KS3 Maths · Year 8 · Chapter 7: Fractions · Lesson 3

Dividing fractions and mixed numbers

Year 8About 65 minutesNo calculator48 marks

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Quick questions to start.

A1
Needed today
Write $3 \frac{3}{4}$ as an improper fraction.
[1 mark]
Answer
A2
Needed today
Work out $\frac{4}{9} \times \frac{3}{10}$ .
[1 mark]
Answer
A3
Last lesson
Work out $2 \frac{1}{3} \times 1 \frac{1}{5}$ .
[1 mark]
Answer
A4
From chapter 1
A coat costs £ $60$ . Its price falls by $15%$ . Work out the new price.
[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

Write down the reciprocal of (a) $7$ (b) $\frac{5}{9}$ (c) $2 \frac{3}{8}$ .

Hint Swap the top and the bottom. A whole number is a fraction over

1

; a mixed number must be made improper first.

B1
Write down the reciprocal of (i) $\frac{3}{11}$ (ii) $4 \frac{2}{5}$ .
[2 marks]
Answer(i) $\dots\dots$ (ii) $\dots\dots$

Example 2

Work out $\frac{5}{6} \div \frac{2}{9}$ .

Hint Keep the first fraction. Multiply by the reciprocal of the second:

\frac{9}{2}

B2
Work out $\frac{4}{7} \div \frac{6}{35}$ .
[2 marks]
Answer

Example 3

Work out (a) $8 \div \frac{2}{5}$ (b) $\frac{3}{4} \div 6$ .

Hint Write each whole number over

1

. In (b) the reciprocal of

6

\frac{1}{6}

B3
Work out (i) $9 \div \frac{3}{7}$ (ii) $\frac{5}{8} \div 10$ .
[2 marks]
Answer(i) $\dots\dots$ (ii) $\dots\dots$

Example 4

Work out $3 \frac{1}{3} \div 1 \frac{7}{8}$ .

Hint Change both to improper fractions, then multiply by the reciprocal of

\frac{15}{8}

B4
Work out $4 \frac{1}{2} \div 2 \frac{5}{8}$ .
[2 marks]
Answer

Example 5

A rectangle has an area of $8 \frac{3}{4}$ m². It is $2 \frac{1}{3}$ m wide. How long is it?

Not drawn accurately

Hint Area = length

\times

width, so length = area

\div

width.

B5
A rectangle has an area of $9 \frac{1}{3}$ m². It is $2 \frac{2}{3}$ m wide. How long is it?
[3 marks]
Not drawn accurately
Answer

Practice

Year 8

C1
Work out the missing number: $□ \times \frac{2}{3} = \frac{5}{6}$ .
[2 marks]
Answer
C2
Two numbers multiply to give $8 \frac{1}{3}$ . One of them is $2 \frac{1}{2}$ . What is the other?
[2 marks]
Answer

C3
How many pieces of ribbon, each $\frac{3}{8}$ m long, can be cut from $5 \frac{1}{4}$ m of ribbon?
[2 marks]
Answer
C4
Without working it out, explain why $6 \div \frac{3}{4}$ is more than $6$ . Then work it out.
[2 marks]
Answer
C5
In a sequence, each term is the term before multiplied by $\frac{3}{4}$ . One term is $3 \frac{3}{8}$ . Work out the two terms just before it.
[2 marks]
Answer $\dots\dots$ and $\dots\dots$

Exam-style questions

GCSE Foundation

D1
Tom works out $2 \frac{1}{2} \div \frac{1}{4}$ . He writes: " $\frac{5}{2} \times \frac{1}{4} = \frac{5}{8}$ ."
Tom is wrong. Explain his mistake and work out the correct answer.
[3 marks]
AnswerCorrect answer $\dots\dots$

D2
A jug holds $2 \frac{1}{4}$ litres of juice. A glass holds $\frac{3}{10}$ of a litre.
(a)
How many glasses can be filled completely from the jug?
[2 marks]
Answer
(b)
How much juice is left in the jug after the glasses are filled?
[2 marks]
Answer
Total for D2: 4 marks
D3
A car travels $52 \frac{1}{2}$ km in $\frac{3}{4}$ of an hour.
(a)
Work out the average speed of the car in km per hour.
[2 marks]
Answer
(b)
At the same speed, how long does the car take to travel $87 \frac{1}{2}$ km? Give your answer in hours and minutes.
[3 marks]
Answer
Total for D3: 5 marks
D4
A cuboid has a volume of $16 \frac{7}{8}$ cm³. Its base is $3 \frac{3}{4}$ cm by $2 \frac{1}{2}$ cm. Work out its height.
[4 marks]
Not drawn accurately
Answer
D5
Show that $4 \frac{2}{3} \div 1 \frac{1}{6}$ and $3 \frac{1}{2} \div \frac{7}{8}$ give the same answer.
[3 marks]

Extension

Stretch

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

E1
A positive number is divided by its own reciprocal. The answer is $6 \frac{1}{4}$ . What is the number? Give it as a mixed number.
[4 marks]
Hint 1 · What to try
Dividing by the reciprocal of a number is the same as multiplying by the number itself.
Hint 2 · The first line
So the number multiplied by itself is $\frac{25}{4}$ .
Hint 3 · The full method
Find a fraction whose square is $\frac{25}{4}$ : the top squared is $25$ and the bottom squared is $4$ .
Answer

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can find the reciprocal of a whole number, a fraction and a mixed number.
I can divide by a fraction by multiplying by its reciprocal.
I can divide mixed numbers by writing them as improper fractions.
I can use dividing fractions to find lengths, speeds and how many fit.

Answers and mark scheme

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