KS3 Maths · Year 7 · Chapter 1: Working with numbers · Lesson 1

Multiplying and dividing negative numbers

Year 7About 60 minutesNo calculator52 marks

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Date

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Quick questions to start.

A1
Needed today
Work out $- 5 + 12$ .
[1 mark]
Answer
A2
Needed today
Work out $3 - 11$ .
[1 mark]
Answer
A3
Needed today
Work out $20 - 12 \div 4$ .
[1 mark]
Answer
A4
Needed today
Work out $- 4 - 9$ .
[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) $- 8 \times 6$

(b) $- 54 \div - 9$

Hint Same signs give a positive answer. Different signs give a negative answer.

B1
Work out
(a) $9 \times - 7$
(b) $- 72 \div - 8$
(c) $- 6 \times - 4 \div - 3$
[3 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$ (c) $\dots\dots$

Example 2

Work out

(a) $- 3 - 20 \div - 4$

(b) $(- 6 + 2) \times - 7$

Hint Brackets first, then multiply and divide, then add and subtract. In (a) the first minus sign is a subtraction.

B2
Work out
(a) $- 2 \times 9 + - 4 \times - 5$
(b) $- 30 \div (- 7 + 2)$
(c) $8 - 18 \div - 3$
[3 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$ (c) $\dots\dots$

Example 3

Work out

(a) $(- 6)^{2}$

(b) $- 6^{2}$

(d) $5 \times (- 3)^{2}$

Hint In

(- 6)^{2}

the bracket says the whole of

- 6

is squared. In

- 6^{2}

only the

6

is squared.

B3
Work out
(a) $(- 11)^{2}$
(b) $- 3 \times (- 4)^{2}$
(c) $(- 1 - 3)^{2} \div - 8$
[3 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$ (c) $\dots\dots$

Example 4

Find the missing number in each calculation.

(a) $□ \times - 6 = 42$

(b) $- 56 \div □ = - 4$

Hint Use the inverse operation, then check the sign by putting your number back in.

B4
Find the missing number in each calculation.
(a) $- 8 \times □ = 72$
(b) $□ \div - 3 = - 11$
(c) $- 4 \times □ \div 2 = 18$
[3 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$ (c) $\dots\dots$

Example 5

Put one pair of brackets in this statement to make it true. $- 2 \times 7 - 10 = 6$

Hint Without brackets the answer is

- 14 - 10 = - 24

. Try brackets round different pairs of numbers.

B5
Put one pair of brackets in each statement to make it true.
(a) $- 12 \div 4 + - 2 = - 6$
(b) $5 - 3 \times - 4 = - 8$
[2 marks]

Practice

Year 7

C1
In this number wall, each brick is the two bricks below it multiplied together. Complete the number wall.
[3 marks]
Answer
C2
The same number goes in each box. Find the number. $□ \times □ \times □ = - 343$
[2 marks]
Answer

C3
Find two whole numbers that multiply to give $- 24$ and add to give $5$ .
[2 marks]
Answer
C4
Work out the mean of these numbers. $- 7, 3, - 12, - 4, 5$
[2 marks]
Answer
C5
Work out $\frac{- 6 \times - 10}{- 4 - 1}$ .
[2 marks]
Answer

Exam-style questions

GCSE Foundation

D1
Work out
(a)
$- 7 \times 8$
[1 mark]
Answer
(b)
$- 48 \div - 6$
[1 mark]
Answer
(c)
$(- 3)^{3}$
[1 mark]
Answer
Total for D1: 3 marks

D2
Here are four number cards. $- 8 - 5 26$
(a)
Kim takes two of the cards and multiplies the numbers. Work out the largest answer she can get.
[2 marks]
Answer
(b)
Work out the smallest answer she can get by multiplying two of the cards.
[2 marks]
Answer
(c)
Kim now divides the number on one card by the number on another card. Work out the smallest answer she can get.
[2 marks]
Answer
Total for D2: 6 marks
D3
In a quiz there are $20$ questions. A correct answer scores $4$ points. A wrong answer scores $- 2$ points. A question not answered scores $0$ points.
(a)
Ana gets $9$ correct, $6$ wrong and does not answer $5$ . Work out Ana's score.
[2 marks]
Answer
(b)
Ben answers all $20$ questions. His score is $- 4$ . How many questions did Ben get correct? You must show your working.
[3 marks]
Answer
Total for D3: 5 marks
D4
Jay says, " $- 2 \times - 3 \times - 5 = 30$ , because two negatives make a positive."
Jay is wrong. Explain why, and give the correct answer.
[2 marks]
D5
In this number wall, each brick is the two bricks below it multiplied together. Work out the number in the top brick. You must show your working.
[3 marks]
Answer

Extension

Stretch

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

E1
This is a multiplication square. Each number inside is the number at the start of its row multiplied by the number at the top of its column. Complete the multiplication square: write the three missing numbers at the top, the three at the start of the rows, then the four missing numbers inside.
[4 marks]
Hint 1 · What to try
Start with the column you know: $- 3 \times row 1 = - 18$ .
Hint 2 · The first line
Row 1 is $6$ . Then $6 \times column 2 = - 30$ , so column 2 is $- 5$ .
Hint 3 · The full method
Row 2: $35 \div - 5 = - 7$ ; column 3: $- 14 \div - 7 = 2$ ; row 3: $27 \div - 3 = - 9$ . Then multiply to fill in the four missing numbers inside.
Answer

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can multiply and divide with negative numbers.
I can use the order of operations with negative numbers.
I can work out powers of negative numbers and find missing numbers.

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