KS3 Maths · Year 7 · Chapter 12: Fractions and decimals · Lesson 4

Multiplication with large and small numbers

Year 7About 75 minutesNo calculator48 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) $6 \times 400$ (b) $50 \times 700$ .

Hint Multiply the non-zero digits first. Then put back all the zeros.

Example 2

Work out (a) $0.007 \times 8$ (b) $0.6 \times 120$ .

Hint

0.007 = 7 \div 1000

. Work out

7 \times 8

, then divide by

1000

Example 3

Work out (a) $0.3 \times 0.8$ (b) $0.06 \times 0.7$ .

Hint Multiply the digits. The answer has as many decimal places as the two numbers have together.

Example 4

Work out (a) $3 0^{2}$ (b) $0. 4^{2}$ .

Hint Squaring means multiplying a number by itself:

3 0^{2} = 30 \times 30

Year 7

C3
Which two of these have the same value?
$A 0.5 \times 80 B 5 \times 0.08$
$C 0.05 \times 800 D 50 \times 0.08$
[2 marks]
Answer $\dots$ and $\dots$
C4
Find each missing number.
(a) $0.3 \times □ = 2.1$
(b) $□ \times 40 = 1.2$
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$
C5
Work out (a) $0. 3^{3}$ , (b) $20 0^{3}$ .
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$

GCSE Foundation

D1
Leo says, " $0.7 \times 0.3 = 2.1$ ."
Leo is wrong. Explain his mistake and give the correct answer.
[2 marks]

D2
A fish tank is a cuboid $60$ cm long, $50$ cm wide and $40$ cm tall.
Not drawn accurately
(a)
Work out its volume in cm³.
[2 marks]
Answer $\dots\dots cm^{3}$
(b)
$1$ litre $= 1000$ cm³. How many litres does the tank hold?
[1 mark]
Answer $\dots\dots$ litres
(c)
Write the lengths in metres, and work out the volume in m³.
[2 marks]
Answer $\dots\dots m^{3}$
Total for D2: 5 marks
D3
Ribbon costs $£0.35$ per metre.
(a)
A shop buys $600$ m of ribbon. Work out the cost.
[2 marks]
Answer $£ \dots\dots$
(b)
Ellie buys $0.4$ m of the ribbon. Work out the cost.
[2 marks]
Answer $£ \dots\dots$
Total for D3: 4 marks
D4
A square floor tile has sides of $0.2$ m.
Not drawn accurately
(a)
Work out the area of one tile in m².
[1 mark]
Answer $\dots\dots m^{2}$
(b)
Jo lays $300$ tiles. What area do they cover?
[2 marks]
Answer $\dots\dots m^{2}$
(c)
Each tile costs $£1.40$ . Work out the cost of $300$ tiles.
[2 marks]
Answer $£ \dots\dots$
Total for D4: 5 marks
D5
Kai says, "When you multiply two numbers, the answer is always bigger than both of them."
Give an example to show Kai is wrong, and explain why.
[2 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 multiply large numbers by putting back the zeros.
I can multiply decimals by counting the decimal places.
I can use these to find areas, volumes and costs.

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