Operations with negative numbers
Adding, subtracting, multiplying and dividing negatives. Sign rules: same signs → positive; different signs → negative.
Year 7 consolidates KS2 negative-number addition/subtraction. Year 8 adds multiplication and division. The two-negatives-make-a-positive rule applies to multiplication/division and to subtracting a negative.
Worked examples
−5 + 3 = −2. Add 3 right of −5.
−5 − (−3) = −2. Subtracting a negative = adding a positive.
−5 × −3 = +15. −5 × 3 = −15. −15 ÷ 3 = −5.
Frequently asked questions
Why does negative × negative = positive?
Reverse of a reverse: ‘take 5 lots of −3 away’ means add 15. Algebraic justification uses distributive law.
How does this connect to BIDMAS?
Sign before a number is part of the number. −3² = −9 (square first); (−3)² = +9.