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Final review: multiplying and dividing positive and negative numbers
Textbook, p. 230
GoalReview multiplying and dividing positive and negative numbers.
New words
sign rule · ishora qoidasiproduct · ko‘paytmaquotient · bo‘linmapower · daraja
Explanation
In multiplication and division the moduli are multiplied or divided, and the sign is decided like this: equal signs give a positive result, different signs a negative one. With several factors, an even number of negatives gives a positive product and an odd number a negative one. We cannot divide by zero. An even power of a negative number is positive and an odd power is negative: (−2)³ = −8 and (−2)⁴ = 16. The order of operations is as usual: powers first, then multiplication and division, then addition and subtraction.
Worked examples
(−6) · (−7) = 42; (−54) : 9 = −6; 3 · (−4) · (−5) = 60 (two negatives).
(−2)³ + 10 : (−5) = −8 + (−2) = −10.
Class activity
“Sign relay”: two teams solve multiplication and division examples. Before each answer the team must say “+” or “−” aloud.
Practice
1
Compute (−12) · 4.
-48
2
Compute (−63) : (−7).
9
3
Compute (−5) · (−2) · (−3).
-30
4
Why is the product positive when the number of negative factors is even?
The negative factors pair up, and each pair gives a positive number.