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KS3 Bitesize

Maths

Negative numbers

Numbers below zero are called negative numbers.

Introduction

This Revision Bite covers:

Ordering

Ordering negative numbers

Any number above zero is a positive number. Positive numbers are written with no sign or a '+' sign in front of them and they are counted from zero to the right.

Any number below zero is a negative number. Negative numbers are always written with a '-' sign in front of them and they are counted from zero to the left.

Always look at the sign in front of a number to see if it is positive or negative.

Positive numbers get higher the further we move right, so 5 is more than 2.

Negative numbers get lower the further we move left, so -5 is less than -2.

Question

Which word, 'higher' or 'lower', would fit correctly in each of these gaps?

a) -7 is ............... than -1
b) + 62 is ............... than -71
c) -136 is ............... than -36

Answer

a) -7 is lower than -1
b) + 62 is higher than -71
c) -136 is lower than -36

Challenge

Now test what you've learnt about negative numbers in the activity below.

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Adding and subtracting

To add and subtract numbers always begin counting from zero.

When dealing with positive numbers count to the right.

When dealing with negative numbers count to the left.

Using a number line

a number line from -5 to 5. Each number between -5 and 5 is marked.

A number line

Example

Calculate 4 - 5 - 3

Imagine moving up and down a number line to get to the answer.

Starting from zero, count up to 4. Then subtract 5. Then subtract 3. The answer is -4.

Number line calculation

A number line from -5 to +5

Calculate 4 - 5 - 3

Number line calculation

arrow showing +4 from 0, which is 4

Starting from zero, count up to 4.

Number line calculation

shows an arrow from 4 to -1 (-5)

Starting from zero, count up to 4. Then subtract 5.

Number line calculation

shows an arrow from -1 to -4 (-3)

Starting from zero, count up to 4. Then subtract 5.

Question

Calculate: - 2 + 9 - 10 + 6

Answer

If you wrote the answer 3 or +3, then well done!

Shows a number line from -8 to 8. Starting from zero, minus 2 (-2), add 9 (7), minus 10 (-3) and add 6 (3)

Two signs

When adding or subtracting negative numbers, remember that when two signs appear next to each other and are different, then you subtract. When two signs are next to each other and they are the same, you add:

+ - and - + equals - but + + and - - equals +
Question

Calculate:

a) 10 + - 7
b) 4 - - 3

Answer

a) 10 + - 7 = 10 - 7 = 3
b) 4 - -3 = 4 + 3 = 7

Multiplying and dividing

The rule for multiplying and dividing is very similar to the rule for adding and subtracting.

  • When the signs are different the answer is negative.
  • When the signs are the same the answer is positive.
Multiplying dividing negative numbers
Question

Calculate:

a) 5 × -4
b) -40 ÷ -8

Answer

a) We have +5 and -4. The signs are different, so the answer will be negative. So, +5 × -4 = -20
b) We have -40 and -8. The signs are the same, so the answer will be positive. So, -40 ÷ -8 = 5

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