Year 4 · Fractions · Lesson 5.2

Year 4: Fractions of amounts

Part of the Year 4 fractions chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)

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5.2

Fractions of amounts

Year 4
Fractions of quantities, Non-unit fractions where the answer is a whole number, Fractions to divide quantities

We can find a fraction of a number, of a sum of money, or of a measurement. It always works the same way. The bottom number says how many equal parts to split into. The top number says how many parts to take.

Unit fractions. To find 1/4 of 12, share 12 into 4 equal groups. Each group is one quarter.

12 counters in 4 equal groups. One group is 1/4 of 12. 12 ÷ 4 = 3.

So 1/4 of 12 = 12 ÷ 4 = 3. Finding a unit fraction is just dividing by the bottom number. 1/2 of a number: divide by 2. 1/5 of a number: divide by 5. 1/10 of a number: divide by 10.

Non-unit fractions. To find 3/4 of 20, first find 1/4 of 20, then take 3 of them. A bar model helps.

20 ÷ 4 = 5. One quarter is 5. Three quarters is 3 × 5 = 15.

The steps are always the same: 1. Divide by the bottom number. 2. Multiply by the top number. This works with money (1/5 of £35) and with measures (3/4 of 20 cm). In this chapter the sums come out as whole numbers.

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts to take. “Of” in “3/4 of 20” means we find a fraction of the amount.

Key ideas

Step 1: divide the amount by the bottom number. This gives ONE part.
Step 2: multiply by the top number. This gives all the parts you need.
Unit fraction (top number 1): only step 1 is needed.
Draw a bar model: the whole on top, equal parts below.
To find what is left, take your answer away from the whole amount.
Put the units (£, p, cm...) in your answer.

Worked example 5.2.1

Work out 1/4 of 12.

Key words. The denominator (bottom) says how many equal parts. The numerator (top) says how many parts to take.

Method. To find a fraction of an amount, divide by the bottom number to find one part. Then multiply by the top number.

Draw a bar and cut it into equal parts. The bottom number of 14 is 4, so we cut the whole amount into 4 equal parts.
The whole amount is 12.
Divide 12 by 4 to find the size of ONE part. 12 is shared into 4 equal parts. One part is 14 of the amount.
12 ÷ 4 = 3
Write the answer. The top number is 1, so we only need one part.
14 of 12 = 3

Check. Multiply back: 3 × 4 = 12. ✓

Watch out. Divide by the bottom number first. Then multiply by the top number.

Worked example 5.2.2

Work out 1/5 of £35.

Key words. The denominator (bottom) says how many equal parts. The numerator (top) says how many parts to take.

Method. To find a fraction of an amount, divide by the bottom number to find one part. Then multiply by the top number.

Draw a bar and cut it into equal parts. The bottom number of 15 is 5, so we cut the whole amount into 5 equal parts.
The whole amount is £35.
Divide £35 by 5 to find the size of ONE part. £35 is shared into 5 equal parts. One part is 15 of the amount.
£35 ÷ 5 = £7
Write the answer. The top number is 1, so we only need one part.
15 of £35 = £7

Check. Multiply back: £7 × 5 = £35. ✓

Watch out. Divide by the bottom number first. Then multiply by the top number.

Worked example 5.2.3

Work out 3/4 of 20.

Key words. The denominator (bottom) says how many equal parts. The numerator (top) says how many parts to take.

Method. To find a fraction of an amount, divide by the bottom number to find one part. Then multiply by the top number.

Draw a bar and cut it into equal parts. The bottom number of 34 is 4, so we cut the whole amount into 4 equal parts.
The whole amount is 20.
Divide 20 by 4 to find the size of ONE part. 20 is shared into 4 equal parts. One part is 14 of the amount.
20 ÷ 4 = 5
Multiply by 3 to get 3 parts. The top number is 3, so we need 3 of the parts.
5 × 3 = 15

Check. The other 1 part makes 5. 15 + 5 = 20. ✓

Watch out. Divide by the bottom number first. Then multiply by the top number.

Worked example 5.2.4

A ribbon is 18 cm long. Amira cuts off 2/3 of it. How long is the piece she cuts off?

Key words. The denominator (bottom) says how many equal parts. The numerator (top) says how many parts to take.

Method. To find a fraction of an amount, divide by the bottom number to find one part. Then multiply by the top number.

Draw a bar and cut it into equal parts. The bottom number of 23 is 3, so we cut the whole amount into 3 equal parts.
The whole amount is 18 cm.
Divide 18 cm by 3 to find the size of ONE part. 18 cm is shared into 3 equal parts. One part is 13 of the amount.
18 cm ÷ 3 = 6 cm
Multiply by 2 to get 2 parts. The top number is 2, so we need 2 of the parts.
6 cm × 2 = 12 cm

Check. The other 1 part makes 6 cm. 12 cm + 6 cm = 18 cm. ✓

Watch out. Divide by the bottom number first. Then multiply by the top number.

Worked example 5.2.5

Noah has £40. He spends 3/8 of his money on a book. How much money does he have left?

Key words. The denominator (bottom) says how many equal parts. The numerator (top) says how many parts to take.

Method. Find the fraction of the amount that is used. If you want what is left, take it away from the whole amount.

Find one part: divide £40 by 8. 38 means 3 out of 8 equal parts, so we first find one part.
£40 ÷ 8 = £5
Find the amount for 3 parts: multiply by 3. The top number of 38 is 3, so we need 3 of the parts.
£5 × 3 = £15
Take it away from £40 to find what is left. What is left is the amount we started with, take away the amount used.
£40 − £15 = £25

Check. The parts left are 5 out of 8. 5 × £5 = £25. ✓

Watch out. Read the question again: do you want the amount used, or the amount left?

Worked example 5.2.6

1/6 of a number is 7. What is the number?

Key words. The denominator (bottom) says how many equal parts. The numerator (top) says how many parts to take.

Method. We know some parts and want the whole. Find the size of one part. Then multiply by the number of parts in the whole.

Draw a bar with the right number of equal parts. The bottom number is 6, so there are 6 equal parts. We shade 1 of them.
1 part makes 7.
Work out one part: divide 7 by 1. One part is the amount we know.
7 ÷ 1 = 7
Work out the whole: multiply one part by 6. The whole is all 6 parts.
7 × 6 = 42

Check. 16 of 42 = 42 ÷ 6 × 1 = 7. ✓

Watch out. Do not divide the whole by the top number. The whole is what we are finding.

Worked example 5.2.7

Which is more: 3/4 of 20 or 2/3 of 24?

Key words. The denominator (bottom) says how many equal parts. The numerator (top) says how many parts to take.

Method. Work out both amounts, then compare the answers. Do not just compare the fractions: the wholes are different.

Work out 34 of 20. Divide by 4, then multiply by 3.
20 ÷ 4 = 5
5 × 3 = 15
Work out 23 of 24. Divide by 3, then multiply by 2.
24 ÷ 3 = 8
8 × 2 = 16
Compare the two answers. The bigger number is the bigger amount.
15 < 16
Answer.
23 of 24 is more.

Check. Check: 15 and 16 are different, and 16 is the bigger one. ✓

Watch out. A bigger fraction of a smaller amount can be less than a smaller fraction of a bigger amount.

Watch out

Divide by the bottom number first. For 3/4 of 20, divide by 4 (not by 3). A common mistake is to divide by the top number. Also remember the units: 3/4 of £20 is £15, not 15.

Exercise 5B Fractions of amounts

Non-calculator

FQuick-fire! Find each unit fraction of the number.

(a)

of 18 =

(b)

of 24 =

(c)

of 32 =

(d)

of 45 =

(e)

of 70 =

(f)

of 42 =

Done

FUse the groups of counters to help you. Work out the fraction of the number.

(a)

of 12 =

(b)

of 20 =

(c)

of 15 =

Done

FQuick-fire! Find each fraction of the number.

(a)

of 12 =

(b)

of 16 =

(c)

of 25 =

(d)

of 40 =

(e)

of 18 =

(f)

of 24 =

Done

FThe bar shows 36 split into quarters.

(a)What is

of 36?

(b)What is

of 36?

Done

FFind the amounts of money.

(a)

of £18 =

(b)

of £45 =

(c)

of £80 =

(d)

of 60p =

Done

FFind the amounts. Remember the units in your answers.

(a)

of 40 cm =

(b)

of 24 litres =

(c)

of 30 minutes =

(d)

of 64 g =

Done

PSThere are 24 children in a class. 3/8 of them walk to school. How many children walk to school?

Done

PSMei’s book has 60 pages. She has read 2/5 of the book. How many pages has she not read yet?

Done

PSA school trip costs £48. A parent pays 1/4 of the cost in the first week. How much do they pay in the first week?

Done

PSLeo has £60. He spends 1/3 of it on a book and 1/4 of it on lunch. How much money does Leo have left?

Done

PSA baker makes 48 rolls. 1/4 of the rolls are chocolate. 1/3 of the rolls are plain. The rest are cheese. How many rolls are cheese?

Done

RWhich is more: 3/5 of 20 or 1/2 of 30? Show how you know.

Done

RJack works out 3/5 of 20. He says the answer is 20 ÷ 3. What mistake has he made? Work out the correct answer.

Done

R1/5 of a number is 8. What is the number?

Done

RAlways, sometimes or never? Half of an even number is a whole number.

Done

R3/4 of a number is 18. What is the number? (Hint: 3 quarters make 18. Find one quarter first.)

Done