Question Video: Applying the Commutative and Distributive Properties of Multiplication

Fill in the blanks: 9 × 7 = _ × 9 = (_ × 8) + 7.


Video Transcript

Fill in the blanks: nine times seven equals blank times nine which equals parentheses blank times eight close the parentheses plus seven.

We can use the commutative property to figure out nine times seven equals blank times nine. Simply, the order of the addends changed. Nine times seven is the same thing as seven times nine. Nine times seven or seven times nine is equal to 63.

We can set 63 equal to our last expression, and we can solve for the blank by letting it be 𝑥. Now we can solve for 𝑥. The first thing that we need to do is subtract seven from both sides of the equation. 63 minus seven is equal to 56.

Now on the right-hand side of the equation, the sevens cancelled. And we have 𝑥 times eight left. So we can go ahead and get rid of the parentheses. Now our last step would be to divide both sides by eight. 56 divided by eight is seven, and on the right the eights cancel.

So our last blank can be filled with a seven. So the first blank can be filled in with seven and so can the last; it can be filled in with seven as well.

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