Theory A · Positive and negative numbers
Numbers greater than 0 are
positive. Numbers smaller than 0 are
negative. Zero is neither positive nor negative.
On a number line, moving right makes numbers larger. Moving left makes numbers smaller.
Example: −3 < 2 because −3 is to the left of 2. The opposite of −5 is 5, and the opposite of 0 is 0.
Remember: Opposite numbers add up to zero: −7 + 7 = 0.
Theory B · Arrows on a number line
To add a positive number, move right. To subtract a positive number, move left.
Example 1: −3 + 5 = 2. Start at −3, move five steps right.
Example 2: −1 − 7 = −8. Start at −1, move seven steps left.
Theory C · Adding negative numbers
Adding a negative number has the same effect as subtracting its positive opposite.
8 + (−3) = 8 − 3 = 5
Worked examples−9 + (−3) = −12
15 + (−16) = −1
−5 + 8 = 3
Tip: If both numbers are negative, add their sizes and keep the minus sign.
Theory D · Subtracting negative numbers
Subtracting a negative number is the same as adding its positive opposite.
15 − (−4) = 15 + 4 = 19
Worked examples8 − (−3) = 8 + 3 = 11
−13 − (−27) = −13 + 27 = 14
−16 − (−2 − 8) = −16 − (−10) = −6
Remember: Work out brackets first. Then change subtraction of a negative number into addition.