Adding and subtracting negative numbers

Explore refreshed revision guide for GCSE Maths: Adding and subtracting negative numbers, with step-by-step slideshows, quizzes, practice exam questions, and more!

A number line can be used to add and subtract negative numbers.

Adding with negative numbers

Example

What is \(-4 + 5\)?

To add -4 and 5, draw the starting number on a number line and count to the right when adding numbers.

So, \(-4 + 5 = 1\)

Subtracting with negative numbers

Example

What is \(-2 - 2\)?

To subtract 2 from -2, start at -2 on a number line, and count to the left when subtracting numbers.

Subtracting -2 from -2 on a number line = 0

\(-2 - 2 = -4\)

Example

What is the difference in temperature between a desert at 40 °C and a mountain top at -2 °C?

Temperature of mountain top and desert, placed on a number line

\(40 - (-2) = 42\), so the difference in temperature between the desert and the mountain top is 42 °C.

Example

What is \(4 - (-2)\)?

To subtract -2 from 4, start at number 4 on a number line, and count to the right. So, \(4 - (- 2) = 6\).

Subtracting -2 from 4 on a number line = +2

Rules for adding and subtracting negative numbers

When two signs are written next to each other, the rules for adding and subtracting numbers are:

two signs that are different become a negative sign
two signs that are the same become a positive sign

Adding a negative number or subtracting a positive number, means you subtract the two numbers. Adding a positive number or subtracting a negative number, means you add the two numbers

Examples

Same signs give a positive: \(3 + (+2) = 3 + 2 = 5\)
Same signs give a positive: \(3 - (-2) = 3 + 2 = 5\)
Different signs give a negative: \(3 + (-2) = 3 - 2 = 1\)
Different signs give a negative: \(3 - (+2) = 3 - 2 = 1\)

Question

Calculate \(-5 + (-4)\).

Question

Calculate \(-1 - (-7)\).