Intro to distributive property
CCSS Math: 3.OA.B.5
Practice decomposing the factors in multiplication problems and see how it affects the product.
Breaking up multiplication
This array is made up of rows with dots in each row. The dots show .
If we add a line dividing the dots into two groups, the total number of dots does not change.
The top group has row with dots. The dots show .
The bottom group has rows with dots in each row. The dots show .
We still have a total of dots.
Distributive property
The math rule that allows us to break up multiplication problems is called the distributive property.
The distributive property says that in a multiplication problem, when one of the factors is rewritten as the sum of two numbers, the product does not change.
Using the distributive property allows us to solve two simpler multiplication problems.
In the example with the dots we started with .
We broke the down into . We can do this because
We used the distributive property to change the problem from to .
The gets distributed to the and and the problem changes to:
Now we need to find the two products:
And finally, the sum:
and
Small numbers
Some numbers like , and are easier to multiply. The distributive property allows us to change a multiplication problem so that we can use these numbers as one of the factors.
For example, we can change into .
The array of dots on the left shows .
The array of dots on the right shows .
Now we can add the expressions to find the total.
Since and are both easy to multiply, using the distributive property for this problem made finding the product easier.
Practice problem 2
The dots represent .
More practice
Working with large numbers
The distributive property is very helpful when multiplying larger numbers. Look at how we can use the distributive property to simplify .
We will start by breaking into . Then we will distribute the to both of these numbers.