Distributive property review

The distributive property says that in a multiplication problem, when one factor is rewritten as the sum of two numbers, the product doesn't change.

Using the distributive property allows us to solve two simpler multiplication problems.

We can change $4 \times 12$4, times, 12 into $4 \times (\tealD{10} + \greenC{2})$4, times, left parenthesis, start color #01a995, 10, end color #01a995, plus, start color #74cf70, 2, end color #74cf70, right parenthesis.

The $4$4 gets distributed to the $\tealD{10}$start color #01a995, 10, end color #01a995 and $\greenC{2}$start color #74cf70, 2, end color #74cf70 and the problem changes to:
$(4 \times \tealD{10}) + (4 \times \greenC{2})$left parenthesis, 4, times, start color #01a995, 10, end color #01a995, right parenthesis, plus, left parenthesis, 4, times, start color #74cf70, 2, end color #74cf70, right parenthesis

The array of dots on the left shows $(\tealD{4 \times 10})$left parenthesis, start color #01a995, 4, times, 10, end color #01a995, right parenthesis. The array of dots on the right shows $(\greenC{4 \times 2})$left parenthesis, start color #74cf70, 4, times, 2, end color #74cf70, right parenthesis.

Now we can add the expressions to find the total.
$(\tealD{4 \times 10}) + (\greenC{4 \times 2})$left parenthesis, start color #01a995, 4, times, 10, end color #01a995, right parenthesis, plus, left parenthesis, start color #74cf70, 4, times, 2, end color #74cf70, right parenthesis
$= \tealD{40} + \greenC{8}$equals, start color #01a995, 40, end color #01a995, plus, start color #74cf70, 8, end color #74cf70
$=48$equals, 48

Want to learn more about the distributive property? Check out this video.

Want to try more problems like this? Check out this exercise.