Level 4 · Ages 13–15
Read it again any time, including while you work through the exercises.
It is -5 degrees this morning, a diver goes down to -12 metres, your game character loses 3 points... Negative numbers are everywhere! Together with the positives, they form the signed numbers. On a number line, negatives stretch out to the left of zero: -7 sits further left (so it is smaller) than -2.
To add two signed numbers, think gains and losses. Two losses pile up: (-3) + (-8) = -11. A gain and a loss offset each other: (-7) + 12 means losing 7 then winning 12, leaving a gain of 5. In practice: same signs, add the distances to zero; opposite signs, subtract them and keep the sign of the stronger one.
To subtract, one single reflex: subtracting a number means adding its opposite. So 5 - (-7) becomes 5 + 7 = 12. Removing a debt of 7 really is gaining 7!
To multiply, the sign rule is simple: two identical signs give a positive result, two opposite signs give a negative result. So (-4) × (-9) = 36 and (-6) × 7 = -42. With several factors, count the minus signs: an even number of minuses gives plus, an odd number gives minus.
Make it a habit to handle the sign first and the distance second: that is the winning duo of signed numbers.
Compute (-7) + 12.
signes contraires
A loss of 7 and a gain of 12: they partly cancel each other out.
12 - 7 = 5
I subtract the distances to zero: 12 - 7 = 5.
signe du plus fort : +
The gain of 12 is stronger than the loss of 7: the result is positive.
Result: (-7) + 12 = 5
Compute (-3) × 5 × (-2).
(-3) × 5 = -15
Opposite signs (minus and plus): the product is negative, and 3 × 5 = 15.
(-15) × (-2) = 30
Same signs (minus and minus): the product is positive, and 15 × 2 = 30.
2 signes moins → résultat positif
Quick check: there are two negative factors, an even number, so the final result is indeed positive.
Result: (-3) × 5 × (-2) = 30