Apply Properties to Multiply and Divide Rational Numbers

The distributive property multiplies a number across a sum.

A number times its reciprocal is 1.

Factors may be regrouped to make easier products.

Read it: Multiplying and dividing signed numbers

−3 × (−4): the sizes multiply, 3 × 4 = 12, and the signs are the same, so the product is positive: 12.

1. Multiply or divide the sizes, as if there were no signs.
2. Look at the signs: the same gives a positive answer, different gives a negative one.
3. Put that sign on the answer.

The pattern 2 × (−4) = −8, 1 × (−4) = −4, 0 × (−4) = 0 goes up by 4 each step, so (−1) × (−4) = 4.

Division undoes multiplication, so it follows the same sign rule: −12 ÷ (−4) = 3.

Factors can be grouped in any order, so pair the ones that are easy to multiply first.

Same signs: positive. Different signs: negative.

(1/9) × (−5) × 9 = ___ — −5. 1/9 × 9 = 1 first, then 1 × (−5) = −5.