Adding relative numbers

Two scenarios to be aware of

When adding two relative numbers, there are two possible scenarios.

Scenario 1: same signs -> add the distances from zero and retain the common sign.

• (+3) + (+5) = +8
• (-4) + (-2) = -6

Case 2: different signs -> subtract the smaller distance from the larger one, and keep the sign of the number with the larger distance from zero.

• (+7) + (-3) = +4 (because 7 – 3 = 4, and 7 > 3, so the sign is +)
• (-9) + (+2) = -7 (because 9 – 2 = 7, and 9 > 2, so the sign is -)

Step-by-step method

1. Check the signs of both numbers
2. If the signs are the same: add the distances together, keep the common sign
3. If the signs are different: subtract (larger distance – smaller distance), keep the sign of the number with the greater distance from zero

Complete example

Calculate (-6) + (+10):

• Different signs
• 10 - 6 = 4
• The number 10 (positive) has the greater distance from zero -> the result keeps the + sign
• Result: +4

Common pitfall

Do not confuse ‘the largest number’ with ‘the greatest distance from zero’. In (-9) + (+2), it is -9 that is furthest from zero (9 > 2), even though +2 is the larger number in terms of numerical order. The result therefore retains the – sign, giving –7.