2 3

2 × 1 43 × 7

2 =

(c) 1 51 × 2 2

1 × 32 = (d) 2 6

1 × 2 52 × 3 4

3 =

(e) 1 92 × 10

3 × 2 95 = (f) 8

3 × 2 32 × 4

1 =

(g) 1 32 × 11

6 × 109 = (h) 3 2

1 × 1 31 × 1 7

1 =

(i) 85 × 20

11 × 334 = (j) 3 4

3 × 98 × 5

1 =

(k) 1 32 × 5

4 × 1 81 = (l) 1 7

5 × 2 21 × 15

14 =

101

2. Pupils are divided in 4 groups, A, B, C and D. 3. A pupil from group A pick a card and shows the question to group B. Pupils from group C

and D can try to solve it. 4. A pupil from group B is chosen to solve the question on the blackboard. 5. If group B cannot answer the question, the question will open to groups C and D. 6. The used card is taken out. 7. The steps can be repeated for other groups. Example: A pupil from group B picks a card

and shows the question to group C. Pupils from groups A and D can try to solve it. 8. Game ends when all the cards have been picked. 9. The winner is determined by their scores. Score: (a) Correct answer - 3 marks (b) Wrong answer - 0 mark (c) Correct in principle but answer is wrong - 1 mark (d) Question answered correctly by other groups - 1 mark

102

Worksheet 3.31

Questions

Calculations Answer in

lowest form

Answer in mixed

number (if any)

1. 1 61 × 2 6

7 × 2 67 × 2 3

7

2. 1 87 × 5

2

3. 3 32 × 7

6

4. 2 31 × 1 8

1

5. 1 75 × 6

1

6. 2 × 3 51

1

3

103

Worksheet 3.32 Copy the questions that were discussed in the game.

Questions Workings/Calculations Answers

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

104

Questions Workings/Calculations Answers

(l)

2. Solve the following questions.

(a) 32 × 7

6 × 212 =

(b) 52 × 13

10 × 83 =

(c) 49 × 25

24 × 32 =

(d) 2 × 911 × 4

1 =

(e) 712 × 17

14 × 272 =

105

Teacher’s Guide Sheet 3.22 Concept: Multiplication of Fractions Learning Outcomes: Solve problems involving multiplication of fractions.

Notes: 1. This lesson consists of one activity. 2. Guide pupils to use the problem solving steps.

Activity 1

Approach Group activity and discussions.

Aim Problems solving involving multiplication of fractions.

Steps 1. Guide pupils to solve the following question using the steps of problem solving by Polya.

Question:

There are 40 pupils in Form 1 Melor. 83 of them are girls and 5

1 of the girls wear spectacles. Determine the number of girls that wear spectacles.

Calculations

Number of girls in the class = 83 × 40

= 15

Number of girls that wear spectacles = 51 from 8

3 × 40

= 51 × 15

= 3 Solve the following multiplication involving combinations.

Number of girls that wear spectacles = 51 from 8

3 from 40

= 51 × 8

3 × 40

= 3 2. Pupils answer Worksheet 3.33.

106

Worksheet 3.33

1. Puan Minah bought 8 tins of margarine. Each tin contains 41 kg of margarine. What is the

total weight of the margarine?

2. Mr. Kim’s monthly salary is RM 850. He used 52 of his salary to pay his housing loan. What

is the monthly instalment for his housing loan?

3. The workers of the company that repairs KL-Karak Highway can cover 103 km in one day.

(a) What is the distance they can cover in 5 21 working days?

(b) What is the distance they can cover in April if they throughout the month?

4. Pak Sameon’s has 280 cattle. 74 of them are dairy cow and the rest are beef cattle. 3

1 of the beef cattle have been exported. (a) How many beef cattle are there? (b) How many beef cattle have been exported?

107

Teacher’s Guide Sheet 3.23 Concept: Division of Fractions Learning Outcomes: Divide a fraction by a whole number.

Teaching Aids: Charts, fraction kits

Notes: 1. This lesson consists of one activity. 2. Initially, diagram is used to explain the concept of division involving

whole numbers and fractions. Then calculations involving division of fractions are introduced.

Activity 1

Approach Explanation

Aim 1. Divide and mark a quantity into several parts.

2. Divide and mark a fraction into several parts.

Steps 1. Explain the concept of division using diagrams. (a) 20 ÷ 4 = 5

In the simplest way,

20 ÷ 4 = 420

= 5

(b) 6 ÷ 4 = 1 21

108

In the simplest way,

6 ÷ 4 = 46

= 1 21

(c) 21 ÷ 2 = 4

1

(d) 51 ÷ 4 = 20

1

2. Introduce the calculation method for division involving a fraction and a

whole number.

With diagram Simplest way by calculation

21 ÷ 2 = 4

1 21 × 2

1 = 41

51 ÷ 4 = 20

1 51 × 4

1 = 201


109

Worksheet 3.34 1. Express the following as fractions in the lowest term. (a) 1 ÷ 5 = (b) 2 ÷ 7 = (c) 9 ÷ 10 = (d) 12 ÷ 3 = (e) 55 ÷ 7 = (f) 4 ÷ 16 = (g) 30 ÷ 5 = (h) 9 ÷ 4 = (i) 36 ÷ 8 = (j) 3 ÷ 10 = 2. Draw diagrams to represent the following divisions. (a) 10 ÷ 3 = (b) 5 ÷ 2 =

(c) 21 ÷ 3 = (d) 4

3 ÷ 2 =

110

3. Write following divisions (involving a fraction and a whole number) in multiplication form and find the answers.

Example: 21 ÷ 4 = 2

1 × 41

= 81

(a) 31 ÷ 5 = (b) 4

3 ÷ 6 =

(c) 98 ÷ 3 = (d) 5

3 ÷ 4 =

(e) 107 ÷ 8 = (f) 15

8 ÷ 4 =

111

Teacher’s Guide Sheet 3.24 Concept: Division of Fractions Learning Outcomes: 1. Divide a fraction by a fraction. 2. Divide a whole number by a fraction. Teaching Aids: Strips of papers

Notes: 1. This lesson consists of two activities. 2. Concrete materials like strips of paper, fraction cards are used to

expand the concept of division involving a whole number with fraction, and a fraction with a fraction.

3. The division is expanded to involve mixed numbers.

Activity 1

Approach Individual activity, discussions and exercises.

Aim 1. Divide a whole number by a fraction. 2. Divide a fraction by a fraction.

Steps 1. Individual activity Pupils are asked to fold the strips of paper into several parts to carry out

following activity:

(a) 1 ÷ 41

(b) 2

1 ÷ 41 As comparison, 4

1 can be put into “ 21 ” two times.

112

2. Repeat with different examples:

(a) 2 ÷ 31

(b) 3 ÷ 41

(c) 51 ÷ 10

1

(d) 31 ÷ 18

1

3. Teacher summarizes with calculations.

With diagram Simplest way by calculation

2 ÷ 31 = 6 2 × 1

3 = 6

3 ÷ 41 = 12 3 × 1

4 = 12

51 ÷ 10

1 = 2 51 × 1

10 = 2

31 ÷ 18

1 = 6 31 × 1

18 = 6


Activity 2

Approach Discussion and exercise

Aim 1. Divide a whole number by a fraction. 2. Divide a fraction by a fraction.

Steps 1. Expand the calculation to involve mixed numbers. Example:

3 21 ÷ 1 4

1 = 27 ÷ 4

5

= 27 × 5

4

= 514

= 2 54

Repeat with different examples. 2. Pupils answer Worksheet 3.36.

Worksheet 3.35 1. Find the answer to following questions.

1 2

113

(a) 3 ÷ 41 =

(b) 2 ÷ 51 =

(c) 52 ÷ 10

1 =

(d) 95 ÷ 3

1 =

2. Draw diagrams to show the following divisions and find the answers.

(a) 1 ÷ 21 =

(b) 2 ÷ 21 =

114

(c) 31 ÷ 9

1 =

(d) 53 ÷ 5

1 =

3. Find answers to the following.

(a) 7 ÷ 32 = (b) 5 ÷ 7

5 =

(c) 94 ÷ 3

1 = (d) 65 ÷ 12

5 =

(e) 127 ÷ 8

3 = (f) 98 ÷ 7

4 =

(g) 91 ÷ 3

1 = (h) 52 ÷ 15

8 =

Worksheet 3.36 1. Solve

115

(a) 4 101 ÷ 1 2

1 =

(b) 98 ÷ 1 3

1 =

(c) 2 32 ÷ 2 =

2. Find the answer when 1 41 is divided by 2

1 .

3. How many 1 61 are there in 2 8

5 ?

Teacher’s Guide Sheet 3.25 Concept: Division of Fractions

116

Learning Outcomes: Solve problems involving division of fractions.

Notes: 1. This lesson consists of one activity. 2. Guide pupils to use the problem solving steps when necessary.

Activity 1

Approach Discussion and exercise.

Aim Problem solving involving division of fractions

Steps 1. Explain the following example using Polya Model.

A big tin contains 5 litre of oil. The oil is poured into a smaller tin with 41

litre capacity. Find the number of the smaller tins needed to pour out all the oil from the big tin.

2. Pupils’ activity Pupils create a story involving the following division and solve it.

20 ÷ 2 51

Guide: Use situations consisting of length, weight, volume, etc. 3. Pupils answer Worksheet 3.37.

Worksheet 3.37

1. A tank contains 10 21 litres of water. The water is poured into glasses with 4

1 litre capacity. How many glasses are needed to pour out all the water from the tank?

117

2. The length of a container train is 114 m. How many containers are there if the length of

each container measures 9 21 m?

3. A 50 21 m rope is cut into small pieces, each measuring 2 4

1 m. How many small pieces of rope can be obtained?

4. A box contains 20 packets of drinking water. Find the weight of 1 packet of drinking water if

the whole box weighs 7 21 kg.

5. A roti canai seller uses 201 kg flour to produce a piece of roti canai. In a single day, he used

11 21 kg flour. How many roti canai can he produce?

Teacher’s Guide Sheet 3.26 Concept: Combined Operation of Fractions

118

Learning Outcomes: Perform computations involving combined operations of addition, subtraction, multiplication and division of fractions, including the use of brackets.

Notes: 1. This lesson consists of two activities. 2. Computations learned in previous lesson are expanded to

combination involving multiplication and division of 3 fractions.

Activity 1


Aim Computation involving combination of multiplication and division of 3 fractions.

Steps 1. Introduce combination of multiplication and division of fractions as below:

(a) 15 × 53 ÷ 6

(b) 52 × 4

3 ÷ 76

(c) 3 41 × 2 2

1 × 2615

Emphasise that the principle of calculation involving combination of multiplication and division is done from left to right.


Activity 2


Aim Perform problem solving

Steps 1. Discuss the problem involving combination of multiplication and division of 3 fractions.

Example:

119

Pail A can contain 4 21 litres of water. 10 pails of water is poured in tank B.

How many glasses of water with capacity of 41 litre can be filled by the

water in tank B? What is required: Number of glasses can be filled with

water from tank B. What are the information given: Tank B contains 10 pails of

water measured with pail A.

Volume of water in pail A is 4 21 litres.

Each glass can be filled with 41 litre

of water. Solving: Amount of water that is poured into

tank B = 4 21 litres × 10

Number of glasses can be filled

= 4 21 × 10 ÷ 4

1

= 29 × 10 × 1

4


Worksheet 3.38

120

Solve the following.

1. 9 × 7 ÷ 3 = 2. 91 × 7 ÷ 3

1 =

3. 152 × 2 4

1 ÷ 103 = 4. 3 7

3 ÷ 2 52 × 3 2

1 =

5. 4 94 ÷ 8 × 3 5

3 = 6. 10 65 × 13

3 ÷ 3 31 =

Worksheet 3.39

121

Solve the following questions. 1. Mr. Halim teaches 20 periods of mathematics from Monday to Friday. If each period takes

32 hour, find the average time that he teaches in a day.

2. Mr. Harun’s monthly salary is RM1200. 151 of the salary is spent on his four children’s

pocket money. How much pocket money does each of his children receive?

3. Mrs. Chan bought 15 packets of flour. Each packet weighs 1 21 kg. Mrs. Chan put the flour

in containers that can store 1 41 kg of flour. How many containers are needed to store all the

flour?

4. Area of an exam room is 85 21 m2. Area allocated for each candidate is 2 4

1 m2. If 5 rooms are used for examination, calculate the number of candidates that can be placed.

Teacher’s Guide Sheet 3.27

122

Concept: Combined Operation of Fractions Learning Outcomes: Solve problems involving combined operations of addition, subtraction, multiplication and division of fractions; including the use of brackets.

Notes: 1. This lesson consists of two activities. 2. Initially, pupils are introduced to calculations involving combination

of operations. Then pupils are guided to solve some more complex questions.

Activity 1


Aim Perform computation involving combination of operation involving brackets.

Steps 1. Discuss the following examples:

(a) ( 41 + 2

1 ) × 3

(b) 15 × (2 41 ÷ 8

5 )

(c) 25 21 – 2 4

1 × 8

Order of operation: (i) Perform operation in brackets (ii) Perform multiplication and division from left to right (iii) Perform addition and subtraction from left to right


Activity 2


Aim Perform problem solving.

123

Steps 1. Discuss using daily life example:

A shopper mixed 10 21 kg of type A with 50 4

1 kg of type B fertilisers. The

mixture is then filled into plastic bags. Each plastic bag can fill 2 41 kg of

fertilisers. Find the number of plastic bags needed to store all the mixture of fertilisers.

Solving:

Amount of mixture = 10 21 kg + 50 4

1 kg

Number of plastic bags needed

= (10 21 + 50 4

1 ) ÷ 2 41

= ( 221 + 4

201 ) ÷ 49

= ( 4201 42 + ) ÷ 4

9

= 4243 × 9

4


Worksheet 3.40

124

Solve following questions:

1. (2 41 + 3 2

1 ) × 5 = 2. (3 32 – 1 3

1 ) × 109 =

3. 11 + 7 × 31 = 4. 4

3 ÷ ( 85 × 15

4 ) =

5. 30 × (5 41 ÷ 8

3 ) = 6. 2 83 – 1 8

1 ÷ 243 =

Worksheet 3.41

125

1. There are 100 pupils in a school hall. 5

1 of them stood at the back of the hall and the rest are seated in 8 rows. Find the number of pupils in each row.

2. A developer, Bina Emas build terrace houses on a piece of land measured 11300m2. Area

of each house is 150 32 m2. 10 houses are reserved for the company staff, how many

houses are going to be sold to the public when the project is completed?

3. Baljit does his revision everyday. He spent 43 hour on mathematics and 2

1 hour for English language. Find the total time spent in five days for both subjects.

4. Mrs. Lim bought 3 21 metres of clothing material. She used 2

1 of the material to sew a dress

and 31 of the material to sew a skirt. How many metres of material left?

5. The length of a piece of batik cloth is 10 21 metres. 1 4

1 metres of the cloth is dirty and

cannot be used. The remaining cloth is cut into smaller pieces of 43 metre each. Find the

number of the smaller pieces that can be obtained from the remaining batik cloth. Test 3.3

126

Name: _____________________________________________________________ Class: _____________________________________________________________

Section A

1. Write two equivalent fraction for 52 .

52 = =

2. Arrange 53 , 10

7 and 21 in ascending order.

_______________________________________________________ 3. Simplify

2718 =

4. Add 4 31 to 1 6

1 .

5. Find the difference between 7 and 3 52 .

6. represent 1

Shade the diagram below to represent product of 4 × 31 .

7. Shade the area to represent product of 32 × 6.

127

8. Solve 4 × 73

9. Solve 52 × 3

10. Solve

(a) 92 from 7

2 (b) 214 × 16

7

(c) 3 × 4 32 × 7

4

11. Find the value of the following:

(a) 127 ÷ 3 = (b) 9

4 ÷ 32 =

12. What is the value when 95 is divided by 3 4

3 ?

13. Solve

(a) 95 × 1 5

1 ÷ 61 (b) ( 7

6 + 143 ) × 10

7

Section B

128

14. A round shape paper is divided into 8 equal parts. If 6 parts is cut off and taken out, what is

the remaining fraction? Answer: ________________

15. In a fresh milk drinking competition, Ah Chai can drink 83 milk from a bottle and Imran can

drink 74 milk from the bottle of same capacity. Who can drink more milk?

Answer: ________________

16. Pn. Azizah bought 2 21 kg of prawn and 1 4

3 kg of fish. If the weight of an empty basket is 81

kg, what is the weight of the basket containing prawn and fish? Answer: ________________ 17. En. Ali wants to give a piece of land to his 3 children, Along, Angah and Busu. Along

received 53 part and Angah received 15

2 parts of the land. How many parts of the land will Busu receive?

Answer: ________________

129

18. Mr. Rizal bought 5 21 kg of rice and his wife bought 8 kg of rice. On first day of Hari Raya,

they cooked 7 32 kg rice to make ketupat. What is the weight of the remaining rice?

Answer: ________________

19. John’s monthly salary is RM1800. He saved 31 from his salary. How much is his monthly

saving? Answer: ________________

20. Lai Meng inherited 83 part from his father’s farm. Then he gave 5

4 of the land to his son Kok Leong. What fraction of the land did Kok Leong received?

Answer: ________________

21. Pn. Siti bought 31 21 m of clothes to make curtains. If each curtain measures 2 4

1 m, how many curtains can be produced?

Answer: ________________

22. Each time Prem pedals, his bicycle will move forward 1 41 m. He is 20 m away from the

finishing line. How far is Prem from the finishing line if he pedalled 15 times? Answer: ________________

130

Answer Worksheet 3.1 1. 2

1 2. 21

3. 2

1 4. 21

5. 2

1 6. 21

7. 5

1 8. 41

9. 3

1 10. 43

11. 3

2 12. 42

13. 15

8 Worksheet 3.2 1. (a) (b)

(c) (d)

(e) (f)

131

(g) (h)

(i) (j)

(k) (l)

2. (a) (b)

(c) (d)

132

(e) (f)

Worksheet 3.3 1. (a) 4

3 (b) 32

(c) 62 , 6

5 2. (a)

(b)

3. Bottom to top: 9

5 , 97 , 9

8 4.

133

Worksheet 3.4 1. (a)

(b)

(c)

2. (a)

(b)

134

Worksheet 3.5 1.

Number Result of multiplication 3 15

6

4 4 54 2

×× = 20

8

5 5 55 2

×× = 25

10

7 7 57 2

×× = 35

14

8 8 58 2

×× = 40

16

10 10 510 2

×× = 50

20

11 11 511 2

×× = 55

22

52 = 10

4 = 156 = 20

8 = 2510 = 35

14 = 4016 = 50

20 = 5522

2.

3. (a) Not equivalent (b) Equivalent (c) Not equivalent (d) Equivalent Worksheet 3.6 1.

Fractions Denominator

85 8

92 9

1511 15

9340 93

229 22

135

2. Lowest Fractions Largest Fractions

(a) 53 5

4

(b) 71 7

4

(c) 92 9

6

(d) 156 15

10

(e) 81 8

6

(f) 123 12

10

(g) 338 33

21

(h) 203 20

16 3.

LCM Denominator Common Denominator Fractions

Lowest Fractions

Largest Fractions

(a) 6 64 and 6

5 32 6

5

(b) 20 204 and 20

5 51 4

1

(c) 18 184 and 18

6 92 6

2

(d) 56 5635 and 56

32 74 8

5

(e) 24 2421 and 9

5 65 8

7

(f) 9 96 and 9

5 95 3

2

(g) 22 228 and 22

7 227 11

4

(h) 45 4535 and 45

36 97 5

4 4. (a) 10

7 (b) 65

Worksheet 3.7 1. (a) 2, 4 (b) 5 (c) 4, 5 (d) 2, 3, 6 (e) 3 2.

HCF Fractions in the lowest terms (a) 2 5

4

(b) - 158

(c) 3 83

(d) 5 75

136

3. (a) 51 (b) 5

1

(c) 32 (d) 5

3

(e) 32 (f) 7

3 Worksheet 3.8 1. (a) 1 (b) 2

1

(c) 41 (d) 1 4

1

(e) 2 21 (f) 3 3

1

(g) 5 21 (h) 1 3

2 2. (a)

(b)

(c)

3. (a)

(b)

(c)

(d)

(e)

137

4. (a) A = 1 32 (b) A = 6 5

3

(c) A = 3 32

5. (a)

(b)

(c)

(d)

6.

7. 5 2

1 km 8.

Worksheet 3.9 1. Proper fraction: 2

1 , 73 , 6

6 , 119 , 10

3

Improper fraction: 911 , 5

17 , 315 , 11

17 , 38

2. (a) 27 (b) 30 (c) 36

138

3. (a) 413 (b) 10

53

(c) 754 (d) 5

53

(e) 653 (f) 8

75 Worksheet 3.10 1. 2. (a) 13 2

1 (b) 4 72

(c) 4 83 (d) 4

23

(e) 9 (f) 12 52

3. (a) 3, 10 (b) 9, 14 (c) 21, 15 (d) 2, 36 (e) 3, 56 4. (a) 6

4 , 96 (b) 3

7 , 921

(c) 810 , 12

15 (d) 1420 , 21

30 5. (a) yes (b) no (c) no (d) yes TEST 3.1 1. 5

2 , 31

2. 3. 8

3 , 87

Improper fractions Mixed numbers (a)

23 1 2

1 (b)

27 3 2

1 (c)

410 2 4

2 (d)

35 1 3

2

139

4.

5. 6

2 , 93

6. (a) 8

7 (b) 52

7. (a) 5

3 (b) 2710

8. 1 3

2 9.

10. (a) 35 (b) 17 (c) 3 11. (a) 2

4 (b) 522

12. (a) 4 (b) 8 6

1 13. 2

3 = 1218

14. 3

1 15. 5

3 Worksheet 3.11 1. (a)

140

(b)

(c)

(d)

2. (a)

(b)

(c)

(d)

141


5 (b) 21

(c) 76 (d) 9

4

(e) 54 (f) 12

7

(g) 32 (h) 1

(i) 1 (j) 43

(k) 43 (l) 5

4

(m) 32 (n) 4

3 2. (a) 3

2 (b) 65

(c) 107 (d) 20

9 3. (a) 3 5

3 (b) 2 92

(c) 5 32 (d) 1 11

6

(e) 4 73

Worksheet 3.13 1. 3

1 + 51 = 15

5 + 153 2. 2

1 + 61 = 6

3 + 61

= 158 = 6

4

= 32

3. 108 4. 20

13 5. 4

3 6. 6047

7. 70

59 8. 87

Worksheet 3.14 1. 3 7

2 2. 5 107

3. 5 4

3 4. 5 21

5. 9 8

7 6. 14 215

7. 5 8. 6 30

23 9. 7 4

3 10. 6 81

142

Worksheet 3.15 1. 4 6

1 km 2. 4 103 kg

3. 5 12

11 Worksheet 3.16 1. 7

2 2. 82

3. 13

4 4. 158

5. 10

3 6. 72

7. 8

5 8. 156

9. 17

3 Worksheet 3.17 1. (a) 3

3 – 31 = 3

1 (b) 1 – 52 = 5

5 – 52

= 53

(c) 1 – 73 = 7

7 – 73 (d) 1 – 6

2 = 64

= 74

(e) 1 – 83 = 8

5 2. (a) 4

1 (b) 1 52

(c) 2 75 (d) 3 8

5

(e) 4 101

3. 2 8

3 Worksheet 3.18 1.

2.

143

3.

4.

5.

Worksheet 3.19 1. 15

2 2. 207

3. 18

1 4. 107

5. 24

19 Worksheet 3.20 1. (a) 1 2

1 (b) 4 65

(c) 5 91

2. (a) 3 4

1 (b) 9 103

(c) 4 21

3. (a) 2 9

4 (b) 2 21

(c) 3 31

4. (a) 5

2 (b) 1 21

(c) 2 73

5. (a) 2 2

1 (b) 1 152

(c) 3 127 (d) 3 2

1

(e) 1 1513

144

Worksheet 3.21 1. 20

11 2. 411 = 2 4

3 3. 10

9 4. 83

Worksheet 3.22 1. 3

2 2. 53

3. 5

3 4. 74

5. 11

4 Worksheet 3.23 1. 1 8

1 2. 83

3. 3

1 4. 1 727

5. 45

29 Worksheet 3.24 1. 1 3

2 2. 169

3. 3 12

71 4. 1 81

5. 15

14 Worksheet 3.25 1. 70

29 2. 3 41

3. 5 70

39 Test 3.2 1. 27

21 2. 52

3. (a) 2 6

5 (b) 6 21

4. 7

18 5. 107

6. (a) 1 17

2 (b) 149

(c) 1211 (d) 1 2

1

145

(e) 6 109 (f) 1 12

1 7. (a) 17

2 (b) 92

(c) 4211 (d) 3 2

1

(e) 1 32 (f) 6 5

3 8. (a) 13

4 (b) 2119

(c) 4537

9. 8

3 10. 1 85

Worksheet 3.26 1. 3 × 5

4 = 512 2. 2 × 3

2 = 34

= 2 52 = 1 3

1 3. 4 × 4

3 = 412

= 3 4.

5. 9

7 6. 113

7. 1 5

3 8. 2 72

146

9. 4 61 10. 2 13

2 Worksheet 3.27 1. (a) 7

4 (b) 2 52

(c) 1 117 (d) 1 13

9

(e) 2 163 (f) 4 7

4 (g) 2 (h) 6 (i) 25 Worksheet 3.28

1. 2.

41 × 8 = 2 6

1 × 18 = 3

3. 4.

53 × 10 = 6 7

2 × 14 = 4

5. 6.

41 × 6 = 1 2

1 32 × 9 = 6

7. 8.

4

1 × 21 = 8

1 41 × 2

2 = 41

147

9. 10.

3

2 × 21 = 6

2 65 × 3

1 = 185

= 31

11.

7

2 × 41 = 28

2

= 141

12. 101 13. 15

8

14. 145 15. 12

1


3 (b) 272

(c) 73 (d) 20

3 2. 6

1 3. 272

4. 3 2

1 5. 21

6. 44

21 Worksheet 3.30

73 × 15

14 = 52 8

1 × 1312 = 26

3

95 × 5

2 = 92 26

21 × 1413 = 4

3

75 × 35

15 = 4915 13

4 × 26 = 8

32 × 12 = 8 20 × 4

3 = 15

109 × 25 = 22 2

1 1211 × 18 = 16 2

1

148

Worksheet 3.31

Question

Calculations Answers in

lowest form

Answers in mixed

number ( if any)

1. 1 61 × 2 6

7 × 2 67 × 2 3

7 2 31

2. 1 87 × 5

2 815 × 5

2 815 × 5

2 43 --

3. 3 32 × 7

6 311 × 7

6 311 × 7

6 722 3 7

1

4. 2 31 × 1 8

1 37 × 8

9 37 × 8

9 821 2 8

5

5. 1 75 × 6

1 712 × 6

1 712 × 6

1 72 --

6. 2 × 3 51 2 × 5

16 532 6 5

2

Worksheet 3.32 1.

Questions Calculations Answers

(a) 76 × 10

7 × 125 = 7

6 × 107 × 12

5 41

(b) 2 32 × 1 4

3 × 72 = 3

8 × 47 × 7

2 34

(c) 1 51 × 2 2

1 × 32 = 5

6 × 25 × 3

2 2

(d) 2 61 × 2 5

2 × 3 43 = 6

13 × 512 × 4

15 239

(e) 1 92 × 10

3 × 2 95 = 9

11 × 103 × 9

23 270253

(f) 83 × 2 3

2 × 41 = 8

3 × 38 × 4

1 41

(g) 1 32 × 11

6 × 109 = 3

5 × 116 × 10

9 119

(h) 3 21 × 1 3

1 × 1 71 = 2

7 × 34 × 7

8 316

(i) 85 × 20

11 × 334 = 8

5 × 2011 × 33

4 241

(j) 3 43 × 9

8 × 51 = 4

15 × 98 × 5

1 32

(k) 1 32 × 5

4 × 1 81 = 3

5 × 54 × 8

9 23

(l) 1 75 × 2 2

1 × 1514 = 7

12 × 25 × 15

14 4

1

3 1

4 1

3

1

2

1

3

1

2

2 2 2

2

3 3

2

3

2 2

2 3 4 2 3

3

2 3

4

2 6

3

2

149

2. (a) 1478 (b) 26

3

(c) 1 2511 (d) 18

11

(e) 15316

Worksheet 3.33 1. 2 kg 2. RM 340 3. (a) 20

33 km (b) 9 km 4. (a) 120 (b) 40 Worksheet 3.34 1. (a) 5

1 (b) 72

(c) 109 (d) 4

(e) 755 (f) 4

1

(g) 6 (h) 49

(i) 29 (j) 10

3 2. (a)

(b)

(c)

3. (a) 15

1 (b) 81

(c) 278 (d) 20

3

10 ÷ 3 = 3 31

5 ÷ 2 = 2 21

150

(e) 807 (f) 15

2 Worksheet 3.35 1. (a) 12 (b) 10 (c) 4 (d) 3

5 2. (a) 1 ÷ 2

1 = 2

(b) 2 ÷ 21 = 4

(c) 3

1 ÷ 91 = 3

(d) 5

3 ÷ 51 = 3

3. (a) 2

21 (b) 7

(c) 34 (d) 2

(e) 914 (f) 9

14

(g) 31 (h) 4

3 Worksheet 3.36 1. (a) 15

41 (b) 32

(c) 34

151

2. 25 3. 4

9 Worksheet 3.37 1. 42 glasses 2. 12 m 3. 9

202 m 4. 83 kg

4. 230 Worksheet 3.38 1. 21 2. 3

7 3. 1 4. 2

35 5. 2 6. 4

3 Worksheet 3.39 1. 3

8 2. RM 20 3. 18 4. 190 Worksheet 3.40 1. 4

115 2. 1021

3. 3

40 4. 29

5. 420 6. – 8

53 Worksheet 3.41 1. 10 pupils 2. 65 houses 3. 4

25 hours 4. 127 m

5. 3

37 m Test 3.3 Section A 1. 5

2 = 104 = 15

6 2. 21 , 5

3 , 107

3. 27

18 = 32 4. 2

11 5. 5

18

152

6. 4 × 31 = 3

4

= 1 31

7. 3

2 × 6 = 4

8. 7

12 9. 56

10. (a) 63

4 (b) 121

(c) 8 11. (a) 36

7 (b) 32

12. 27

4 13. (a) 4 (b) 4

3 Section B 14. 4

1 15. Imran 16. 8

35 kg 17. 154

18. 6

35 kg 19. RM 600 20. 10

3 21. 14 22. 4

5 m

Chapter 3 Fractions

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Transcript of Chapter 3 Fractions