Chapter 4 Decimals

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Teacher’s Guide Sheet 4.1 Concept: Represent fractions with denominators 10, 100, 1000 as decimals.

Learning Outcomes: 1. Represent fractions 101 and 100

1 as decimals and vice-versa.

2. Represent fractions with denominators 10, 100 and 1000 as decimals. 3. Read and write decimals to thousandths. 4. Compare the values of two given decimals. 5. Arrange decimals in order. Teaching Aids: Concrete materials or diagrams that show decimals, rulers, coins, erasers, sharpeners and flash cards that show decimals in numbers and words.

Notes: This lesson consists of four activities that are Activity 1 – 4. Worksheet 4.1 is also included. The time needed to complete this activity is 40 minutes. Since decimals had been taught in primary school (up to 3 decimal places), teacher has to consider pupils’ weaknesses and make necessary adjustments to the activities so that the lesson would be more effective and interesting. These activities are related to questions in Worksheet 4.1: Activity 1: Question 1 Activity 2: Question 2 Activity 3: Question 3, 4, 5, 6, 7 Activity 4: Question 8, 9.

Activity 1

Approach Class

Aim To show the existence of decimals in real life situations.

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Steps 1. Show concrete materials or diagrams that have decimals on them. Example: (a) The volume of the grape juice is 1.25 litres. (b) The mass of the Milo in the tin is 1.5 kg. (c) The distance of the

road is 2.8 km. 2. Ask pupils to state the type of numbers that shown in 1(a), 1(b) and 1(c). 3. Encourage pupils to give other examples that show decimals in their

daily lives. Then, ask pupils to answer Question 1 in Worksheet 4.1.

Activity 2

Approach Individual or in pairs

Aim To record the length, the thickness or the breadth of objects in decimals through measuring activities.

Steps 1. Pupils measure the thicknesses of a coin, an eraser and exercise book using a ruler.

2. Pupils record their answer in cm (in fractions or decimals) on Question 2 in Worksheet 4.1.

3. Discuss pupils’ answers and explain to them how to write fraction with denominator 10(tenth).

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Activity 3

Approach Class

Aim Pupils will be able to read and write decimals fluently.

Steps 1. Introduce the lesson by reading any decimals from 0.1 to 0.9. Accordingly, ask pupils to write the numbers in words.

2. Show flash cards that have decimals (0.1 – 0.9) and asks pupils to read the numbers.

3. Emphasise that 102 = 0.2 but 5

2 ≠ 0.2.

Pupils answer Question 3 – 7 (or parts of them).

Activity 4

Approach Individual

Aim State the order of 0.1 – 0.9 on a number line.

Steps 1. Have pupils draw a straight line in their exercise books and ask them to divide the line into 10 equal parts.

2. Guide pupils to mark 0, 0.1, 0.2… 0.9 and 1 on the number line. 3. Draw a number line that is divided into 10 equal small parts and then,

mark the points 0 and 1. 4. Ask pupils to mark the decimals (stated by the teacher) on the number

line. Pupils answer Question 8 in Worksheet 4.1.

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Worksheet 4.1 1.

What is the type of number shown in the above diagrams? 2. By measuring, determine: (a) The thickness of a 50 sen. _________________ cm (b) The thickness of two 50 sen. _________________ cm (c) The thickness of an eraser. _________________ cm (d) The thickness of an exercise book. _________________ cm 3. Write the following fractions in decimals.

(a) 101 = (b) 10

2 = (c) 103 =

(d) 104 = (e) 10

5 = (f) 106 =

(g) 107 = (h) 10

8 = (i) 109 =

4. Convert to decimals.

(a) 108 = (b) 10

4 =

(c) 105 = (d) 10

9 =

5

5. Write in fractions. (a) 0.1 = (b) 0.2 = (c) 0.3 = (d) 0.4 = (e) 0.5 = (f) 0.6 = (g) 0.7 = (h) 0.8 = (i) 0.9 = 6. Convert to fractions. (a) 0.4 = (b) 0.9 = (c) 0.6 = (d) 0.1 = 7. Convert from decimals to fractions in tenth or vice versa.

(a) 103 = (b) 0.5 =

(c) 0.7 = (d) 103 =

(e) 108 = (f) 0.2 =

8. Complete the following number lines. (a) (b) (c) 9. Arrange the following decimals in ascending order. (a) 0.6, 0.2, 0.4, 0.1 _________________________________ (b) 1, 0.6, 0.4, 0.8 _________________________________ (c) 0.3, 0, 0.5, 0.2 _________________________________

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 1

0 0.1 0.2 0.9 0.4 0.8 0.6 0.7 1

0 0.1 0.8 0.3 0.4 0.5 0.6 1

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Teacher’s Guide Sheet 4.2 Concept: Represent fractions with denominators 10, 100, 1000 as decimals. Learning Outcomes: 1. Represent fractions 10

1 and 1001 as decimals and vice-versa.

2. Represent fractions with denominators 10, 100 and 1000 as decimals. 3. Read and write decimals to thousandths. 4. Arrange decimals in order. Teaching Aids: (a) A special one-meter ruler for teacher (b) A few one-meter rulers for pupils to do the activities in groups or pairs. (c) Cuts Appendix A into scales and paste it to the back of the ruler in (b) continuously (90 cm long).

(d) Flash Cards.

Note: This lesson consists of two activities. The time given is 40 minutes. These activities are related to the question in Worksheet 4.2: Activity 2: Question 1 – 7.

Activity 1

Approach Class

Aim To introduce 1 cm = 1001 m = 0.01 m.

Steps 1. Use a one-metre ruler to introduce

1 cm = 1001 m = 0.01 m.

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2. Explain that the value of 1001 = 0.01, 100

2 = 0.02. Guide pupils to read 0.25 as ‘zero point two five’ and not ‘zero point twenty-five’.

3. Give exercise to pupils on how convert fractions with denominators of 100 and vice versa using a one-metre ruler.

Example: Teacher shows point 25 cm on the ruler. Pupil A says ‘twenty-five

hundredths metre’; Pupil B says ‘zero point two five metres’.

Activity 2

Approach Groups / in pairs.

Aim To recognize that 1001 = 0.01 m, 100

2 = 0.02 m. And compare the number value correct to 2 decimal places.

Steps 1. Distributes a one-metre ruler to every groups or pairs and then guide pupils to mark the following numbers on the ruler:

0, 0.1, 0.2, 0.3, 0.4, …, 0.9 0, 0.01, 0.02, 0.03, …, 0.09 Check pupils work. 2. Guides pupils to mark 0.11, 0.84 and 0.96 on the ruler. 3. Read any decimals correct to 2 decimal places that are less than 1 and

ask pupils to point the respective scales on their rulers. Ask pupils to answer Question 1 – 4 (or parts of them if the time allocated is not enough).

4. Give exercise to pupils on how to convert fractions in hundredth to decimals and vice versa.

5. Guide pupils to compare the values of 0.1 and 0.01, 0.25 and 0.5 . 6. By using the rulers, let pupils discuss on

0.10 = 10010 = 10

1 = 0.1

0.20 = 10020 = 100

2 = 0.2,

Then, have pupils answer Question 5, 6, and 7.

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Appendix

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Worksheet 4.2 1. Convert to decimals.

(a) 10025 = 0.25 (b) 100

18 =

(c) 10075 = (d) 100

5 =

(e) 1006 = (f) 100

3 =

2. Convert to fractions.

(a) 0.65 = 10065 (b) 0.47 =

(c) 0.94 = (d) 0.02 = (e) 0.07 = (f) 0.05 = 3. Convert the following decimals to fractions in hundredth or vice versa.

(a) 1007 = (b) 0.34 =

(c) 10015 = (d) 0.72 =

(e) 1009 = (f) 0.36 =

4. Complete the following number lines: (a)

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(b)

5. Underline the largest number. (a) 0.01 and 0.1 (b) 0.25 and 0.5 (c) 0.06 and 0.6 (d) 0.49 and 0.5 (e) 0.59 and 0.09 6. Complete the followings.

(a) 0.10 = 10010 = 10

1 = 0.1 (b) 0.20 = = =

(c) 0.30 = = = (d) 0.40 = = = (e) 0.50 = = = (f) 0.60 = = = (g) 0.70 = = = (h) 0.80 = = = (i) 0.90 = = = 7. Arrange the following numbers in ascending order. (a) 0.75, 0.46, 0.88, 0.35 _____________________________ (b) 0.38, 0.10, 0.65, 0.28 _____________________________ (c) 0.7, 0.23, 0.5, 0.46 _____________________________ (d) 0.20, 0.06, 0.5, 0.42 _____________________________

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Teacher’s Guide Sheet 4.3 Concept: Represent fractions with denominators 10, 100, 1000 as decimals. Learning Outcome: 1. Represent fractions with denominators 10, 100 and 1000 as decimals. 2. Read and write decimals to thousandths. 3. Change fractions to decimals and vice-versa. 4. Arrange decimals in order. Teaching Aids: Pencils and rulers brought by the pupils.

Note: This lesson consists of three activities. Time allocated is 40 minutes. These activities are related to questions in Worksheet 4.3 Activity 1: Question 1 – 4 Activity 2: Questions 5 and 6 Activity 3: Question 7

Activity 1

Approach Class

Aim To recognise decimals that have more than two decimal places.

Steps 1. Through discussion, extend the decimals up to 3 decimal places or more based on pattern:

101 = 0.1 10

2 = 0.2

1001 = 0.01 100

2 = 0.02

10001 = 0.001 1000

2 = 0.002

000 101 = 0.0001

2. Discuss how to convert the following fractions in thousandth to decimals :

10008 = 0.008 1000

11 = 0.011

10009 = 0.009 1000

12 = 0.012

12

100010 = 0.010

3. Discuss how to write the following fractions in decimals:

100098 = 0.098 1000

101 = 0.101

100099 = 0.099 1000

102 = 0.102

1000100 = 0.100

4. Discuss how to convert the following fractions in decimals:

10004 = 0.004

100044 = 0.044

1000444 = 0.444

5. Discuss how to convert fractions with denominators of 10 000, 100 000 to decimals and vice versa.

Example:

000 105 = 0.0005 000 10

325 = 0.0325

000 10045 = 0.00045

6. Guide pupils to obtain the following rules:

Ask pupils to answer Questions 1 – 4 in Worksheet 4.3.

Activity 2

Approach Individual / Class

Aim To recognize decimals that are larger than 1.

Steps 1. Have pupils measure the length of a pencil and the length/breadth of a textbook. Then, ask them to record their findings in cm up to one decimal place.

2. Explain how to convert mixed numbers with denominators of 10 to decimals form and vice versa.

Example: 1 101 = 1.1

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(Explain 1 101 = 1 and 10

1

= 1 and 0.1 = 1.1)

2.3 = 2 103

(Explain 2.3 = 2 and 0.3

= 2 and 103

= 2 103 )

3. Explain how to convert mixed numbers of denominator 100 to decimals and vice versa.

Example:

1 1001 = 1.01 (Explain 1 100

1 = 1 and 1001

= 1 and 0.01 = 1.01)

3.45 = 3 10045 (Explain 3.45 = 3 and 0.45

= 3 and 10045

= 3 10045 )

4. Explain how to convert mixed numbers of denominators 1000 and 10 000 to decimals and vice versa. Pupils answer Questions 5 and 6 in Worksheet 4.3.

Activity 3

Approach Individual

Aim To recognize the positions of decimals that are more than 1 on the number line.

Steps 1. Have pupils measure the length of a pencil and the length/breadth of a textbook.

Ask pupils to mark 1.1, 1.5, 1.7 and 1.9 on the number line. 2. Guide pupils to draw a number line as follow:

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Ask pupils to mark 1.12, 1.15, 1.17 and 1.18 on the number line. Draw a number line as follow:

Ask pupils to point the position of 0.021, 0.024, and 0.028 on the number

line. Pupils answer Question 7 in Worksheet 4.3.

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Worksheet 4.3 1. Complete:

(a) 101 = 0.1 (b) 100

1 =

(c) 10001 = (d) 000 10

1 =

(e) 000 1001 =

2. Write in decimals.

(a) 10002 = (b) 1000

7 =

(c) 100036 = (d) 1000

84 =

(e) 1000428 = (f) 1000

583 =

(g) 000 10496 = (h) 000 100

37 =

3. Write in decimals.

(a) 103 = (b) 100

30 =

(c) 10067 = (d) 1000

16 =

(e) 1000258 = (f) 000 10

462 =

4. Write in fractional form without simplifying them. (a) 0.003 = (b) 0.02 = (c) 0.132 = (d) 0.056 = (e) 0.68 = (f) 0.0349 = 5. Convert to decimals.

(a) 2 106 = (b) 1 100

4 =

16

(c) 5 105 = (d) 1 100

85 =

(e) 2 10003 = (f) 1 1000

24 =

(g) 4 1000165 = (h) 2 000 10

549 =

(i) 3 000 10257 =

6. Convert to mixed number and express in the simplest form (if possible).

(a) 1.2 = 1 102 = 1 5

1 (b) 2.5 =

(c) 3.07 = (d) 2.18 = (e) 1.009 = (f) 2.403 = (g) 1.067 = (h) 2.0645 = (i) 1.8704 = 7. Mark the given numbers on the number lines. (a) 1.3, 1.6, 1.8

(b) 2.15, 2.17, 2.13

(c) 1.103, 1.105, 1.108

(d) 5.314, 5.309, 5.321

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Teacher’s Guide Sheet 4.4 Concept: Represent fractions with denominators 10, 100, 1000 as decimals. Learning Outcome: State the place value and value of each digit in decimals. Teaching Aids: Abacus, flash cards

Note: This lesson consists of two activities. Time given is 40 minutes. These activities are related to questions in Worksheet 4.4 Activity 1: Questions 1 and 2 Activity 2: Questions 3 – 5

Activity 1

Approach Class

Aim To identify the number of decimal places in decimals.

Steps 1. Explain that the whole number is named according to its number of digit. Example: 25 - - two digits number 467 - - three digits number Decimal is known according to its number of places after the decimal

point. Example: 0.7 - - decimals with one decimal place 0.25 - - decimals with two decimal places 2.463 - - decimals with three decimal places Introduce the abbreviation d.p. as decimal places. 2. Ask pupils to identify the number of decimal places for the given

numbers. Pupils answer Questions 1 and 2 in Worksheet 4.4.

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Activity 2

Approach Class/Groups

Aim To identify the place value for the digits in decimals and the value represented by each digit.

Steps 1. Revise the place value for a whole number: units, tens, hundreds, and thousands.

Example: For 427, ask pupils to state the value of digit 7, 2 and 4. 2. Show the abacus:

Explain how to represent decimals using abacus. Each pole represents

ten, one, tenth, hundredth and thousandth. 3. Show a number on the abacus and ask pupils to read the number.

Emphasise the place value for each digit. 4. Guide pupils to represent the decimals given on the abacus using beads.

5. Guide pupils to recall that 0.1 = 101 , 0.01 = 100

1 , 0.001 = 10001 .

Discuss and complete the table given.

Hundreds Tens Units Tenths Hundredths Thousandths

427

42.7

0.427

4.27

6. For 4.7689, ask pupils to state the digit that is in place value units, tenths,

hundredths, thousandths and ten thousandths. 7. Discuss the digit value for each digit in 0.425 and 0.333. Emphasise that

the same digit in the different place has different value. Give other examples such as 0.222 and 8.999.

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Worksheet 4.4 1. State the number of decimal places in the following numbers: (a) 0.01 _____ (b) 0.014 _____ (c) 0.426 _____ (d) 8.0406 _____ (e) 9.0007 _____ (f) 6.002 _____ (g) 10.1 _____ (h) 10.03 _____ 2. Write a number that has (a) One decimal place _______________________ (b) Two decimal places _______________________ (c) Three decimal places _______________________ (d) Four decimal places _______________________ 3. State the place value for digit 3 in the following numbers. (a) 6.13 _________________ (b) 15.436 _________________ (c) 41.203 _________________ (d) 10.3 _________________ (e) 253.06 _________________ 4. State the digit of the hundredth place, thousandth place and tenth place for the

given number. (a) 2.135 The hundredth _________ The thousandth _________ The tenth _________ (b) 4.3698 The hundredth _________ The thousandth _________ The tenth _________

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(c) 34.1679 The hundredth _________ The thousandth _________ The tenth _________ 5. For each number below, state the digit 5 in fractions. (a) 2.53 _________ (b) 0.25 _________ (c) 0.135 _________ (d) 4.1085 _________ 6. Using digits 6, 7, 8, 9 and 0, form a three decimal places number that is (a) the largest; (b) the smallest. The digit can be used once only for each number.

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Teacher’s Guide Sheet 4.5 Concept: Represent fractions with denominators 10, 100, 1000 as decimals. Learning Outcome: Round off decimals to the nearest whole number or up to three decimal places. Teaching Aids: Flash cards

Note: This lesson consists of two activities. Time given is 40 minutes. These activities are related to questions in Worksheet 4.5. Activity 1: Question 1 - 5 Activity 2: Question 6 – 8

Activity 1

Approach Class/Groups

Aim To introduce on how to round off decimals.

Steps 1. Inform pupils that decimals can also be rounded off like whole numbers. Example: (a) (Whole number) 42 589 can be rounded off to 42 600 if we round off to the nearest

hundred or 43 000 if we round off to the nearest thousand. (b) (Decimals) A company has a capital of RM17.254 million. To make it easier for

certain discussion, we can state the number as RM17 million or RM17.3 million or RM17.25 million.

2. Have pupils discuss in small group on: (a) How to round off the decimal numbers to whole numbers? 15.2, 15.4, 15.5, 15.6, 15.7 15.61, 15.62, 15.63, 15.64, 15.65, 15.66 (b) How to round off the following numbers to one decimal place? 15.42, 15.44, 15.45, 15.46, 15.47 15.441, 15.442, 15.443, 15.444, 15.445, 15.446

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3. Introduce the clues of round off decimals: Retain the digit in the stated decimal place that we want to round off if

the digit in the right is less than 5. Add 1 to the digit in the stated decimal place that we want to round off if

the digit in the right is 5 or more.

4. In groups, extend the activities to two and three decimal places. Give

some examples. Example: 15.4452 rounding off to two decimal places 15.4452 rounding off to three decimal places 5. Discuss cases such as 0.304 is equal 0.30: if we round off to two decimal

places. 0.495 equals 0.50 if rounded off to two decimal places; 0.495 equals 0.5 if rounded off to one decimal place. Pupils answer Question 1 – 5 in Worksheet 4.5.

Activity 2

Approach Class

Aim Pupils will be able to competently round off decimals.

Steps 1. Show 1.5 on a card and state that the number has been rounded off to 1 decimal place. Discuss with pupils what the possible number is.

2. Expand this activity to numbers with more than one decimal places.

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Worksheet 4.5 1. Round off the following numbers to the nearest whole numbers. (a) 42.7 ___________ (b) 1.6 ___________ (c) 100.5 ___________ (d) 17.4 ___________ (e) 2.45 ___________ (f) 0.48 ___________ 2. Round off the following numbers to one decimal place. (a) 0.34 ___________ (b) 10.36 ___________ (c) 0.05 ___________ (d) 3.44 ___________ (e) 1.047 ___________ (f) 58.95 ___________ 3. Round off the following numbers to two decimal places. (a) 8.148 ___________ (b) 0.014 ___________ (c) 1.657 ___________ (d) 20.105 ___________ (e) 5.397 ___________ (f) 3.1995 ___________ 4. Round off the following numbers to three decimal places. (a) 0.0055 ___________ (b) 1.0464 ___________ (c) 23.9732 ___________ (d) 0.1048 ___________ (e) 0.14647 ___________ (f) 2.3997 ___________ 5. Round off the following numbers to 3 d.p., 2 d.p. and 1 d.p.: (a) 9.5843 ___________ (3 d.p.) (b) 12.7459 ___________ (3 d.p.) ___________ (2.d.p.) ___________ (2 d.p.) ___________ (1 d.p.) ___________ (1 d.p.)

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(c) 0.4949 ___________ (3 d.p.) (d) 0.1296 ___________ (3 d.p.) ___________ (2 d.p.) ___________ (2 d.p.) ___________ (1 d.p.) ___________ (1 d.p.) (e) 2.60548 ___________ (3 d.p.) (f) 0.09947 ___________ (3 d.p.) ___________ (2 d.p.) ___________ (2 d.p.) ___________ (1 d.p.) ___________ (1 d.p.) 6. When we round off a number, the answer is 4.54. Which of the following is the

possible number? (a) 4.5846 (b) 4.593 (c) 4.597 (d) 4.546 (e) 4.539 (f) 4.543 7. When we round off a number, the answer is 5.60. Which of the following is the

possible number? (a) 5.604 (b) 5.595 (c) 5.590 (d) 5.606 (e) 5.592 (f) 5.605 8. Miss Goh needs 3.7 m cloth to make a baju kurung. She has a piece of cloth

measuring 3.65 m. Is it possible for Miss Goh to make the baju kurung? ____________________________ Give reason for your answer: ___________________________________________________________________ __________________________________________________________________

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Test 4.1 Name: _______________________________________________________

Class: _______________________________________________________

1. Write the following fractions in decimals.

(a) 107 = (b) 100

15 =

(c) 2 1008 = (d) 1000

8 =

(e) 11 1000104 =

2. Convert the decimals to fractions or mixed number in its simplest form. (a) 0.8 = (b) 0.45 = (c) 0.025 = (d) 5.31 = (e) 4.064 = 3. Fill in the blanks on the number lines below: (a)

(b)

(c)

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(d)

(e)

4. Underline the largest number. (a) 0.2, 0.02, 0.002 (b) 0.9, 0.39, 0.93 (c) 0.478, 0.784, 0.487 (d) 6.1, 6.099, 6.0999 (e) 11.356, 11.386, 11.366 5. Underline the smallest number. (a) Zero point three nine four Zero point four eight six (b) Zero point six eight nine Zero point six nine eight (c) Five point zero four eight Five point zero four six 6. Fill in the blanks with the numbers given in the brackets. (a) 0.3 is larger than _____________. (0.33, 0.003) (b) 4.07 is smaller than ___________. (4.7, 4.007) (c) 1.14 is equal to ______________. (1.140, 1.014) 7. Arrange the following numbers in ascending order. (a) 0.57, 0.64, 0.44, 0.35 ________________________________ (b) 0.05, 0.084, 0.066, 0.83 ________________________________

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8. Arrange the following numbers in descending order. (a) 10.088, 10.090, 10.086, 10.092 _________________________________ (b) 34.20, 34.07, 34.5, 34.49 _________________________________ 9. Round off the following numbers to the nearest place as stated in the brackets. (a) 5.045 ___________________ (1 d.p.) (b) 14.8079 ___________________ (2 d.p.) (c) 0.19023 ___________________ (3 d.p.) 10. Round off 42.6495 to (a) 3 decimal places ___________________ (b) 2 decimal places ___________________ (c) 1 decimal place ___________________ 11. For each number, write the value of underlined digit. (a) 7.8264 ___________________ (b) 0.6748 ___________________ (c) 0.3846 ___________________

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Teacher’s Guide Sheet 4.6 Concept: Add Decimals Learning Outcomes: Add decimals Teaching Aids: Flash Card

Note: This lesson consists of four activities. Time allocated is 40 minutes. These activities are related to questions in Worksheet 4.6. Activity 1: Questions 1(a) – (d), 2(a) – (b), 3(a) – (d) Activity 2: Questions 1(e) – (h), 2(c) – (h), 3(e) – (f) Activity 3: Questions 5 and 6

Activity 1

Approach Class

Aim To recognize addition of the whole number with the decimal and addition of two decimals (in one decimal place) and the sum is less than 1.

Steps 1. Discuss the example as below:

3 105 = 3 + 10

5

Hence, 3.5 = 3 + 0.5 Show on the number line:

Verbal discussion: 1 + 0.2 = ____________________ 0.4 + 2 = ____________________ 2. Discuss this example 0.2 + 0.6 = ____________________ and show on

the number line:

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3. Recognize

Emphasise that the decimals should be arranged vertically based on

their place values. Carry out the verbal lesson with flash card. 4. Pupils answer question 1(a) – (d), 2(a) – (b) and 3(a) – (d) or a few

questions from that.

Activity 2

Approach Class

Aim To recognize addition of decimals that includes regrouping.

Steps 1. Discuss case that includes regrouping such as: 0.8 + 0.4 = _____________. Show on the number line and carry out the

verbal exercise.

2. Ask pupils to observe the pattern: 0.4 + 0.1 = 0.5 0.4 + 0.2 = 0.6 0.4 + 0.3 = 0.4 + 0.4 = ………………...... 0.4 + 0.9 =

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3. Explain the case such as 3.2 + 1.4 = _______________ (without

regrouping) and show on the number line (use two lines):

Show how to add

4. Pupils answer question 1(e) – (h), 2(c) – (h) and 3(e) – (f) or a few

questions from that.

Activity 3

Approach Class

Aim To recognize addition of decimals to two decimal places.

Steps 1. Discuss how to add decimals up to two decimal places in standard algorithm (without regrouping):

Emphasise the importance of arranging decimals based on their place

values. Use flash card as below to carry out the activity:

2. Discuss the regrouping case. 3. Pupils answer Question number 4 and 5.

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Activity 4

Approach Quiz

Aim To reinforce addition of decimals skill

Steps 1. Read five questions. 2. Pupils write the answers in a paper.

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Worksheet 4.6 1. Find the sum of the following: (a) 2 + 0.7 = (b) 0.8 + 8 = (c) 0.6 + 7 = (d) 0.3 + 0.5 = (e) 0.4 + 0.9 = (f) 0.4 + 0.6 = (g) 1.5 + 2.6 = (h) 10.6 + 6.7 = 2. Find the sum of: (a) (b)

(c) (d)

(e) (f)

(g) (h)

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3. Add 0.5 to each of the following: (a) 2 ________ (b) 5 ________ (c) 13 ________ (d) 0.3 ________ (e) 0.6 ________ (f) 2.7 ________ 4. Add: (a) (b)

(c)

5. Calculate: (a) 0.13 + 0.24 = (b) 2.59 + 1.24 = (c) 18.18 + 1.43 = (d) 0.42 + 0.64 = (e) 1.08 + 3.02 = (f) 4.65 + 3.36 =

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Teacher’s Guide Sheet 4.7 Concept: Add Decimals Learning Outcomes: 1. Add decimals. 2. Solve problems involving addition of decimals.

Note: This lesson consists of one activity only and pupils can try to answer Worksheet 4.7. The time allocated is 40 minutes.

Activity 1

Approach Class

Aim To solve problems involving addition of decimals up to two decimal places.

Steps 1. Discuss daily situation which involves calculation of decimals such as 2.5 + 3.2 = 5.7.

Example: Two watermelons have masses of 2.5 kg and 3.2 kg. A customer buys

both of them. What is the total mass of the watermelons? 2. Encourage pupils to create their own story based on mathematical

sentences such as 2.5 + 3.2 = 5.7. 3. Ask pupils to create any problem which involves addition of decimals up

to two decimal places. Have pupils solve the problem. 4. Pupils answer Worksheet 4.7.

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Worksheet 4.7 1. The total height of Ahmad and the box =

2. The total mass of Siti and the cat =

3. The total volume of water in container A after water in container B had been poured

in it =

4. Mr. Hassan’s family used 20.8 units of electric power in January. In February, they

used 24.6 units of electric power. Find the total units of electric power that had been used in those 2 months.

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5. Car journey from town A to town B needs 45.26 litres petrol. Journey from town B to town C needs 36.75 litres petrol. Find the total amount of petrol needed for journey from town A to town C through town B.

6. The mass and height of Bala is 55.4 kg and 1.42 m respectively. Pek Hong’s mass

is 54.6 kg and his height is 1.5 m. Find the total of their masses. 7. There are four chickens with masses 1.21 kg, 1.82 kg, 1.56 kg, and 1.42 kg

respectively. Ali buys two chickens that have less masses and Fatimah buys another two.

(a) Calculate the total weight of the chickens bought by Ali. (b) Calculate the total weight of the chickens bought by Fatimah.

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Teacher’s Guide Sheet 4.8 Concept: Addition of Decimals Learning Outcomes: Addition of decimals

Note: This lesson consists of four activities. Time given is 40 minutes. These activities are related to questions in Worksheet 4.8. Activity 1: Questions 1 & 2 Activity 2: Questions 4(a) – (f), 5(a) & (d), 6(a) – (d) Activity 3: Questions 3, 4(g) – (h), 5 (b) – (c) & (e) – (f) Activity 4: Questions 7 & 8

Activity 1

Approach Class

Aim To recognize addition of decimals with different decimal places (up to two decimal places).

Steps 1. Discuss how to add decimals with different decimal places in standard form.

Emphasise that the questions in sentence form should be converted to the standard form before doing the calculation.

Emphasise that while converting to standard form, the digits must be arranged according to place value and empty space must be filled with zero so that the number of decimal places are equal.

Give first example that does not involve regrouping process and after that followed by example that involves regrouping process.

2. Pupils answer Questions 1 and 2.

Activity 2

Approach Class

Aim To recognize addition of two decimals with three decimal places.

38

Steps 1. Introduce addition of two decimals that have three decimal places – the

same method with addition of decimals that have one or two decimal places.

2. Pupils answer Questions 4(a) – (f), 5(a) & (d), 6(a) – (d).

Activity 3

Approach Class

Aim To recognize addition of more than two decimals that have equal or unequal decimal places.

Steps 1. Guide pupils to add decimals that have more than two decimal places. 2. Explain on how to add decimals with different number of decimal places. 3. Pupils answer Question 3, 4(g) – (h), 5(b) – (c) & (e) – (f).

Activity 4

Approach Class

Aim To solve problems involving addition of decimals up to three decimal places.

Steps 1. Show problems that involve addition of (a) two decimals up to 3 decimal places. (b) more than two decimals, and discuss how to solve the problems. Remind pupils to write the solution in the form of mathematical sentence. 2. Pupils answer Questions 7 & 8.

39

Worksheet 4.8 1. Find the sum of: (a) (b)

(c) (d)

(e) (f)

2. Calculate: (a) 2.5 + 0.24 = (b) 4.65 + 10.7 = (c) 1.03 + 9.7 = (d) 4.51 + 6.5 = (e) 24.1 + 5.93 = (f) 13.89 + 7.1 = 3. Find the sum of: (a) (b)

40

(c) (d)

(e) (f)

4. Find the sum of: (a) (b)

(c) (d)

(e) (f)

(g) (h)

41

5. Find the sum of: (a) 0.025 + 1.147 = (b) 1.14 + 0.024 + 1.19 = (c) 0.5 + 4.207 + 1.19 = (d) 15.651 + 14.39 = (e) 1.11 + 0.012 + 2.202 = (f) 4 + 0.009 + 5.43 = 6. Add each pair of given numbers and give the answer in 2 decimal places. (a) 0.189, 1.172 (b) 4.65, 5.097 (c) 11.35, 6.009 (d) 1.072, 3.888 7. Aminah bought 3 jackfruits that weigh 1.245 kg, 1.6 kg and 2.85 kg respectively.

Find the total mass of the jackfruits. If she carries all of the fruits inside a basket that weighs 0.68 kg, find the total mass that she is carrying.

8. Adam’s weight is 28.87 kg. His father’s weight is 35.46 kg more than Adam’s. Find

the total weight of Adam and his father.

42

Teacher’s Guide Sheet 4.9 Concept: Subtraction of decimals Learning Outcomes: Subtraction of decimals

Note: This lesson consists of two activities and the time given is 40 minutes. These activities are related to questions in Worksheet 4.9. Activity 1: Questions 1, 2 & 3 Activity 2: Questions 4 & 5

Activity 1

Approach Class

Aim To recognize subtraction of decimals up to 3 decimal places without regrouping.

Steps 1. Explain how to subtract decimals (1 decimal place) less than 1 on the number line.

Example: 0.8 – 0.2 = 0.6

2. Explain how to subtract decimals in standard form. Example: (a) (b)

Emphasise that decimal points should be arranged vertically. 3. Explain how to subtract decimals (2 decimal places and 3 decimal

places) without regrouping.

43

Examples: (a) (b)

(c) (d)

4. Discuss on how to subtract decimals with different decimal places. (a) (b)

5. Pupils try out Questions 1, 2 & 3.

Activity 2

Approach Class

Aim To recognize subtraction of decimals up to 3 decimal places (including regrouping).

Steps 1. Explain how to subtract decimals (1 decimal place) in standard form with regrouping.

Examples: (a) (b)

2. Explain how to subtract decimals (2 decimal places) in standard form

with regrouping. Example:

44

3. Explain how to subtract decimals (3 decimal places) in standard form with regrouping.

Example:

4. Give some examples on subtraction of decimals with different decimal

places. Example: (a) (b)

5. Reinforce pupils’ understanding on the similarity of subtracting whole

numbers with subtracting decimals and the importance of the decimal point.

6. Pupils answer Questions 4 and 5.

45

Worksheet 4.9 1. Solve the subtractions below: (a) 0.7 – 0.2 = (b) 0.8 – 0.5 = (c) 1.6 – 0.3 = (d) 2.4 – 0.4 = (e) 4.6 – 1.5 = 2. Solve: (a) 0.26 – 0.12 = (b) 0.54 – 0.04 = (c) 2.18 – 1.16 = (d) 0.719 – 0.306 = (e) 1.843 – 1.623 = (f) 2.086 – 1.074 = 3. Calculate: (a) 0.75 – 0.4 = (b) 1.43 – 1.2 = (c) 1.316 – 0.2 = (d) 4.625 – 1.42 =

46

4. Solve: (a) (b) 3.5 – 1.8 =

(c) (d)

(e) 4.36 – 2.58 = (f) 3.826 – 2.765 = 5. Calculate: (a) 3 – 1.5 = (b) 2 – 1.35 = (c) 3.4 – 2.416 = (d) 2.5 – 1.63 = (e) 1.06 – 0.128 = (f) 3.275 – 0.89 =

47

Teacher’s Guide Sheet 4.10 Concept: Subtraction of decimals Learning Outcomes: 1. Subtraction of decimals. 2. Solve problems involving subtraction of decimals.

Note: This lesson consists of one activity and the time given is 40 minutes. Have pupils try out Worksheet 4.10.

Activity 1

Approach Class

Aim Solve problems involving subtraction of decimals.

Steps 1. Discuss any daily situations that involve calculation of decimals such as 1.74 – 1.59 = Example: Mr. Ali is 1.74 m tall and his son is 1.59 m tall. Find the difference

between their heights. 2. Have pupils create their own situations based on “1.74 – 1.59”. 3. Have pupils create any situation involving subtraction of two decimals

and ask them to solve it. 4. Pupils solve Worksheet 4.10. Example: The height of Mr. Ali: 1.74 m The height of his son: 1.59 m Difference: 1.74 m – 1.59 m =

48

Worksheet 4.10 1.

(a) Height of Ali = Height of Abu = Height of Bakar = (b) Find the difference of heights between Abu and Ali. (c) Find the difference of heights between Abu and Bakar. (d) How many metres is Bakar higher than Ali? 2.

(a) Volume of water in container A = Volume of water in container B =

49

(b) Find the difference between the volumes of water in container A and container B.

3. The area of En. Samad’s orchard is 94.5 m2. He planted it with durian and rambutan

trees. 28.3 m2 of the area was planted with rambutan trees. Is the area planted with durian trees larger than that of rambutan trees? Find the difference between both areas.

4. The 1.5 litres glass container contains 0.7 kg sugar. 0.55 kg of the sugar was used

to bake a cake. How much sugar is left in the container? 5. Nona has a piece of 4.5 m cloth. She wants to make two shirts that need 1.8 m cloth

and 2.3 m cloth respectively. (a) Find the total of cloth that needs to be used. (b) How many metres of cloth are left?

50

Teacher’s Guide Sheet 4.11 Concept: Subtraction of decimals Learning Outcome: Subtraction of decimals

Note: This lesson consists of two activities and the time given is 40 minutes. These activities are related to questions in Worksheet 4.11: Activity 1: Questions 1 – 3 Activity 2: Questions 4 – 7

Activity 1

Approach Class

Aim To recognize combined operations of decimals involving addition and subtraction.

Steps 1. Discuss some examples of combined operations for whole numbers that involve addition and subtraction. (Revision).

2. Discuss how to calculate combined operations that include decimals. Example: (a) 1.35 + 1.26 – 0.87 (b) 4.6 – 2.14 + 1.2 Emphasise that the important rule to do the addition and subtraction is

from left to right. 3. Pupils try out questions 1 – 3 on Worksheet 4.11 or part of the questions.

Activity 2

Approach Class

Aim Solve problems involving combined operations of addition, subtraction, multiplication and division of decimals.

51

Steps 1. Discuss daily situations that involve combined operations of decimals. Example: Hasnah wants to make a cake. She needs 0.7 kg flour but she only has

0.3 kg flour. She buys another 0.5 kg flour. After she makes the cake, how much flour is left?

2. Pupils try out questions 4 – 7.

52

Worksheet 4.11 1. Solve: (a) 1.5 + 3.8 – 2.9 = (b) 3.12 + 1.63 – 2.85 = (c) 4 + 2.76 – 5.28 = (d) 3.145 + 1.673 – 2.418 = (e) 10.25 + 5.64 – 8.007 = 2. Calculate: (a) 2.6 – 1.8 + 2.3 = (b) 4.6 – 1.27 + 0.3 = (c) 5 – 2.34 + 2.34 = (d) 5 – 2.3 + 2.35 = (e) 3.674 + 1.086 + 2.334 =

53

3. Calculate: (a) 13.3 + 8.9 – 21.4 = (b) 20 – 13.78 + 15.5 = (c) 12.374 + 18.06 – 30 = (d) 0.617 – 0.508 + 1.9 = 4. En. Kassim wants to bring two luggages on flight. The weights of the luggages are

10.5 kg and 12.82 kg. If he is only allowed to bring along 20 kg, how many kg is the bags overweigh?

5. During a festival, Shamsul prepared 50 litres of syrup in a container. 37.4 litres

syrup were consumed by noon. Then he prepared another 46.8 litres of syrup. How much syrup was in the container now?

6. Devi has 4.38 m ribbon. She gives Sarah 2.5 m to wrap a present. Then Devi buys

another 3.75 m ribbon. How many metres of ribbon does Devi have? 7. Ali poured 0.75 litre of water into a container that contains 0.6 litre water initially. If

the container can take only 1.2 litres, how much water will spill out?

54

Test 4.2 Name: _______________________________________________________

Class: _______________________________________________________

1. Find the sum of (a) (b)

(c) (d)

2. Calculate (a) (b)

(c) (d

3. Solve (a) (b)

(c) (d)

55

4. Solve (a) 7.74 + 2.06 (b) 56.419 + 18.69 (c) 70.5 – 4.44 (d) 68.168 – 39.2 5. Add (a) 0.56 + 1.48 + 4.67 (b) 1.08 + 0.9 + 8.137 6. Solve (a) 6.048 – 4.326 + 3.109 (b) 3.25 + 7.212 – 6.369 7. The mass of four chickens are 2.4 kg, 1.8 kg, 3 kg and 1.5 kg respectively. Find the

total mass for all the chickens. 8. En. Abu’s car tank contains 40 litres of petrol. After a journey, the car used 3.7 litres

of petrol. Then, he fills up another 8.9 litres. How many litres of petrol are in the tank now?

9. A seller had 60.4 m white cloth. He sold part of the cloth to his customer and still

had 44.6 m of cloth. Find the length of the cloth that he sold. 10. Ali brought 25.6 kg of langsat from his orchard. On his way back, he gave 6.3 kg of

the langsat to Abu and another 8.6 kg to Chong Fatt. How many kg of langsat does Ahmad still have?

56

Teacher’s Guide Sheet 4.12 Concept: Multiplication of decimals Learning Outcomes: Multiply two or more decimals

Note: This lesson is consisting of three activities. The time needed is 80 minutes. These activities are related to questions in Worksheet 4.12: Activity 1: Question 1 & 2 Activity 2: Question 3 & 4 Activity 3: Question 5 & 6

Activity 1

Approach Class

Aim Understand the meaning of 10 × 0.1, 0.1 × 10, 10 × 0.2, 0.2 × 10; and also the multiplication of decimals by 10 in algorithm method.

Steps 1. Discuss the meaning of 10 × 0.1 and 0.1 × 10 2. Explain that 10 × 0.1 = 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 or

10 × 0.1 = 10 × 101 (10 times 10

1 )

= 1, and

0.1 × 10 = 101 × 10

= 1 Thus 10 × 0.1 = 0.1 × 10. 3. Discuss 10 × 0.2 = 0.2 × 10 = 2 10 × 0.3 = 0.3 × 10 = 3

57

Guide pupils to arrive at the clues of shifting the decimal point to the right for multiplication of decimals by 10.

* Emphasise that the product is larger than the given decimals. 4. Explain the multiplication of decimals by 10 in algorithm method. Example:

Emphasise the following clues: 1) Ignore the decimal point when multiplying. 2) Find the total number of decimal places of the numbers being

multiplied. 3) Based on step 2, put the decimal point to your answer. 5. Discuss the steps to multiply decimals that are greater than 1 (1 d.p.) by

10. Example: 2.4 × 10 = 24.0 = 24

6. Explain the multiplication of decimals with 2 d.p. and 3 d.p. by 10. Example: (a)

(b)

7. Pupils answer Questions 1 & 2 in Worksheet 4.12.

58

Activity 2

Approach Class

Aim Multiply decimals by 100.

Steps 1. Explain 0.1 × 100 = 0.1 × 10 × 10 = 1 × 10 = 10

2. Discuss the multiplication of decimals by 100. Examples: (a)

(b)

(c)

3. Pupils answer questions 3 & 4 in Worksheet 4.12.

59

Activity 3

Approach Class

Aim Multiply decimals by 1000.

Steps 1. Explain 0.1 × 1000 = 0.1 × 10 × 100 = 1 × 100 = 100

2. Discuss the multiplication of decimals by 1000. Examples: (a)

(b)

(c)

3. Pupils answer questions 5 & 6 in Worksheet 4.12.

60

Worksheet 4.12 1. Solve (a) 0.3 × 10 = (b) 7.5 × 10 = (c) 3.82 × 10 = (d) 1.467 × 10 = (e) 10 × 1.5 = (f) 10 × 2.46 = (g) 10 × 15.489 = 2. Solve (a) (b)

(c) (d)

(e)

3. Solve (a) 0.4 × 100 (b) 0.25 × 100 (c) 1.47 × 100 (d) 0.356 × 100 (e) 6.407 × 100 (f) 100 × 14.6 (g) 100 × 0.08 (h) 100 × 3.333

61

4. Calculate (a) (b)

(c) (d)

5. Solve (a) 0.5 × 1000 (b) 7.4 × 1000 (c) 0.03 × 1000 (d) 6.95 × 1000 (e) 1000 × 0.49 (f) 1000 × 44.9 (g) 1000 × 0.008 (h) 1000 × 1.196 6. Calculate (a) (b)

(c) (d)

(e)

62

Teacher’s Guide Sheet 4.13 Concept: Multiplication of decimals Learning Outcome: Multiply two or more decimals

Note: This lesson consists of two activities and the time needed is 40 minutes. Relation between activities and the questions in Worksheet 4.13: Activity 1: Questions 1 – 3 Activity 2: Questions 4, 5 & 6

Activity 1

Approach Class

Aim Multiply decimals by one digit numbers.

Steps 1. Discuss the method to calculate 3 × 0.2 and 0.2 × 3. 3 × 0.2 = 0.2 + 0.2 + 0.2 = 0.6

3 × 0.2 = 3 × 102

= 106

= 0.6

0.2 × 3 = 102 × 3

= 106

= 0.6 2. Explain the calculation in standard algorithm form.

3. Discuss other examples that involve multiplication of decimals with one

decimal place by one digit numbers.

63

Example:

4. Discuss the method of multiplying decimals with two decimal places by

one digit numbers. Example: (a) (b)

5. Discuss the method of multiplying decimals with three decimal places by

one digit numbers. Example: (a) (b)

6. Pupils answer Questions 1, 2 & 3 in Worksheet 4.13.

Activity 2

Approach Class

Aim Multiply decimals by two digits numbers.

Steps 1. Discuss the method of multiplying decimals with one decimal place by two digits numbers.

Example:

Emphasise that the multiplication is carried out the same as the

64

multiplication of whole numbers, but make sure the number of decimal places in the product is the same as those of decimals being multiplied.

2. Discuss the method of multiplying decimals with two decimal places by two digits numbers.

Example:

3. Discuss the method of multiplying decimals with three decimal places by

two digits numbers. Example:

4. Pupils answer Questions 4, 5 & 6 in Worksheet 4.13.

65

Worksheet 4.13 1. (a) 0.8 × 4 = (b) 5.5 × 5 = (c) 20.2 × 3 = (d) 6 × 0.7 = (e) 8 × 1.5 = (f) 5 × 12.4 = 2. (a) 0.67 × 8 = (b) 2.34 × 5 = (c) 19.07 × 3 = (d) 2 × 0.35 = (e) 7 × 8.42 = (f) 6 × 58.94 = 3. (a) 0.286 × 7 = (b) 4.158 × 9 = (c) 14.973 × 4 = (d) 6 × 0.109 = (e) 5 × 8.742 = (f) 3 × 45.666 =

66

4. (a) 40 × 0.2 = (b) 34 × 1.2 = (c) 25 × 4.6 = (d) 0.6 × 44 = (e) 3.2 × 16 = (f) 4.5 × 21 = 5. (a) 12 × 0.08 = (b) 37 × 1.69 = (c) 60 × 3.88 = (d) 0.92 × 15 = (e) 8.04 × 23 = (f) 12.12 × 56 = 6. (a) 27 × 0.111 = (b) 7.213 × 16 = (c) 29 × 3.505 = (d) 10.514 × 67 = (e) 86 × 0.234 = (f) 1.009 × 50 =

67

Teacher’s Guide Sheet 4.14 Concept: Multiplication of Decimals Learning Outcome: Multiply two or more decimals Teaching Aids: 100 squares grid paper

Note: This lesson consists of four activities and the time needed is 80 minutes. The relationship between activity and question in Worksheet 4.14: Activity 1: Question 1 Activity 2: Question 2 Activity 3: Question 3 Activity 4: Question 4

Activity 1

Approach Class

Aim Pupils will be able to competently multiply two decimals with one decimal place.

Steps 1. Discuss the meaning of 0.2 × 0.3 with area concept.

Also show that : 0.2 × 0.3 = 102 × 10

3

= 1006

68

= 0.06 2. Explain the multiplication of two decimals (1 d.p.) in algorithm method. Example: (a)

Emphasise that the number of decimal places in the product is equal to

the sum of decimal places of the numbers being multiplied. If necessary, write zero to the left of the product to complete the decimals.

(b)

3. Pupils answer Question 1 in Worksheet 4.14.

Activity 2

Approach Class

Aim Pupils will be able to competently multiply decimal (2 d.p.) by decimal (1 d.p.) in algorithm method.

Steps 1. Discuss the steps to multiply decimal (2 d.p.) by decimal (1 d.p.) in algorithm method.

Example: (a)

Also shows in fractions:

0.03 × 0.2 = 1003 × 10

2

= 10006

= 0.006

69

(b)


Activity 3

Approach Class



Example: (a)

0.03 × 0.02 = 100

3 × 1002

= 100006

= 0.0006 (b)


70

Activity 4

Approach Class



Example: (a)

0.003 × 0.2 = 1000

3 × 102

= 100006

= 0.0006 (b)


71

Worksheet 4.14 1. Calculate (a) 0.5 × 0.6 (b) 0.8 × 1.9 (c) 2.3 × 5.6 (d) 1.2 × 1.2 (e) 34.5 × 1.6 (f) 10.5 × 11.2 2. Calculate (a) 0.14 × 0.3 (b) 2.02 × 0.5 (c) 12.34 × 0.2 (d) 0.6 × 0.07 (e) 2.4 × 1.56 (f) 0.8 × 6.7 3. Calculate (a) 0.05 × 0.67 (b) 2.34 × 0.6

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(c) 6.06 × 6.06 (d) 14.29 × 1.15 (e) 50.01 × 2.28 (f) 12.13 × 20.54 4. Calculate (a) 0.125 × 0.8 (b) 3.003 × 0.9 (c) 5.408 × 4.1 (d) 1.3 × 0.618 (e) 6.2 × 6.147 (f) 11.027 × 3.4

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Teacher’s Guide Sheet 4.15 Concept: Multiplication of decimals Learning Outcome: Solve problems involving multiplications of decimals.

Note: This lesson consists of only one activity and time needed is 40 minutes.

Activity 1

Approach Class

Aim Pupils will be able to competently solve problems involving multiplication of decimals.

Steps 1. Discuss examples of problem solving that involves multiplication of decimals by whole numbers and multiplication of decimals by decimals.

Example 1: The thickness of a mathematics text book is 2.3 cm. If 8 mathematics

text books are being stacked together, what is the height of the book stack?

Guide pupils to write and calculate 2.3 cm × 8 = Example 2: The cost of a kilogram of rice is RM1.55. What is the total cost of 3.5 kg

of rice? Guide pupils to get RM 1.55 × 3.5 = RM 5.425 = RM 5.43 (to the nearest sen)

2. Pupils answer questions in Worksheet 4.15.

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Worksheet 4.15 1. (a)

Find the area of the above rectangle. (b)

The above diagram shows the base of a house. Find the area. 2. A litre petrol costs RM1.13. If Ali buys 10.5 litres petrol, what is the total cost of the

petrol? Give your answer to the nearest sen. 3. A kilogram of watermelon costs RM1.45. If Hassan buys 3.7 kg of watermelon, how

much he should pay? Give your answer to the nearest sen. 4. A bottle contains 1.25 litres Sarsi. Guests of a birthday party drank 34 bottles of

Sarsi. How many litres of Sarsi have been drunk? 5. A meter of cloth costs RM4.99. Pn. Rohani bought 2.75 meter cloth to make a pair

of clothes for her daughter. Find the cost of a meter cloth. Give your answer to the nearest sen.

75

Test 4.3 Name: _______________________________________________________

Class: _______________________________________________________

1. Calculate (a) 1.4 × 10 (b) 0.8 × 10 (c) 0.32 × 100 (d) 6.04 × 100 (e) 2.158 × 1000 (f) 0.97 × 1000 2. Solve (a) 21.3 × 4 (b) 4.65 × 7 (c) 20 × 0.813 (d) 1.7 × 13 (e) 3.28 × 36 3. Calculate (a) 0.2 × 0.3 (b) 4.5 × 3.6

76

(c) 0.81 × 2.7 (d) 1.5 × 0.519 (e) 12.4 × 12.4 4. What is the volume of 12 bottles drink if a bottle contains 1.25 litres drink? 5. The diagram below shows a base of a house in rectangular shape with15.8 m length

and 7.6 m width. Find the (a) perimeter; (b) area.

6. Pn. Salmah buys two slices of meat weighed 3.8 kg and 2.8 kg. Mrs. Lee buys a

slice of meat weighed 2.7 kg. Find the difference of weights between the meats they bought.

77

Teacher’s Guide Sheet 4.16 Concept: Division of Decimals Learning Outcome: Divide a decimal by a whole number. Teaching Aids: Flash card

Note: This lesson consists of two activities and the time needed is 40 minutes. The relationship between activity and question in Worksheet 4.16: Activity 1: Question 1 – 3.

Activity 1

Approach Class

Aim Calculate the division of whole numbers by 10, 100 and 1000 where the quotient is decimals.

Steps 1. Revise the fraction concept as numerator divided by denominator. Example:

52 = 2 ÷ 5

Thus, 2 ÷ 5 = 52

2. Discuss the division of whole numbers by 10, which gives the quotient to the nearest 1 d.p..

Example:

(a) 2 ÷ 10 = 102

= 0.2

(b) 25 ÷ 10 = 1025

= 2 105

= 2.5

78

(c) 124 ÷ 10 = 10124

= 12 104

= 12.4 Guide pupils to observe the pattern as follows: When a whole number is divided by 10, rewrite the whole number

then make it as decimals with 1 d.p. 3. Pupils answer Question 1 in Worksheet 4.16. 4. Discuss the division of whole numbers by 100, which gives the quotient

to the nearest 2 d.p.. Example:

(a) 5 ÷ 100 = 1005

= 0.05

(b) 25 ÷ 100 = 10025

= 0.25

(c) 125 ÷ 100 = 100125

= 1 10025

= 1.25 Guide pupils to observe the pattern as follows: When a whole number is divided by 100, rewrite the whole number

then make it as decimals with 2 d.p.. 5. Pupils answer Question 2 in Worksheet 4.16. 6. Discuss the division of whole numbers by 1000, which gives the quotient

to the nearest 3 d.p.. Example:

(a) 5 ÷ 1000 = 10005

= 0.005

(b) 25 ÷ 1000 = 100025

= 0.025

(c) 125 ÷ 1000 = 1000125

= 0.125

(d) 3125 ÷ 1000 = 10003125

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= 3 1000125

= 3.125 Guide pupils to observe the pattern as follows: When a whole number is divided by 1000, rewrite the whole number then

make it as decimals with 3 d.p.. 7. Pupils answer Question 3 in Worksheet 4.16.

Activity 2

Approach Competition

Aim Pupils will be able to competently divide whole numbers by 10, 100 and 1000 where the quotient is decimals.

Steps 1. Divide pupils into two groups to perform the division of whole numbers by 10, 100 and 1000.

2. Use flash cards only to ask questions or display the questions. Pupils answer verbally.

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Worksheet 4.16 1. Give your answer in decimals: (a) 6 ÷ 10 = (b) 10 ÷ 10 =

(c) 234 ÷ 10 = (d) 1084 =

(e) 10260 = (f) 10

3579 =

2. Give your answer in decimals: (a) 4 ÷ 100 = (b) 37÷ 100 =

(c) 592 ÷ 1000 = (d) 1008 =

(e) 10050 = (f) 100

63 =

3. Give your answer in decimals: (a) 5 ÷ 1000 = (b) 50 ÷ 1000 =

(c) 559 ÷ 1000 = (d) 1000125 =

(e) 10004321 =

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Teacher’s Guide Sheet 4.17 Concept: Division of decimals Learning Outcomes: Divide a decimal by a whole number.

Note: This lesson consists of two activities and time needed is 40 minutes. The relationship between activity and question in Worksheet 4.17: Activity 1: Question 1 & 2 Activity 2: Question 3

Activity 1

Approach Class

Aim Divide decimals (1 d.p.) by 10 and 100 also divide decimals (2 d.p.) by 10.

Steps 1. Discuss the steps to divide decimals (1d.p.) by 10. Example:

(a) 0.2 ÷ 10 = 100.2

= 10 1010 0.2

××

= 1002

= 0.02

(b) 1.2 ÷ 10 = 101.2

= 10 1010 1.2

××

= 10012

= 0.12

(c) 31.2 ÷ 10 = 1031.2

= 10 1010 31.2

××

82

= 100312

= 3.12 Guide pupils to observe the pattern as follows: When a decimal is divided by 10, rewrite the decimal and then move one

decimal place to the left. 2. Pupils answer Question 1 in Worksheet 4.17. 3. Discuss the steps to divide decimals (1d.p.) by 100. Example:

(a) 0.2 ÷ 100 = 1000.2

= 10 10010 0.2 ××

= 10002

= 0.002

(b) 1.2 ÷ 100 = 1001.2

= 10 10010 1.2 ××

= 100012

= 0.012

(c) 31.2 ÷ 100 = 10031.2

= 10 10010 31.2

××

= 1000312

= 0.312

(d) 131.2 ÷ 100 = 100131.2

= 10 10010 131.2

××

= 10001312

= 1.312 Guide pupils to observe the pattern as follows: When a decimal is divided by 100, rewrite the decimal and then move

two decimal places to the left. 4. Pupils answer Question 2 in Worksheet 4.17.

83

Activity 2

Approach Individual

Aim Divide decimals (2 d.p.) by 10.

Steps 1. Give a few questions on the division of decimals with two decimal places by 10.

Example: 0.25 ÷ 10 = 1.25 ÷ 10 = Pupils are asked to obtain the answers by referring to the pattern in

Activity 1. 2. Check the answers with the complete calculations as follows:

(a) 0.25 ÷ 10 = 100.25

= 100 10100 0.25

××

= 100025

= 0.025

(b) 1.25 ÷ 10 = 101.25

= 100 10100 1.25

××

= 1000125

= 0.125

(c) 31.25 ÷ 10 = 1031.25

= 100 10100 31.25

××

= 10003125

= 3.125 Emphasise that answers can be obtained directly as follows: 0.25 ÷ 10 = 0.025 1.25 ÷ 10 = 0.125 3. Pupils answer Question 3 in Worksheet 4.17.

84

Worksheet 4.17 Give your answer in decimals.

1. (a) 100.3 = (b) 10

4.5 =

(c) 1053.1 = (d) 0.5 ÷ 10 =

(e) 6.7 ÷ 10 = (f) 89.2 ÷ 10 =

2. (a) 1000.7 = (b) 100

5.9 =

(c) 10072.1 = (d) 0.1 ÷ 100 =

(e) 6.3 ÷ 100 = (f) 86.4 ÷ 100 =

3. (a) 100.09 = (b) 10

1.24 =

(c) 1024.56 = (d) 0.36 ÷ 10 =

(e) 6.24 ÷ 10 = (f) 98.76 ÷ 10 =

85

Teacher’s Guide Sheet 4.18 Concept: Division of Decimals Learning Outcomes: Solve problems involving division of decimals.

Note: This lesson consists of three activities. The duration is 80 minutes. The relationship between activities and questions in Worksheet 4.18: Activity 1: Questions 1 & 2 Activity 2: Questions 3 & 4 Activity 3: Question 5

Activity 1

Approach Class

Aim Divide a whole number by a whole number in which the quotient is in decimals.

Steps 1. Discuss the division of a whole number by a whole number in which the quotient is in decimals (1d.p.).

Example: (a)

(b)

Emphasise 4 ÷ 8 ≠ 8 ÷ 4

86

(c)

2. Discuss the division of a whole number by a whole number in which the

quotient is in decimals (2 d.p.). Example: (a)

(b)

(c)

3. Discuss the division of a whole number by a whole number in which the

quotient is in decimals (3 d.p.). Example: (a)

87

(b)

Pupils answer Questions 1 & 2 in Worksheet 4.18.

Activity 2

Approach Class

Aim Divide a whole number by a whole number in which the quotient is in decimals.

Steps 1. Discuss the division of a whole number by a whole number in which the quotient is in decimals (3 d.p.).

Example: 83 = 3 ÷ 8

= 0.375 2. Discuss a few examples of fractions that can be

converted to the nearest decimals.

Example: 31 = 1 ÷ 3

= 0.333 (3 d.p.) 3. Pupils answer Questions 3 and 4 in Worksheet 4.18.

88

Activity 3

Approach Class

Aim Divide decimals by a whole number.

Steps 1. Discuss a few examples on division of decimals by a whole number. Example: (a) 8.5 ÷ 5 = 1.7 (b) 0.24 ÷ 3 = 0.08 For example (b), introduce the above steps of division as an introduction

before writing the summary: 0.24 ÷ 3 = 0.08 (c) 3.125 ÷ 25 = 0.125 2. Discuss a few examples on division of decimals by a whole number

which needs an addition of zero to its dividend. Example: 5.3 ÷ 4 = 1.325

89


90

Worksheet 4.18 1. Write answer in decimals:

(a) 2 3 (b) 5 167

(c) 4 41 (d) 25 4

(e) 12 57 (f) 5 3

2. Find the quotient in decimals: (a) 3 ÷ 5 (b) 70 ÷ 4 (c) 45 ÷ 8 (d) 138 ÷ 12 (e) 106 ÷ 8 (f) 245 ÷ 20 3. Convert the fractions into decimals:

(a) 21 (b) 4

3

91

(c) 501 (d) 25

12

(e) 403

4. Convert the fractions into decimals. Give the answers in three decimal places.

(a) 65 (b) 7

1

(c) 94 (d) 11

3

(e) 165 (f) 24

7

5. Write the answer in decimals: (a) 1.8 ÷ 9 (b) 3.5 ÷ 2 (c) 1.5 ÷ 4 (d) 8.4 ÷ 12 (e) 1.2 ÷ 16 (f) 45.6 ÷ 8 (g) 69.75 ÷ 5 (h) 78.64 ÷ 16

92

Test 4.4 Name: _______________________________________________________

Class: _______________________________________________________

1. Calculate the following and give answer in decimals. (a) 8 ÷ 10 = (b) 173 ÷ 100 =

(c) 495 ÷ 1000 = (d) 1023 =

(e) 10076 = (f) 1000

2031 =

2. Calculate (a) 0.9 ÷ 10 = (b) 2.38 ÷ 100 = (c) 7.453 ÷ 100 = (d) 26.51 ÷ 10 = 3. Solve the following and give answer in decimal form. (a) 9 ÷ 2 = (b) 53 ÷ 5 = (c) 21 ÷ 25 = (d) 87 ÷ 12 =

93

(e) 49 ÷ 8 = (f) 29 ÷ 40 = 4. Convert the following fractions into decimals.

(a) 52 = (b) 4

3 =

(c) 209 =

5. Convert the following fractions into decimals. Give answer in decimal form (3 d.p.).

(a) 72 = (b) 12

5 =

6. Calculate (a) 4.5 ÷ 3 = (b) 8.26 ÷ 4 = (c) 6.25 ÷ 25 =

94

Teacher’s Guide Sheet 4.19 Concept: Division of Decimals Learning Outcome: -

Note: This lesson consists of three activities. The duration is 40 minutes. Teachers have to note that the skill of dividing numbers by decimals is a new skill that is taught in Form 1. The relationship between activities and questions in Worksheet 4.19: Activity 1: Question 1 Activity 2: Questions 2 & 3 Activity 3: Questions 4 & 5

Activity 1

Approach Class

Aim Divide whole numbers by decimals (1 d.p.) which are less than 1.

Steps 1. Discuss the steps to divide whole numbers by decimals (1d.p) which are less than 1, that is, by converting the divisor into a whole number.

Example:

(a) 8 ÷ 0.4 = 0.48

= 10 0.410 8××

= 480

= 20

(b) 36 ÷ 0.9 = 0.936

= 10 0.910 36××

= 9360

= 40

95

2. Guide pupils to use the method of moving decimal points as follows:


Activity 2

Approach Class


Steps 1. Discuss the steps to divide a whole number by decimal (2 d.p.) which is less than 1, that is, by converting the divisor into a whole number.

Example:

8 ÷ 0.04 = 0.044

= 100 0.04100 8×

×

= 4800

= 200 2. Guide pupils to use the method of moving decimal points as follows:


96

Activity 3

Approach Class


Steps 1. Discuss the steps to divide a whole number by decimal (1 d.p.) which is less than 10, that is, by converting the divisor into a whole number.

Example:

(a) 6 ÷ 1.5 = 1.56

= 10 1.510 6××

= 1560

= 4

(b) 12 ÷ 2.5 = 2.512

= 10 2.510 12××

= 25120

= 4.8 2. Guide pupils to use the method of moving decimal points as follows:


97

Worksheet 4.19 1. Solve (a) 6 ÷ 0.3 (b) 27 ÷ 0.9 (c) 13 ÷ 0.2 (d) 1 ÷ 0.8 (e) 17 ÷ 0.4 2. Solve (a) 1 ÷ 0.02 (b) 12 ÷ 0.75 (c) 8 ÷ 0.05 (d) 10 ÷ 0.16 (e) 9 ÷ 0.24

98

3. Write your answer in 3 decimal places. (a) 2 ÷ 0.3 (b) 10 ÷ 0.6 (c) 7 ÷ 0.11 (d) 28 ÷ 4. Solve (a) 6 ÷ 4.8 (b) 24 ÷ 7.5 (c) 112 ÷.6 (d) 1 ÷ 2.5 5. Write your answer in 2 decimal places. (a) 4 ÷ 3.5 (b) 18 ÷ 1.2

99

Teacher’s Guide Sheet 4.20 Concept: Division of Decimals Learning Outcome: Divide a decimal by a decimal.

Note: This lesson consists of two activities and the duration is 40 minutes. The relationship between activities and questions in Worksheet 4.20: Activity 1: Questions 1 & 2 Activity 2: Questions 3 & 4

Activity 1

Approach Class

Aim Divide decimals by decimals (1 d.p.)

Steps 1. Discuss a few examples on division of decimals by decimals (1 d.p.) which is less than 1.

Example:

(a) 2.4 ÷ 0.6 = 0.62.4

= 624

= 4

(b) 4.65 ÷ 0.5 = 0.54.65

= 546.5

= 9.3 2. Discuss a few examples on division of decimals by decimals (1 d.p.)

which is less than 10. Example:

(a) 4.8 ÷ 1.2 = 1.24.8

= 1248

= 4

100

(b) 93.31 ÷ 3.1 = 3.193.31

= 31933.1

= 30.1 3. Pupils answer Questions 1 & 2 in Worksheet 4.20.

Activity 2

Approach Class

Aim Divide decimals by decimals (2 d.p.) that are less than 1.

Steps 1. Discuss a few examples on division of decimals by decimals (2 d.p.) that are less than 1.

Example: (a)

(b) 1.68 ÷ 0.35 = 0.35

1.68

= 35168

= 4.8 (c)


101

Worksheet 4.20 1. Solve (a) 0.6 ÷ 0.2 (b) 0.9 ÷ 0.4 (c) 2.5 ÷ 0.5 (d) 3.45 ÷ 0.3 (e) 0.147 ÷ 0.7 2. Solve (a) 6.8 ÷ 3.4 (b) 4.95 ÷ 4.5 (c) 0.156 ÷ 1.3 (d) 1.728 ÷ 2.4 3. Solve (a) 0.9 ÷ 0.15 (b) 3.6 ÷ 0.04 (c) 2.76 ÷ 0.23 (d) 0.096 ÷ 0.12 4. Solve and give the answer correct to two decimal places. (a) 0.66 ÷ 0.13 (b) 0.7 ÷ 0.09 (c) 2.3 ÷ 1.1 (d) 3.5 ÷ 0.6

102

Teacher’s Guide Sheet 4.21 Concept: Division of decimals Learning Outcome: Solve problems involving division of decimals Note This lesson consists of one activity and the time needed is 40 minutes. Pupils answer Worksheet 4.21 after the explanation.

Activity 1

Approach Class

Aim Solve problems involving division of decimals.

Steps 1. Discuss a few examples of problem solving. Example: (a) A piece of 12 m rope is cut into 100 equal parts. What is the length

of each part, in metre? Each part = 12 m ÷ 100

= 100m 12

= 0.12 m (b) 5 litres of water is poured equally into 4 bottles. What is the amount

of water in each of the bottles? Amount of water in each of the bottles = 5 litres ÷ 4

= 4litres 5

= 1.25 litres (c) 2.25 kg flour is packed into a few packets. If the amount of flour in

each packet is 0.15 kg, how many packets of flour are packed? Number of packets = 2.25 kg ÷ 0.15 kg

= 0.152.25

= 15225

= 15

103

(d) A piece of 3 m wood is cut into a few pieces of equal length which are 0.25 m each. Calculate the number of pieces of equal length wood that can be obtained.

Number of pieces = 3 m ÷ 0.25 m

= m 0.25m 3

= 25300

= 12

104

Worksheet 4.21 Solve the following problems. 1. Ali bought 3 kg of rambutan that costs RM4.47. Calculate the cost of 1 kg rambutan. 2. Mr. Hassan divides 73.5 kg of sugar into a few sacks. How many sacks he has to

prepare if each sack can contain 0.35 kg of sugar? 3. A lab assistant wants to fill 1 litre of salt solution into 5 flasks. Each flask contains

same amount of solution. Find the volume of solution in litres in each flask. 4. Samy paid RM 3.95 for 3.5 litres fuel. What is the cost of a litre of fuel? Give the

answer to the nearest sen. 5. Pn. Ramona bought 2.8 m cloth to make a short pant for his son. How many short

pants can she make if a short pant needs 0.6 m of cloth? Explain your answer.

105

Teacher’s Guide Sheet 4.22 Concept: Division of decimals Learning Outcome: Perform computations involving combined operations of multiplication and division of decimals. Note: This lesson consists of two activities and the time needed is 40 minutes. Relation between the activities and questions in Worksheet 4.22: Activity 1: Question 1 Activity 2: Question 2

Activity 1

Approach Class

Aim Multiplication and division between a few decimals.

Steps 1. Discuss and give examples about the steps of multiplication and division between a few decimals.

Example: (a) 1.5 × 2.4 ÷ 0.9 = 3.6 ÷ 0.9

= 0.93.6

= 936

= 4 Emphasise that calculation must be done from left to right.

(b) 8.75 ÷ 2.5 × 0.31 = 2.58.75 × 0.31

= 2587.5 × 0.31

= 3.5 × 0.31 = 1.085

106

(c) 12 ÷ 0.5 × 0.03 = 0.512 × 0.03

= 5120 × 0.03

= 24 × 0.03 = 0.72 2. Pupils answer Question 1 in Worksheet 4.22.

Activity 2

Approach Class

Aim Pupils will be able to competently solve problems involving multiplication and division of decimals.

Steps 1. Give a few examples of problems involving multiplication and division of decimals and discuss the answers.

Examples: (a) Pak Ali buys three container of vinegar. Each container contains

22.5 litres of vinegar. He then pours the vinegar into a few bottles with 0.75 litres each. How many bottles he has to prepare?

Solution: The number of bottles he needs = (22.5 × 3) ÷ 0.75 = 67.5 ÷ 0.75

= 0.7567.5

= 0.7567.50

= 756750

= 90 (b) A housewife bought 10 kg of rice with RM14.90. How much is the

price of 3.5 kg of that rice? Give the answer into the nearest sen. Solution: The price of 3.5 kg rice = RM14.90 ÷ 10 × 3.5 = RM1.49 × 3.5 = RM5.22 (to the nearest sen) 2. Pupils answer Question 2 in Worksheet 4.22.

107

Worksheet 4.22 1. Solve (a) 5 × 1.2 ÷ 0.3 (b) 2.4 × 1.6 ÷ 3 (c) 1.28 × 0.6 ÷ 0.12 (d) 60 ÷ 1.2 × 0.04 (e) 7.2 ÷ 3 × 1.07 (f) 2.34 ÷ 0.03 × 1.23 2. Solve (a) 6 cans of drink contain 1.5 litres of drink. Find the volume of 24 cans of the

drink in litre. (b) Mr. Wong’s motorcycle can travel 135 km with 5.4 litres petrol. With 2.5 litres of

petrol, how far can he travel? (c) David saves RM0.35 per day for 6 days. Then he spends his savings on a few

cones of ice cream which cost RM0.65 each. How many cones of ice cream can David buy? How much is the balance?

108

Teacher’s Guide Sheet 4.23 Concept: Division of decimals Learning outcome: Perform computations involving combined operations of addition, subtraction, multiplication and division of decimals, including the use of brackets. Note: This lesson consists of two activities and the time needed is 40 minutes. Relation between the activities and questions in Worksheet 4.23: Activity 1: Question 1 Activity 2: Question 2

Activity 1

Approach Class

Aim Calculation involving combined operations on decimals.

Steps 1. Give a few examples which involve a few operations. Examples: (a) 0.3 + 1.2 × 6 – 4.7 = 0.3 + 7.2 – 4.7 = 7.5 – 4.7 = 2.8 Emphasise that calculation that involves division or multiplication must

be performed first, and then only followed by addition or subtraction from left to right.

(b) 10 – 0.05 ÷ 0.2 + 1.47 = 9.75 + 1.47 = 11.22

109

(c) 100 × 0.18 – 6.24 ÷ 0.4 = 18 – 15.6 = 2.4 (d) 0.28 + 3.1 × 5 – 4.67 ÷ 10 = 0.28 + 15.5 – 0.467 = 15.78 – 0.467 = 15.313 2. Pupils answer Question 1 in Worksheet 4.23.

Activity 2

Approach Class

Aim Solve problems involving combined operations of addition, subtraction, multiplication and division of decimals, including the use of brackets.

Steps 1. Pose a few problems and discuss the solutions. Examples: (a) Ms. Lim bought 2 kg sugar which is RM1.25 per kilogram and 0.5 kg

coffee powder which is RM3.20 per kilogram from a grocery. If she paid with a RM5 note, how much is the balance?

Solution: Balance = RM 5 – 2 × RM 1.25 – 0.5 × RM 3.20 = RM 5 – RM 2.50 – RM 1.60 = RM 2.50 – RM 1.60 = RM 0.90 (b) A sheet of rectangular paper is measured 10 cm by 15.6 cm. If a

rectangle measured 8.5 cm by 7.2 cm is cut from this sheet of paper, calculate the area of the remained paper.

Solution: Area of the remained paper = (10 × 15.6 – 8.5 × 7.2) cm2 = (156 – 61.2) cm2 = 94.8 cm2 2. Pupils answer Question 2 in Worksheet 4.23.

110

Worksheet 4.23 1. Solve (a) 7.6 + 0.02 × 34 – 5.5 (b) 24.3 – 0.2 ÷ 4 + 5.732 (c) 2.4 ÷ 8 × 0.3 – 0.007 (d) 36.9 ÷ (0.2 + 1.03) – (25 × 0.6) 2. Solve the following problems: (a) Aini poured 0.3 litres of syrup equally into 6 glasses. Then she poured 2.4 litres

water equally into these 6 glasses. What is the volume of syrup water in each of the glasses now?

(b) Pn. Aminah bought three chickens that weigh 1.8 kg, 1.5 kg and 1.9 kg

respectively. The price of chicken is RM4.30 per kilogram. If Pn. Aminah paid with a RM50 note, how much is the balance?

(c) Miss Susi has a 10 m cloth. She uses 4.62 m of it to make a curtain. The

remaining is going to be used for five cushion covers in which each of them needs 1.25 m of cloth. Is the remaining cloth enough for the cushion covers? Why?

111

Test 4.5 Name: _______________________________________________________

Class: _______________________________________________________

1. Solve (a) 9 ÷ 0.3 (b) 34 ÷ 0.8 (c) 2 ÷ 0.04 (d) 75 ÷ 0.25 (e) 3 ÷ 2.4 2. Calculate (a) 0.54 ÷ 2 (b) 10.8 ÷ 0.12 (c) 0.624 ÷ 5.2 (d) 8.9 – 6.2 × 0.25 + 7.39 (e) (64.2 – 52.28) ÷ 10 + 5.71

112

3. A piece of 12.8 m rope is cut into 4 equal parts. Calculate the length of each part. 4. An apple is sold at RM0.75. If Ali has RM12.00, how many apples can he buy? 5. 19.2 kg sugar is packed into a few packets. The mass of each packet is 1.2 kg. How

many packets can be packed? 6. 1 Intan class planned to sell cookies during the Canteen Day. They decided to bring

0.6 kg flour each person. One mixture of cookies needs 1.2 kg flour. How many mixtures can be prepared if the class consists of 42 pupils?

7. Pn. Jarjeet Kaur bought 4 bottles of liquid soap in which each of them contains 1.25

litres. If she used 4.46 litres of the liquid soap, how many litres of the liquid is remained?

8. Pn. Kong paid RM 47.15 for three ducks weigh 2.8 kg, 3.2 kg and 2.2 kg

respectively. What is the price of the ducks per kilogram?

113

Answer Worksheet 4.1 1. Decimals 2. (a) Based on pupil’s respond (b) Based on pupil’s respond (c) Based on pupil’s respond 3. (a) 0.1 (b) 0.2 (c) 0.3 (d) 0.4 (e) 0.5 (f) 0.6 (g) 0.7 (h) 0.8 (i) 0.9 4. (a) 0.8 (b) 0.4 (c) 0.5 (d) 0.9 5. (a) 10

1 (b) 102

(c) 103 (d) 10

4

(e) 105 (f) 10

6

(g) 107 (h) 10

8

(i) 109

6. (a) 10

4 (b) 109

(c) 106 (d) 10

1 7. (a) 0.3 (b) 10

5

(c) 107 (d) 0.3

(e) 0.8 (f) 102

8. (a) 0.8, 0.9 (b) 0.3, 0.5 (c) 0.2, 0.7 9. (a) 0.1, 0.2, 0.4, 0.6 (b) 0.4, 0.6, 0.8, 1 (c) 0, 0.2, 0.3, 0.5 Worksheet 4.2 1. (a) 0.25 (b) 0.18 (c) 0.75 (d) 0.05 (e) 0.06 (f) 0.03 2. (a) 100

65 (b) 10047

(c) 10094 (d) 100

2

114

(e) 1007 (f) 100

5 3. (a) 0.07 (b) 100

34

(c) 0.15 (d) 10072

(e) 0.09 (f) 10036

4. (a) 0.14, 0.25 (b) 0.56, 0.67 5. (a) 0.1 (b) 0.5 (c) 0.6 (d) 0.5 (e) 0.59 6. (a) 100

10 = 101 = 0.1 (b) 100

20 = 102 = 0.2

(c) 10030 = 10

3 = 0.3 (d) 10040 = 10

4 = 0.4

(e) 10050 = 10

5 = 0.5 (f) 10060 = 10

6 = 0.6

(g) 10070 = 10

7 = 0.7 (h) 10080 = 10

8 = 0.8

(i) 10090 = 10

9 = 0.9 7. (a) 0.35, 0.46, 0.75, 0.88 (b) 0.10, 0.28, 0.38, 0.65 (c) 0.23, 0.46, 0.5, 0.7 (d) 0.06, 0.20, 0.42, 0.5 Worksheet 4.3 1. (a) 0.1 (b) 0.01 (c) 0.001 (d) 0.0001 (e) 0.00001 2. (a) 0.002 (b) 0.007 (c) 0.036 (d) 0.084 (e) 0.428 (f) 0.583 (g) 0.0496 (h) 0.00037 3. (a) 0.3 (b) 0.3 (c) 0.67 (d) 0.016 (e) 0.258 (f) 0.0462 4. (a) 1000

3 (b) 1002

(c) 1000132 (d) 1000

56

(e) 10068 (f) 1000

349 5. (a) 2.6 (b) 1.04 (c) 5.5 (d) 1.85 (e) 2.003 (f) 1.024 (g) 4.165 (h) 2.0549 (i) 3.0257

115

6. (a) 1 102 = 1 5

1 (b) 2 105 = 1 2

1

(c) 3 1007 (d) 2 100

18 = 2 509

(e) 1 10009 (f) 2 1000

403

(g) 1 10067 (h) 2 000 10

645 = 2 2000129

(i) 1 000 108704 = 1 625

544 7. (a)

(b)

(c)

(d)

Worksheet 4.4 1. (a) 2 d.p. (b) 3 d.p. (c) 3 d.p. (d) 4 d.p. (e) 4 d.p. (f) 3 d.p. (g) 1 d.p. (h) 2 d.p. 2. (a) Sample answer: 2.3 (b) Sample answer: 2.31 (c) Sample answer: 2.312 (d) Sample answer: 2.3123 3. (a) hundredths (b) hundredths (c) thousandths (d) tenths (e) units 4. (a) 3, 5, 1 (b) 6, 9, 3 (c) 6, 7, 1 5. (a) 10

5 (b) 1005

(c) 10005 (d) 000 10

5 6. (a) 98.760 (b) 60.789

116

Worksheet 4.5 1. (a) 43 (b) 2 (c) 101 (d) 17 (e) 2 (f) 0 2. (a) 0.3 (b) 10.4 (c) 0.1 (d) 3.4 (e) 1.0 (f) 59.0 3. (a) 8.15 (b) 0.01 (c) 1.66 (d) 20.11 (e) 5.40 (f) 3.20 4. (a) 0.006 (b) 1.046 (c) 23.973 (d) 0.105 (e) 0.146 (f) 2.400 5. (a) 9.584 (b) 12.746 9.58 12.75 9.6 12.7 (c) 0.495 (d) 0.130 0.49 0.13 0.5 0.1 (e) 2.605 (f) 0.099 2.61 0.10 2.6 0.1 6. (e) and (f) 7. (a), (b) and (c) 8. No, because 3.65 m is less than 3.7 m. Test 4.1 1. (a) 0.7 (b) 0.15 (c) 2.08 (d) 0.008 (e) 11.104 2. (a) 5

4 (b) 209

(c) 401 (d) 5 100

31

(e) 4 25016

3. (a) 0.4, 0.7 (b) 0.1, 0.6 (c) 2.2, 2.9 (d) 5.5, 5.8 (e) 1.4, 1.7 4. (a) 0.2 (b) 0.93 (c) 0.784 (d) 6.1 (e) 11.386

117

5. (a) Zero point three nine four (b) Zero point six eight nine (c) Five point zero four six 6. (a) 0.003 (b) 4.7 (c) 1.140 7. (a) 0.35, 0.44, 0.57, 0.64 (b) 0.05, 0.066, 0.084, 0.83 8. (a) 10.092, 10.090, 10.088, 10.086 (b) 34.5, 34.49, 34.20, 34.07 9. (a) 5.0 (b) 14.81 (c) 0.190 10. (a) 42.650 (b) 42.65 (c) 42.6 11. (a) 0.006 (b) 0.07 (c) 0.0006 Worksheet 4.6 1. (a) 2.7 (b) 8.8 (c) 7.6 (d) 0.8 (e) 1.3 (f) 1 (g) 4.1 (h) 17.3 2. (a) 0.9 (b) 0.9 (c) 3.9 (d) 12.5 (e) 1.6 (f) 3.5 (g) 13.2 (h) 20.0 3. (a) 2.5 (b) 5.5 (c) 13.5 (d) 0.8 (e) 1.1 (f) 3.2 4. (a) 5.37 (b) 8.01 (c) 11.30 5. (a) 0.37 (b) 3.83 (c) 2.61 (d) 1.06 (e) 4.10 (f) 8.01 Worksheet 4.7 1. 1.6 m 2. 40.8 kg 3. 3.7 λ 4. 45.4 units 5. 82.01 litres 6. 110 kg 7. (a) 2.63 kg (b) 3.38 kg

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Worksheet 4.8 1. (a) 2.74 (b) 7.48 (c) 13.33 (d) 4.74 (e) 4.76 (f) 31.19 2. (a) 2.74 (b) 15.35 (c) 10.73 (d) 11.01 (e) 30.03 (f) 20.99 3. (a) 21.62 (b) 18.81 (c) 20.19 (d) 9.44 (e) 20.91 (f) 36.74 4. (a) 25.858 (b) 1.101 (c) 5.206 (d) 11.010 (e) 12.003 (f) 25.038 (g) 15.143 (h) 73. 484 5. (a) 1.172 (b) 2.354 (c) 5.897 (d) 30.041 (e) 3.324 (f) 9.439 6. (a) 1.36 (b) 9.75 (c) 17.36 (d) 4.96 7. Total mass altogether = 5.695 kg, Total mass she carries out = 6.375 kg. 8. 93.2 kg Worksheet 4.9 1. (a) 0.5 (b) 0.3 (c) 1.3 (d) 2 (e) 3.1 2. (a) 0.14 (b) 0.5 (c) 1.02 (d) 0.413 (e) 0.22 (f) 1.012 3. (a) 0.35 (b) 0.23 (c) 1.116 (d) 3.205 4. (a) 0.7 (b) 1.7 (c) 0.78 (d) 0.29 (e) 1.78 (f) 1.061 5. (a) 1.5 (b) 0.65 (c) 0.984 (d) 0.87 (e) 0.932 (f) 2.385

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Worksheet 4.10 1. (a) 1.42 m, 1.63 m, 1.71 m (b) 0.21 m (c) 0.08 m (d) 0.29 m 2. (a) 3.45 λ, 4.18 λ (b) 0.73 λ 3. Durian tree, 37.9 m2 4. 0.15 kg 5. (a) 4.1 m (b) 0.4 m Worksheet 4.11 1. (a) 2.4 (b) 1.9 (c) 1.48 (d) 2.4 (e) 7.883 2. (a) 3.1 (b) 3.63 (c) 5 (d) 5.05 (e) 7.094 3. (a) 0.8 (b) 21.72 (c) 0.434 (d) 2.009 4. 3.32 kg 5. 59.4 litres 6. 5.63 m 7. 0.15 litres Test 4.2 1. (a) 1.99 (b) 17.87 (c) 59.39 (d) 87.145 2. (a) 0.22 (b) 11.54 (c) 35.4 (d) 93.143 3. (a) 8.5 (b) 113.529 (c) 28.8 (d) 135.6 4. (a) 9.8 (b) 75.109 (c) 66.06 (d) 28.968 5. (a) 6.71 (b) 10.117 6. (a) 4.831 (b) 4.093 7. 8.7 kg 8. 45.2 litres 9. 15.8 m 10. 10.7 kg Worksheet 4.12 1. (a) 3 (b) 75 (c) 38.2 (d) 14.67

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(e) 15 (f) 24.6 (g) 154.89 2. (a) 86 (b) 2.8 (c) 2.4 (d) 55.74 (e) 0.67 3. (a) 40 (b) 25 (c) 147 (d) 35.6 (e) 640.7 (f) 1460 (g) 8 (h) 333.3 4. (a) 60 (b) 225 (c) 60 (d) 904.1 5. (a) 500 (b) 7400 (c) 30 (d) 6950 (e) 490 (f) 44 900 (g) 8 (h) 1196 6. (a) 700 (b) 25 (c) 0.8 (d) 4567 (e) 8004 Worksheet 4.13 1. (a) 3.2 (b) 27.5 (c) 60.6 (d) 4.2 (e) 12 (f) 62 2. (a) 5.36 (b) 11.7 (c) 57.21 (d) 0.7 (e) 58.94 (f) 353.64 3. (a) 2.002 (b) 37.422 (c) 59.892 (d) 0.654 (e) 43.71 (f) 136.998 4. (a) 8 (b) 40.8 (c) 115 (d) 26.4 (e) 51.2 (f) 94.5 5. (a) 0.96 (b) 62.53 (c) 232.8 (d) 13.8 (e) 184.92 (f) 678.72 6. (a) 2.997 (b) 115.408 (c) 101.645 (d) 704.438 (e) 20.124 (f) 50.45 Worksheet 4.14 1. (a) 0.3 (b) 1.52

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(c) 12.88 (d) 1.44 (e) 55.2 (f) 117.6 2. (a) 0.042 (b) 1.01 (c) 2.468 (d) 0.042 (e) 3.744 (f) 5.36 3. (a) 0.0335 (b) 1.404 (c) 36.7236 (d) 16.4335 (e) 114.0228 (f) 249.1502 4. (a) 0.1 (b) 2.7027 (c) 22.1728 (d) 0.8034 (e) 38.1114 (f) 37.4918 Worksheet 4.15 1. (a) 13.8 cm² (b) 62.9 cm² 2. RM 11.87 3. RM 5.37 4. 42.5 litres 5. RM 13.72 Test 4.3 1. (a) 14 (b) 8 (c) 32 (d) 604 (e) 2158 (f) 970 2. (a) 85.2 (b) 32.55 (c) 16.26 (d) 22.1 (e) 118.08 3. (a) 0.06 (b) 16.2 (c) 2.187 (d) 0.7785 (e) 153.76 4. 15 litres 5. (a) 46.8 cm (b) 120.08 cm² 6. 3.9 kg Worksheet 4.16 1. (a) 0.6 (b) 1 (c) 23.4 (d) 8.4 (e) 26 (f) 357.9 2. (a) 0.04 (b) 0.37 (c) 0.592 (d) 0.08 (e) 0.5 (f) 0.63 3. (a) 0.005 (b) 0.05

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(c) 0.559 (d) 0.125 (e) 4.321 Worksheet 4.17 1. (a) 0.03 (b) 0.45 (c) 5.31 (d) 0.05 (e) 0.67 (f) 8.92 2. (a) 0.007 (b) 0.059 (c) 0.721 (d) 0.001 (e) 0.063 (f) 0.864 3. (a) 0.009 (b) 0.124 (c) 2.456 (d) 0.036 (e) 0.624 (f) 9.876 Worksheet 4.18 1. (a) 1.5 (b) 33.4 (c) 10.25 (d) 0.16 (e) 4.75 (f) 0.6 2. (a) 0.6 (b) 17.5 (c) 5.625 (d) 11.5 (e) 13.25 (f) 12.25 3. (a) 0.5 (b) 0.75 (c) 0.02 (d) 0.48 (e) 0.075 4. (a) 0833 (b) 0.143 (c) 0.444 (d) 0.273 (e) 0.313 (f) 0.292 5. (a) 0.2 (b) 1.75 (c) 0.375 (d) 0.7 (e) 0.075 (f) 5.7 (g) 13.95 (h) 4.915 Test 4.4 1. (a) 0.8 (b) 1.73 (c) 0.495 (d) 2.3 (e) 0.76 (f) 2.031 2. (a) 0.09 (b) 0.0238 (c) 0.07453 (d) 2.651 3. (a) 4.5 (b) 10.6 (c) 0.84 (d) 7.25 (e) 6.125 (f) 0.725 4. (a) 0.4 (b) 0.75

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(c) 0.45 5. (a) 0.286 (b) 0.417 6. (a) 1.5 (b) 2.065 (c) 0.25 Worksheet 4.19 1. (a) 20 (b) 30 (c) 65 (d) 1.25 (e) 42.5 2. (a) 50 (b) 16 (c) 160 (d) 62.5 (e) 37.5 3. (a) 6.667 (b) 16.667 (c) 63.634 (d) 62.222 4. (a) 1.25 (b) 3.2 (c) 18.667 (d) 0.4 5. (a) 1.14 (b) 15 Worksheet 4.20 1. (a) 3 (b) 2.25 (c) 5 (d) 11.5 (e) 0.21 2. (a) 2 (b) 1.1 (c) 0.12 (d) 0.72 3. (a) 6 (b) 90 (c) 12 (d) 0.8 4. (a) 5.08 (b) 7.78 (c) 2.09 (d) 5.83 Worksheet 4.21 1. RM 1.49 2. 210 sacks 3. 0.2 litre 4. RM 1.13 5. 5 Worksheet 4.22 1. (a) 20 (b) 1.28 (c) 6.4 (d) 2 (e) 2.568 (f) 95.94 2. (a) 6 (b) 62.5 km

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(c) 3 cones of ice cream, 15 sen Worksheet 4.23 1. (a) 2.78 (b) 29.982 (c) 0.083 (d) 15 2. (a) 0.45 litres (b) RM 27.64 (c) No, the remaining cloth not enough for the cushion cover. Test 4.5 1. (a) 30 (b) 42.5 (c) 50 (d) 300 (e) 1.25 2. (a) 0.27 (b) 90 (c) 0.12 (d) 14.47 (e) 6.902 3. 3.2 m 4. 16 apples 5. 16 packets 6. 21 mixtures 7. 0.54 litre 8. RM5.75

Chapter 4 Decimals

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