KS3 Maths · Year 8 · Chapter 7: Fractions · Lesson 2

Multiplying fractions and mixed numbers

Year 8About 65 minutesNo calculator48 marks

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Quick questions to start.

A1
Needed today
Write $\frac{18}{24}$ in its simplest form.
[1 mark]
Answer
A2
Needed today
Write $2 \frac{3}{5}$ as an improper fraction.
[1 mark]
Answer
A3
Last lesson
Work out $3 \frac{2}{5} + 1 \frac{3}{4}$ .
[1 mark]
Answer
A4
From chapter 6
A right-angled triangle has shorter sides $9$ cm and $12$ cm. Work out the longest side.
[1 mark]
Answer

Example, then your turn

Year 8

Your teacher works through each example with you. Then try the one beside it.

Example 1

Work out (a) $\frac{9}{14} \times \frac{7}{12}$ (b) $12 \times \frac{5}{8}$ .

Hint Cancel before you multiply:

9

and

12

share a factor of

3

;

7

and

14

7

. A whole number is a fraction over

1

B1
Work out (i) $\frac{8}{15} \times \frac{5}{12}$ (ii) $6 \times \frac{5}{8}$ . Give each answer in its simplest form.
[2 marks]
Answer(i) $\dots\dots$ (ii) $\dots\dots$

Example 2

Work out $\frac{3}{5}$ of $2 \frac{1}{4}$ .

Hint "Of" means multiply. Write

2 \frac{1}{4}

as an improper fraction first.

B2
Work out $\frac{5}{6}$ of $3 \frac{3}{5}$ .
[2 marks]
Answer

Example 3

Work out $2 \frac{1}{4} \times 1 \frac{5}{6}$ .

Hint Change both to improper fractions. Cancel the

9

and the

6

before you multiply.

B3
Work out $2 \frac{2}{3} \times 1 \frac{4}{5}$ .
[2 marks]
Answer

Example 4

Work out $(2 \frac{1}{2})^{2}$ . Explain why the answer is not $4 \frac{1}{4}$ .

Hint Squaring means multiplying the number by itself:

\frac{5}{2} \times \frac{5}{2}

B4
Work out $(1 \frac{3}{4})^{2} - (1 \frac{1}{4})^{2}$ .
[3 marks]
Answer

Example 5

A rectangular patio is $4 \frac{2}{3}$ m long and $2 \frac{1}{4}$ m wide. Work out its area.

Not drawn accurately

Hint Area = length

\times

width. Use improper fractions.

B5
A rectangular rug is $3 \frac{1}{2}$ m long and $2 \frac{3}{5}$ m wide. Work out its area.
[3 marks]
Not drawn accurately
Answer

Practice

Year 8

C1
Work out the missing fraction: $\frac{3}{4} \times □ = \frac{9}{20}$ .
[2 marks]
Answer
C2
Explain why $3 \frac{2}{5} \times 5 \frac{1}{2}$ must be more than $15$ and less than $24$ . Then work it out.
[3 marks]
Answer

C3
Work out $\frac{3}{5} \times \frac{10}{9} + \frac{1}{6}$ .
[2 marks]
Answer
C4
Cheese costs £ $6$ per kilogram. Ali buys $2 \frac{5}{8}$ kg. How much does he pay?
[2 marks]
Answer
C5
Work out $\frac{6}{7} \times \frac{14}{15} \times \frac{5}{12}$ . Cancel before you multiply.
[2 marks]
Answer

Exam-style questions

GCSE Foundation

D1
Zoe works out $3 \frac{1}{2} \times 2 \frac{1}{3}$ . She writes: " $3 \times 2 = 6$ and $\frac{1}{2} \times \frac{1}{3} = \frac{1}{6}$ , so the answer is $6 \frac{1}{6}$ ."
Zoe is wrong. Explain her mistake and work out the correct answer.
[3 marks]
AnswerCorrect answer $\dots\dots$

D2
A rectangular lawn is $6 \frac{1}{4}$ m long and $4 \frac{2}{5}$ m wide.
Not drawn accurately
(a)
Work out the area of the lawn.
[2 marks]
Answer
(b)
One box of grass seed covers $4$ m². A box costs £ $3.20$ . Work out the cost of enough boxes to cover the lawn.
[3 marks]
Answer
Total for D2: 5 marks
D3
A recipe for $4$ people uses $2 \frac{1}{4}$ cups of flour.
(a)
How much flour is needed for $6$ people?
[2 marks]
Answer
(b)
Ravi has a bag holding $5$ cups of flour. Show that $3 \frac{3}{8}$ cups is less than $\frac{3}{4}$ of the bag.
[2 marks]
Total for D3: 4 marks
D4
A cuboid measures $3 \frac{3}{4}$ cm by $2 \frac{2}{3}$ cm by $1 \frac{1}{2}$ cm. Work out its volume.
[3 marks]
Not drawn accurately
Answer
D5
A cyclist rides at $12 \frac{1}{2}$ km per hour for $2 \frac{2}{5}$ hours. How far does she ride?
[2 marks]
Answer

Extension

Stretch

No route is given. The hints are at the end of the sheet. Use one at a time.

E1
Which of $1 \frac{2}{3}$ , $1 \frac{3}{4}$ and $1 \frac{5}{7}$ is the best estimate for $3$ ? Show how you decide.
[4 marks]
Hint 1 · What to try
Square each fraction and see how close it is to $3$ .
Hint 2 · The first line
$(1 \frac{2}{3})^{2} = \frac{25}{9}$ , $(1 \frac{3}{4})^{2} = \frac{49}{16}$ , $(1 \frac{5}{7})^{2} = \frac{144}{49}$ .
Hint 3 · The full method
The gaps from $3$ are $\frac{2}{9}$ , $\frac{1}{16}$ and $\frac{3}{49}$ . Compare $\frac{1}{16} = \frac{49}{784}$ with $\frac{3}{49} = \frac{48}{784}$ .
Answer

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can multiply fractions, cancelling before I multiply.
I can multiply mixed numbers by writing them as improper fractions.
I can find a fraction of an amount and square a mixed number.
I can use multiplying fractions to work out areas, volumes and costs.

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