The rules for multiplying integers - and WHY they work (incl. negative times negative and exponents)

This is a basic lesson on multiplying integers for pre-algebra or 7th grade math. I explain where we get the various rules for the SIGNS in integer multiplication, and give examples.

For example, a positive times a negative integer can be modeled with counters. 4 × (−6) would be four groups of six negatives. The answer is negative (−24).

A positive times a negative can be "turned around" because multiplication is commutative, so it also gives a negative answer.

I present the situation with negative times a negative with a PATTERN. If we follow the pattern in a logical manner, we find that a negative times a negative MUST be positive.

In the end, we look at multiplying several integers plus powers with negative bases, such as (−2)⁵ or (−10)⁸, and notice that when the exponent is ODD, the answer is negative, and when the exponent is EVEN, the answer is positive.

See also

Division of integers — a video lesson

Math Mammoth Integers — a self-teaching worktext with explanations & exercises for all operations with integers

Math Mammoth Grade 7 complete curriculum

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