KS3 Maths · Year 7 · Chapter 12: Fractions and decimals · Lesson 2

Multiplying fractions and integers

Year 7About 75 minutesNo calculator46 marks

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Quick questions to start.

A1
Last lesson
Work out $2 \frac{3}{4} + 1 \frac{2}{3}$ .
[1 mark]
Answer
A2
Needed today
Write $\frac{23}{6}$ as a mixed number.
[1 mark]
Answer
A3
Needed today
Work out $\frac{1}{5}$ of $35$ .
[1 mark]
Answer
A4
From chapter 4
Work out $25%$ of $48$ .
[1 mark]
Answer

Example, then your turn

Year 7

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

Example 1

Work out (a) $\frac{3}{5}$ of $20$ (b) $\frac{2}{3} \times 7$ .

Hint "Of" means times. To multiply a fraction by a whole number, multiply the top and keep the bottom.

B1
Work out each one. Give fractions as mixed numbers.
(a) $\frac{4}{9}$ of $27$
(b) $\frac{5}{6} \times 4$
(c) $9 \times \frac{3}{4}$
[3 marks]
Answer(a) $\dots$ (b) $\dots$ (c) $\dots$

Example 2

Work out $2 \frac{3}{5} \times 4$ in two ways.

Hint Either change

2 \frac{3}{5}

to an improper fraction, or multiply the

2

and the

\frac{3}{5}

separately.

B2
Work out each one.
(a) $3 \frac{2}{7} \times 3$
(b) $5 \times 1 \frac{5}{6}$
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$

Example 3

Work out $10 \times 2 \frac{7}{15}$ .

Hint

2 \frac{7}{15} = \frac{37}{15}

. The

10

and the

15

share a factor of

5

: divide both by

5

before you multiply.

B3
Work out each one. Cancel first if you can.
(a) $12 \times 3 \frac{5}{8}$
(b) $2 \frac{4}{9} \times 6$
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$

Example 4

Work out the area of this rectangle.

Not drawn accurately

Hint Area = length

\times

width. Multiply the whole number part and the fraction part by

6

B4
For this rectangle, work out (a) its area, (b) its perimeter.
[3 marks]
Not drawn accurately
Answer(a) $\dots\dots$ (b) $\dots\dots$

Practice

Year 7

C1
$16 \frac{2}{3} % = \frac{1}{6}$ . Use this to work out (a) $16 \frac{2}{3} %$ of $42$ , (b) $83 \frac{1}{3} %$ of $42$ .
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$
C2
$3 \frac{1}{4} \times 5 = 16 \frac{1}{4}$ . Use this to work out (a) $3 \frac{1}{4} \times 15$ , (b) $6 \frac{1}{2} \times 10$ .
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$

C3
Show that $\frac{3}{8} \times 5$ and $\frac{5}{8} \times 3$ have the same value.
[2 marks]
C4
Find each missing number.
(a) $□ \times \frac{3}{4} = 6$
(b) $\frac{2}{5} \times □ = 6$
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$
C5
One batch of flapjack needs $\frac{2}{3}$ of a cup of oats. How many cups of oats are needed for $8$ batches?
[2 marks]
Answer $\dots\dots$ cups

Exam-style questions

GCSE Foundation

D1
Ben says, " $3 \times \frac{2}{7} = \frac{6}{21}$ ."
Ben is wrong. Explain his mistake and give the correct answer.
[2 marks]

D2
A tin holds $3 \frac{3}{4}$ litres of paint. Jo buys $6$ tins.
(a)
How many litres of paint does Jo buy?
[2 marks]
Answer $\dots\dots$ litres
(b)
She uses $18 \frac{2}{3}$ litres. How much paint is left?
[2 marks]
Answer $\dots\dots$ litres
(c)
One tin covers $13 \frac{1}{3}$ m² of wall. What area can all $6$ tins cover?
[2 marks]
Answer $\dots\dots m^{2}$
Total for D2: 6 marks
D3
A regular hexagon has sides of $2 \frac{5}{6}$ cm. Work out its perimeter.
[2 marks]
Not drawn accurately
Answer $\dots\dots$ cm
D4
A coat costs $£96$ . In a sale, all prices are cut by $37 \frac{1}{2} %$ .
(a)
Work out the sale price of the coat. ( $37 \frac{1}{2} % = \frac{3}{8}$ .)
[3 marks]
Answer $£ \dots\dots$
(b)
Later the sale price is cut by a further $16 \frac{2}{3} %$ . Work out the new price.
[2 marks]
Answer $£ \dots\dots$
Total for D4: 5 marks
D5
Put these in order of size, smallest first.
$\frac{3}{8} \times 165 \times 1 \frac{1}{4} \frac{2}{3} \times 81 \frac{3}{5} \times 4$
[3 marks]
Answer $\dots\dots$ , $\dots\dots$ , $\dots\dots$ , $\dots\dots$

Extension

Stretch

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

E1
$\frac{3}{k}$ is a fraction in its simplest form, and $k$ is a whole number bigger than $3$ .
$\frac{3}{k} \times 20$ is a whole number. Find all the possible values of $k$ .
[4 marks]
Hint 1 · What to try
$\frac{3}{k} \times 20 = \frac{60}{k}$ .
Hint 2 · The first line
So $k$ must divide $60$ exactly. List the factors of $60$ bigger than $3$ .
Hint 3 · The full method
In its simplest form, $3$ and $k$ share no factor. Cross out the multiples of $3$ .
Answer $k = \dots\dots$

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can multiply a fraction by a whole number.
I can multiply a mixed number by a whole number, cancelling first when I can.
I can use fractions to find areas, amounts and percentages.

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