Adding and subtracting negative numbers

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.

Adding 5 to -4 on a number line = +1

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.

curriculum-key-fact
To subtract a negative number, count to the right. Subtracting a negative number is like adding a positive number.

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).

-5 + (-4) = -5 - 4 = -9

Question

Calculate -1 - (-7).

-1 - (-7) = -1 + 7 = 6