KS3 Maths · Year 7 · Chapter 12: Fractions and decimals · Lesson 3

Dividing with integers and fractions

Year 7About 75 minutesNo calculator46 marks

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Quick questions to start.

Year 7

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

Example 1

Work out (a) $\frac{2}{3} \div 4$ (b) $\frac{6}{7} \div 3$ .

Hint Dividing by

4

means finding a quarter. That is the same as multiplying by

\frac{1}{4}

Example 2

How many quarters are there in $3$ ? Work out $3 \div \frac{1}{4}$ .

Hint There are

4

quarters in each whole. Dividing by

\frac{1}{4}

is the same as multiplying by

4

Example 3

Work out (a) $\frac{3}{5} \div \frac{1}{2}$ (b) $\frac{2}{9} \div \frac{1}{3}$ .

Hint To divide by a fraction, multiply by its reciprocal. The reciprocal of

\frac{1}{2}

2

Example 4

Work out (a) $3 \frac{1}{3} \div 5$ (b) $1 \frac{3}{4} \div \frac{1}{2}$ .

Hint Change the mixed number to an improper fraction first.

Year 7

C1
Find each missing number.
(a) $6 \div □ = 30$
(b) $□ \div \frac{1}{4} = 22$
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$
C2
A jug holds $2 \frac{2}{3}$ litres of juice. How many glasses holding $\frac{1}{6}$ litre each can be filled from the jug?
[2 marks]
Answer $\dots\dots$ glasses

C3
A regular pentagon has a perimeter of $7 \frac{1}{2}$ cm. Work out the length of one side.
[2 marks]
Not drawn accurately
Answer $\dots\dots$ cm
C4
Solve each equation.
(a) $4 x = 2 \frac{2}{3}$
(b) $5 y = \frac{3}{4}$
[2 marks]
Answer(a) $x = \dots$ (b) $y = \dots$
C5
Work out (a) $\frac{1}{3} \div 6$ , (b) $6 \div \frac{1}{3}$ . Are they the same?
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$

GCSE Foundation

D1
Mia says, " $\frac{1}{4} \div 2 = 8$ ."
Mia is wrong. Explain her mistake and give the correct answer.
[2 marks]

D2
A baker has $6 \frac{3}{4}$ kg of flour. Each loaf uses $\frac{1}{4}$ kg.
(a)
How many loaves can she make?
[2 marks]
Answer $\dots\dots$ loaves
(b)
She shares $4 \frac{1}{2}$ kg of butter equally into $6$ tubs. How much butter goes in each tub?
[2 marks]
Answer $\dots\dots$ kg
Total for D2: 4 marks
D3
This rectangle has an area of $5 \frac{1}{3}$ m². Its length is $4$ m.
Not drawn accurately
(a)
Work out its width.
[2 marks]
Answer $\dots\dots$ m
(b)
Work out its perimeter.
[2 marks]
Answer $\dots\dots$ m
Total for D3: 4 marks
D4
Tom has $3 \frac{1}{2}$ litres of lemonade. He pours $\frac{1}{4}$ litre into each cup.
(a)
How many cups can he fill?
[2 marks]
Answer $\dots\dots$ cups
(b)
He wants to fill $20$ cups. How much more lemonade does he need?
[2 marks]
Answer $\dots\dots$ litres
(c)
Instead he shares his $3 \frac{1}{2}$ litres equally between $20$ cups. How much goes in each cup?
[2 marks]
Answer $\dots\dots$ litre
Total for D4: 6 marks
D5
Sam says, " $6 \div \frac{1}{5} = 30$ , and $\frac{2}{5}$ is double $\frac{1}{5}$ , so $6 \div \frac{2}{5} = 60$ ."
Is Sam right? Give a reason and work out $6 \div \frac{2}{5}$ .
[3 marks]

Stretch

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

Colour one circle on each line.

	Not yet	Nearly	Yes
I can divide a fraction or a mixed number by a whole number.
I can divide by a unit fraction by multiplying by its reciprocal.
I can use division with fractions to solve problems.

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