Subtracting relative numbers

The golden rule

Subtracting a relative number is always the same as adding its opposite. This is the most important rule to remember:

a – b = a + (-b)

In other words, we turn every subtraction into an addition by changing the sign of the number being subtracted.

Examples

• (+5) - (+3) = (+5) + (-3) = +2
• (+5) - (-3) = (+5) + (+3) = +8
• (-4) - (+6) = (-4) + (-6) = -10
• (-4) - (-6) = (-4) + (+6) = +2

Step-by-step method

1. Identify the ‘-’ subtraction sign and the number that follows it
2. Replace the subtraction with an addition
3. Change the sign of the number that was being subtracted (take its opposite)
4. Apply the addition rules covered previously

Simplified notation

At secondary school, we often simplify the notation by removing unnecessary brackets:

• (+5) + (-3) is written as 5 - 3
• (+5) + (+3) is written as 5 + 3

Common pitfall

The most common mistake is forgetting to change the sign when removing brackets. For example, (-4) - (-6) is NOT equal to -4 - 6 = -10. It must be rewritten as (-4) + (+6) = +2. Whenever you ‘remove’ a subtraction in front of a set of brackets, the sign inside changes.