Multiplying integers (7th grade math/prealgebra video lesson)

THow does multiplying with negative numbers work? You can think of a positive times negative as so many groups of negatives. For example, 5 × (−2) is five groups of two negatives, for a total of 10 negatives. A positive times a negative is negative.

So also is negative times a positive (multiplication is commutative... this also is like so many groups of negatives). But what about a negative times a negative? This topic has baffled mathematicians in the past, so don't worry if it confuses you, too.

We look at a simple pattern to help justify the rule that a negative times a negative is a positive. (There are other ways to justify it also, such as a demonstration that uses the distributive property but it is not covered in the video.)

Multiplying several integers

Let's say we have several integers to multiply, such as 5 × (−2) × (−1) × 3 × (−2). If you pair the negative ones, each pair will produce a positive answer. In the end, if there is an EVEN number of negative numbers to multiply, the result will be positive, and if an ODD number, the result will be negative.

After looking at examples of such, I also find the value of various powers with a negative base, such as −2³ and others.

We also look at enlarging a geometric figure in the coordinate grid. This simply involves multiplying its coordinates by the same number.

See also

Division of integers — a video lesson

Math Mammoth Integers — a self-teaching worktext with explanations & exercises

Math Mammoth Grade 7 Curriculum

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