Learning negative numbers — below zero
"Negative numbers begin where counting stops: temperatures below zero, debts, basement floors. They extend the number line to the left and turn ordering, adding and multiplying into a new game with clear rules."
What is this topic about?
Negative numbers describe values below zero: −3 °C is three degrees below freezing. The number line is the key image — −7 lies LEFT of −2, so −7 < −2, which feels reversed because the value shrinks. Two rules carry everything: same signs add their distances (−3 + −2 = −5); opposite signs subtract and keep the sign of the larger distance (−6 + 4 = −2). For multiplying and dividing, two like signs give plus and two unlike give minus — grades 7–8 add products like (−3) × (−4) = 12 and the coordinate system.
The best way to learn it
Read the sign as a direction on the number line: minus = steps to the left.
Adding unlike signs is “difference with the sign of the stronger” — whoever brings more steps wins.
Two minus signs cancel: −(−5) = 5, like turning around twice.
Frequently asked questions
Practise negative numbers in a duel
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