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- END UNIT 1 ASSIGNMENTOpened: Saturday, 27 May 2023, 12:00 PMDue: Monday, 29 May 2023, 12:00 AM
UNIT 5:Multiplication and division of decimals
5.1 Decimal fractions
A tenth
Activity 5.1
Materials needed: knife and an orange.
Steps:(a) Cut an orange into ten equal parts.
(b) Name each part you have cut.
(c) Write 4/10 in words.(d) Explain your observations to the class. Discuss.
A hundredth
Activity 5.2
Materials: a pair of scissors, manila paper, a ruler, a pencil
Steps:
(a) Draw a square of 10 cm. Do it on manila paper.
(b) Draw smaller squares each measuring 1 cm inside the bigger square.
(c) Count the number of small squares.
(d) Shade four of the small squares.
(e) What fraction have you shaded?(f) Write this fraction in words.
(g) Present and explain your work.
A thousandth
Activity 5.3
Materials: a pair of scissors, manila paper, a ruler, a pencil
Steps
Do the following;– Draw a cube measuring 4 cm.
– In it, draw 1 cm cubes.
– Count the number of 1 cm cubes you have drawn. Let us make a 4 cm
cube using wet clay. We can cut a 1 cm cube using a sharp knife.
– Repeat the process above for a cube with 10 cm sides. What decimal
fraction is 705/1000? Write in words. Discuss your findings
TIP
Example 5.1
(i) Read and write the decimals in words.
(a) 0.02 (b) 0.3 (c) 0.005
(d) 0.85 (e) 0.850
(ii) Write the following in figures.
(a) Three hundredths (b) Seven tenths
(c) Nine thousandths (d) Four point nine
Solution
(i) (a) 0.02 is read as zero point zero two. It is written as two
hundredths.
(b) 0.3 is read as zero point three. It is written as three tenths.
(c) 0.005 is read as zero point zero zero five. It is written as five
thousandths.
(d) 0.85 is read as zero point eight five. It is written as eighty five
hundredths.
(e) 0.850 is read as zero point eight five zero. It is written as eight
hundred fifty thousandths.(ii) (a) 0.03 (b) 0.7 (c) 0.009 (d) 4.9
Practice Activity 5.1
Work out the following:1. Fill in the table below.
2. From each diagram below, write the fraction and decimal fraction.
3. Study the figure below. Explain your observation.
(a) Write the decimal fraction for the shaded part.
(b) Write the decimal fraction for the part that is not shaded.
4. Read and write the following decimal fractions in words. Present your
answer.
(a) 0.256 (b) 2.513 (c) 436.2
(d) 196.261 (e) 0.75 (f) 0.4
5. Read and write the following decimal fractions in figures. Discuss your
answer.
(a) Zero point two three five.
(b) Zero point three seven eight.
(c) Six hundredths.
(d) Eight hundred seven thousandths.
(e) Four thousand and two hundredths.(f) Six and two tenths.
5.2 Place value of decimalsLet us do the activity below.
Discuss your results.
Tip: Tenths, hundredths and thousandths are examples of place valuesfor decimals. For example, the place values of the digits in 3.647 are:
Practice Activity 5.2
1. Fill in the following table.
2. What is the place value of the digit 4 in the following numbers?
(a) 356.4 (b) 236.254 (c) 196.456
(d) 0.004 (e) 0.245
3. Discuss and write the name of the place value of the digit 2 in the
following numbers.
(a) 56.235 (b) 43.325 (c) 0.002
(d) 9.362 (e) 156.267
4. Present the place value of the digit 3 in the following numbers.
(a) 925.53 (b) 0.023 (c) 123.564(d) 135.267 (e) 85.364
5.3 Comparing decimal numbers
We use these symbols to compare decimals.
< means less than. For example, 0.009 < 0.01.
> means greater than. For example, 0.02 > 0.01.
= means equals to. For example, 0.1 = 0.10 = 0.100.Now do the activity below.
Activity 5.5
Compare these decimals. Use >, < or =.
(a) 0.3 — 0.4 (b) 0.07 — 0.09
(c) 0.001 — 0.009 (d) 0.01 — 0.010
(e) 0.2 — 0.02 — 0.002Explain your answers
Tip:
• Tenths are greater than hundredths and thousandths.• Thousandths are less than hundredths and tenths.
Example 5.2
Which is greater?
Compare the following. Use >, <, =.
(a) 0.2 — 0.4 (b) 0.05 — 0.08
(c) 0.009 — 0.004 (d) 0.009 — 0.04 — 0.1
Solution(a) Draw similar strips below. Shade 0.2 and 0.4.
From the diagram, 0.4 is greater than 0.2. We can say 0.2 is less than
0.4. Thus, 0.2 < 0.4
(b) Draw a number line and represent the numbers on it.
0.05 is less than 0.08.
Thus, 0.05 < 0.08
(c) Draw a number line and represent the numbers 0.009 and 0.004 on it.
0.009 is greater than 0.004.
We write 0.009 > 0.004
(d) If we draw number lines, tenths is greater than hundredths.
Hundredths is greater than thousandths. Thus, 0.009 < 0.04 < 0.1.Draw this on a paper and discuss your answer.
Practice Activity 5.31. Copy and complete the number lines below.
2. Use >, < and = to fill the blanks correctly.
(a) 0.005 ___ 0.007 (b) 0.003 ___ 0.008
(c) 3.40 ___ 3.040 (d) 0.77 ___ 0.770
(e) 0.825 ___ 0.826 (f) 0.23 ___ 0.023
3. Use >, < and = to compare the following. Discuss your answer.
(a) 0.006 ___ 0.007 (b) 4.105 ___ 3.05
(c) 0.9 ___ 0.8 (d) 0.77 ___ 0.770
4. Arrange the following from the smallest to the largest. You can use >,
< or =. Present your answers.
(a) 0.01, 0.05, 0.02, 0.04 (b) 0.006, 0.003, 0.005, 0.007
(c) 0.452, 0.252, 0.436 (d) 0.5, 0.4, 0.6, 0.8
5. A farmer collected 10 eggs and harvested 10 apples. The mass of each
egg was 23 g while each apple was 25 g.
(a) Find the mass of the eggs in kilograms.
(b) Find the mass of the apples in kilograms.
(c) Compare the total mass of eggs and apples using >.
Which items had smaller mass? Explain.6. A farmer recorded the amount of milk from her farm as follows:
(a) In which day had the farmer recorded the highest amount of milk?
(b) Arrange the recorded amount of milk from the largest to the smallest. Justify your answer.
5.4 Conversion of fractions to decimals
We can change a fraction into a decimal. For example 3/10 = 0.3.Do the activity below.
Activity 5.6
– Get two strips of manila paper that are the same size.
– Fold one paper into five equal parts. Cut out two of the five parts.
– Then fold the second paper strip into ten equal parts. Cut out fourof the ten parts.
– Compare the parts you have cut. Write them as fractions.
– What did you discover?
– Now, write the cut parts as decimals.– Explain your observations.
4. John gave an orange to four pupils to share equally. Find the decimal
fraction of the orange each got. Use a diagram to present decimalfraction of an orange got by each pupil.
5.5 Conversion of decimals to fractions
We can change a decimal into a fraction. For example, 0.5 = 5/10 = 1/2 Do theactivity below.
Activity 5.7
Change the following into fractions.
(a) 0.8 (b) 0.7 (c) 0.45 (d) 0.658What steps do you follow?
Tip:
To convert a decimal into a fraction, know the decimal places. For example
0.4 is 4 tenths, 0.40 is 40 hundredths etc. Thus, 0.4 = 4/10; 0.40 = 40/100. Wethen simplify the fraction. Look at the following example.
Practice Activity 5.5
1. Change into fractions.
(a) 0.75 (b) 0.455 (c) 0.625 (d) 0.075
2. Change the following decimals into fractions.
(a) 0.41 (b) 0.009 (c) 1.8 (d) 0.62
(e) 0.136 (f) 0.005 (g) 1.450.28
3. Write the following as fractions and explain how to simplify.
(a) 0.75 (b) 0.52 (c) 0.5 (d) 0.006(e) 0.25 (f) 2.4 (g) 20.4
4. Which one is greater? Justify your answer
(a) 3/5 or 0.007 (b) 1/5 or 0.75 (c) 2/5 or 0.25
5. Discuss and arrange the following from the smallest to the largest.
(a) 0.56, 3/10, 0.09 (b) 3/10, 0.84, 0.25 (c) 0.44, 1/4, 0.5
6. Match the decimals to the fractions.
5.6 Multiplication of decimal fractions
We can multiply a decimal number by a whole number. We can also multiplya decimal number by a decimal number. Let us study the following activity.
Activity 5.8
• Cut 2 oranges into halves. Each half is 0.5 of an orange. Put three
halves together. What decimal number is three halves?
• Now, multiply the following:
(i) 0.5 × 3 (ii) 0.5 × 6 (iii) 0.5 × 0.5
What do you notice?• Present your findings
Example 5.6
Multiply the following:(a) 0.8 × 4 (b) 0.2 × 0.7 (c) 0.4 × 0.16
Practice Activity 5.6
1. Work out the following.
(a) 0.06 × 7 (b) 2.2 × 7 (c) 3.502 × 2
(d) 7.04 × 4 (e) 15.23 × 8 (f) 0.105 × 9
(g) 2.66 × 11
2. Multiply each of the following decimal fractions.
(a) 0.2 × 0.6 (b) 0.14 × 0.2 (c) 1.5 × 0.02
(d) 0.17 × 0.3 (e) 0.2 × 0.04 (f) 1.5 × 1.2
(g) 1.3 × 3.3
3. Multiply the following.
(a) 2.25 × 10 (b) 0.039 × 10 (c) 0.245 × 10
(d) 8.91 × 10 (e) 35.4 × 10 (f) 116.7 × 10
4. Multiply the following. Justify your answers.
(a) 0.089 × 100 (b) 2.533 × 100 (c) 33.52 × 100
(d) 1.485 × 100 (e) 4.008 × 100 (f) 22.7 × 100
5. Multiply the following. Discuss and present your steps.
(a) 0.006 × 1 000 (b) 4.005 × 1 000 (c) 21.06 × 1 000
(d) 13.507 × 1 000 (e) 0.015 × 1 000 (f) 0.267 × 1 000
6. A motorcycle consumes 1 litre of petrol to cover 5.25 km. Calculate the
distance it would cover with 1.5 litres of petrol.
7. I cut an orange into ten equal pieces. How many pieces of tenths would
I cut from 9 oranges? Explain your answer.
8. 20 pupils were each given 0.5 loaf of bread. How many loaves of bread
were given in total? Discuss your answer.
9. A small bottle holds 0.3 litres of milk. Discuss how much milk is heldby 12 such small bottles?
5.7 Division of decimal fractions
Let us do the activity below.
Activity 5.9
• Cut an orange into two equal parts.
• Share half of the orange equally among 4 pupils. What fraction of
orange do each of the four get? Now, discuss the following.
(i) 0.5 ÷ 4 (ii) 0.5 ÷ 5
(iii) 0.5 ÷ 0.5 (iv) 0.005 ÷ 0.04• Present your findings.
Tip:
Identify number of decimals in the denominator. If it is in tenths, multiply
by 10/10. If it is in hundredths, multiply by 100/100. If the denominator is in
thousandths, multiply by 1000/1000.
Practice Activity 5.7
1. Work out the following.
(a) 0.2 ÷ 5 (b) 0.44 ÷ 1.1 (c) 6.4 ÷ 1.6
(d) 4 ÷ 0.02 (e) 1.792 ÷ 0.07 (f) 2.4 ÷ 0.08
2. Work out the following. Discuss the steps you followed.
(a) 12.22 ÷ 26 (b) 8.648 ÷ 0.23 (c) 0.13 ÷ 0.05
3. A roll of cloth 540 m long was cut into equal pieces, each 3.6 m. Each
piece was enough to make a dress. Calculate the number of dresses
made from the roll.
4. The perimeter of a rectangular piece of land is 525 m. Poles are put at
a fixed spacing of 0.25 m. How many poles are required to fence the
entire piece of land? Justify your answer.
5. A quarter of an orange is shared equally by 5 pupils. What size oforange does each pupil get? Explain your steps to answer.
5.8 Mixed operations for multiplication and division
Activity 5.10
Work out the following
(a) 0.6 × 0.2 ÷ 0.04 (b) 0.02 × 0.6/0.04
Practice Activity 5.8
1. Work out the following.
(a) 0.4 × 0.2 ÷ 0.8 (b) 0.5 × 0.2 ÷ 0.4 (c) 0.04 × 0.2 ÷ 0.4(d) 5 × 1.6 ÷ 0.08 (e) 29.14 × 9.2 ÷ 0.2
2. Work out and explain the steps you followed.
Revision Activity 5
1. Multiply 0.23 by 0.23.
2. Divide 3 ÷ 0.3
3. What is the place value of 3 in 264.235?
4. Change 1/2 into a decimal fraction. Discuss the steps followed.
5. Write 0.236 as a fraction.
6. Arrange in order starting from the smallest to the largest.
0.02, 0.85, 0.26. Present your answers.
7. Use >, <, or = to fill in the blanks. Discuss your answers.
(a) 0.081 — 0.095 (b) 0.25 — 0.205 (c) 0.65 — 0.650
8. Read and write these in figures.
(a) Six hundred sixty seven thousandths.
(b) Seventy two hundredths.
(c) One and one tenth.
9. Write 2/10 as a decimal.
10. Work out 1.44 ÷ 1.2.
11. Share two oranges equally among twenty people. What decimal
fraction would each person get? Discuss your steps.
12. Work out 0.2 × 0.5 ÷ 0.01. Explain the steps you followed.
13. Solve 5.2 × 0.2/0.05
14. Identify the place value of the digit 3 in 0.253. Explain your steps.15. Write 52.067 in words.
Word list
Tenths Hundredths Thousands Place value
Figures Words Decimals Fractions
Convert Matching Multiply Divide >, <, =
Task
Do the following.
(i) Read each word aloud to your friend.
(ii) Write the meaning of each of the words above. Discuss with your friend.(iii) Write sentences using each of the words above. Read with your friend.