Year 6 · Fractions · Lesson 4.5

Year 6: Multiplying fractions

Part of the Year 6 fractions chapter. Chapter overview · whole chapter on one page

4.5

Multiplying fractions

Year 6
Multiply simple pairs of proper fractions and write the answer in its simplest form, Find a fraction of a fraction and of an amount

To multiply two proper fractions, multiply the tops and multiply the bottoms. Then simplify. The picture shows 12 × 14 as an area. The square is cut into 2 columns (halves across) and 4 rows (quarters up). The blue columns show a half. The orange rows show a quarter. The green overlap is the answer: one of the eight small squares, so 12 × 14 = 18.

Finding a fraction of an amount means the same as multiplying. 12 of 14 is also 18.

Blue: a half across. Orange: a quarter up. Green: the overlap, which is one eighth of the whole square.

Key ideas

To multiply fractions: tops × tops and bottoms × bottoms.
Multiplying two proper fractions gives a smaller answer than either fraction, because you take a part of a part.
Simplify the answer at the end. You can also simplify early by dividing a top and a bottom by a common factor.
A fraction of an amount is a multiplication: 23 of 12 is 23 × 12 = 8.

Worked example 4.5.1

Work out 14 × 12. Use the area picture above to check.

Key words. To multiply two fractions, multiply the tops and multiply the bottoms. A fraction of an amount means the same as multiplying by that fraction.

Method. Multiply the tops, multiply the bottoms, then simplify.

Multiply the top numbers. The top of the answer is the product of the two tops.
1 × 1 = 1
Multiply the bottom numbers. The bottom of the answer is the product of the two bottoms.
4 × 2 = 8
Write the answer in its simplest form. The top and bottom have no shared factor except 1.
18

Check. The answer is smaller than both 14 and 12, because we took a part of a part. ✓

Watch out. You may divide a top and a bottom by a common factor before you multiply, to keep the numbers small. The answer is the same.

Worked example 4.5.2

Work out 23 × 35. Give your answer in its simplest form.

Key words. To multiply two fractions, multiply the tops and multiply the bottoms. A fraction of an amount means the same as multiplying by that fraction.

Method. Multiply the tops, multiply the bottoms, then simplify.

Multiply the top numbers. The top of the answer is the product of the two tops.
2 × 3 = 6
Multiply the bottom numbers. The bottom of the answer is the product of the two bottoms.
3 × 5 = 15
Write the answer as one fraction. Put the two results together.
23 × 35 = 615
Simplify. Divide the top and the bottom by their HCF, 3.
615 = 25

Check. The answer is smaller than both 23 and 35, because we took a part of a part. ✓

Watch out. You may divide a top and a bottom by a common factor before you multiply, to keep the numbers small. The answer is the same.

Worked example 4.5.3

Work out 34 × 23.

Key words. To multiply two fractions, multiply the tops and multiply the bottoms. A fraction of an amount means the same as multiplying by that fraction.

Method. Multiply the tops, multiply the bottoms, then simplify.

Multiply the top numbers. The top of the answer is the product of the two tops.
3 × 2 = 6
Multiply the bottom numbers. The bottom of the answer is the product of the two bottoms.
4 × 3 = 12
Write the answer as one fraction. Put the two results together.
34 × 23 = 612
Simplify. Divide the top and the bottom by their HCF, 6.
612 = 12

Check. The answer is smaller than both 34 and 23, because we took a part of a part. ✓

Watch out. You may divide a top and a bottom by a common factor before you multiply, to keep the numbers small. The answer is the same.

Worked example 4.5.4

Work out 56 × 310.

Key words. To multiply two fractions, multiply the tops and multiply the bottoms. A fraction of an amount means the same as multiplying by that fraction.

Method. Multiply the tops, multiply the bottoms, then simplify.

Multiply the top numbers. The top of the answer is the product of the two tops.
5 × 3 = 15
Multiply the bottom numbers. The bottom of the answer is the product of the two bottoms.
6 × 10 = 60
Write the answer as one fraction. Put the two results together.
56 × 310 = 1560
Simplify. Divide the top and the bottom by their HCF, 15.
1560 = 14

Check. The answer is smaller than both 56 and 310, because we took a part of a part. ✓

Watch out. You may divide a top and a bottom by a common factor before you multiply, to keep the numbers small. The answer is the same.

Watch out

Do not add the tops and bottoms. 12 × 13 is 16, not 25. Also, the answer is smaller than both fractions. If you get a bigger answer, check your working.

Exercise 4E Multiplying fractions

Non-calculator

FMultiply each pair of fractions. Give each answer in its simplest form.

(a)12 × 12

(b)13 × 14

(d)34 × 13

(e)23 × 56

(f)35 × 13

Done

FWork out each fraction of a fraction. Give each answer in its simplest form.

(a)34 of 25

(b)23 of 910

(d)47 of 34

Done

FMultiply and simplify each pair. Write each answer in its simplest form.

(a)23 × 38

(b)45 × 512

Done

PSA rectangle is 12 m wide and 23 m long. What is its area? Give your answer in m².

Done

PSPriya has 25 of a cake. She gives 12 of her share to Ben. What fraction of the whole cake does Ben get?

Done

PSSam reads 34 of a book on Monday. On Tuesday he reads 23 of the part that is left. What fraction of the whole book does he read on Tuesday?

Done

RIs 12 × 12 = 12? Explain your answer.

Done

RAlways, sometimes or never? When you multiply two proper fractions, the answer is smaller than both of them.

Done

RChallenge: which proper fraction, with a bottom number less than 10, multiplied by 34 gives 320? Write it in its simplest form.

Done

PSRavi has 56 of a jug of lemonade. He pours 35 of it into cups. What fraction of the whole jug goes into cups? Give your answer in its simplest form.

Done