35
Multiplying positive and negative numbers
Textbook, pp. 165–167
GoalKnow and apply the sign rules for multiplying positive and negative numbers.
New words
sign rule · ishora qoidasiproduct · ko‘paytmafactor · ko‘paytuvchiabsolute value · modul
Explanation
To multiply numbers, first multiply their moduli, then decide the sign. The product of numbers with equal signs is positive: (+)(+) = +, (−)(−) = +. The product of numbers with different signs is negative: (+)(−) = −, (−)(+) = −. For example (−4) · 6 = −24 and (−5) · (−7) = 35. With several factors, an even number of negatives gives a positive product and an odd number gives a negative one. Multiplying by zero always gives 0.
Worked examples
(−4) · 6: 4 · 6 = 24, signs differ, answer −24. (−5) · (−7): 35, signs equal, answer +35.
(−2) · (−3) · (−4): three negatives (odd), so the product is negative: −(2 · 3 · 4) = −24.
Class activity
“Sign race”: cards show multiplication examples. First only the sign must be said (positive/negative), then the full answer. Teams score for the correct sign.
Practice
1
Compute (−7) · 8.
-56
2
Compute (−9) · (−6).
54
3
Compute (−2) · (−3) · (−4).
-24
4
Why is (−1) · (−2) = 2? Look at the row 3 · (−2), 2 · (−2), 1 · (−2), 0 · (−2).
The row is −6, −4, −2, 0, growing by 2 each time. Continuing the pattern gives (−1) · (−2) = 2.