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Rewrite the expression five times 9 minus 4-- that's in
parentheses-- using the distributive law of
multiplication over subtraction.
Then simplify.
So let me just rewrite it.
This is going to be 5 times 9 minus 4, just like that.
Now, if we want to use the distributive property, well,
you don't have to.
You could just evaluate 9 minus 4 and then
multiply that times 5.
But if you want to use the distributive property, you
distribute the 5.
You multiply the 5 times the 9 and the 4, so you end up with
5 times 9 minus 5 times 4.
Notice, we distributed the 5.
We multiplied it times both the 9 and the 4.
In the first distributive property video, we gave you an
idea of why you have to distribute the 5, why it makes
sense, why you don't just multiply it by the 9.
And we're going to verify that it gives us the same answer as
if we just evaluated the 9 minus 4 first. But anyway,
what are these things?
So 5 times 9, that is 45.
So we have 45 minus-- what's 5 times 4?
Well, that's 20.
45 minus 20, and that is equal to 25, so this is using the
distributive property right here.
If we didn't want to use the distributive property, if we
just wanted to evaluate what's in the parentheses first, we
would have gotten-- let's go in this direction-- 5 times--
what's 9 minus 4?
9 minus 4 is 5.
Let me do that in a different color.
5 times 9 minus 4.
So it's 5 times 5.
5 times 5 is just 25, so we get the same
answer either way.
This is using the distributive law of multiplication over
subtraction, usually just referred to as the
distributive property.
This is evaluating the inside of the parentheses first and
then multiplying by 5.