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Studying for a test? Prepare with these 7 lessons on Arithmetic properties.

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# Distributive property exercise examples

Video transcript

We're asked to rewrite
the expression 7 times open parentheses 5
plus 11 close parentheses as the sum of 35 and
another whole number. So really what they're
asking us to do is just apply the
distributive property. We have 7 times the
quantity 5 plus 11. Now this is easy to calculate. You could just say 5 plus 11 is
16 and then 16 times 7 is what? That's 70 plus 42
which would be 112. But that's not what
they're asking us to do. They're not saying
just calculate this. They're saying
express this as a sum of 35 and another whole number. So let's apply the
distributive property and let's see if we
can get a sum of 35 and another whole number. So 7 times 5 plus 11, that's
the same thing as 7 times 5 plus 7 times 11. And you can see with
this expression editor right over here,
it tells you-- it puts it kind of the
nice math formatting for what it looks
like for the computer. So if we're distributing
the 7 over the 5 and the 11, it's 7 times 5 plus 7 times 11. Well, 7 times 5 is 35. And 7 times 11 is 77. Now, have we done what
they're asking us? They said rewrite
this expression as the sum of 35 and
another whole number. Well, we've done that. We've written it as a sum of
35 and another whole number and we were able to do it using
the distributive property. So let's check to make sure
that we got the right answer. Yes, we did. Let's do one more of these. Rewrite the expression 12 plus
75 in the following form-- a times 4 plus c where a and
c represent whole numbers. Now this might look
complex, but they're really asking us to factor
out an a-- factoring out an a out of this
expression right over here. Seeing how much
we can factor out so that one of these
two numbers becomes a 4. So let's think about
how to do that. If we look at these two numbers,
the greatest common divisor of 12 and 75 looks like it is 3. Both of them are divisible by 3. So you can write 12. 12 is the same
thing as 3 times 4. And 75 is the same
thing as 3 times 25. Now what we could do is we could
essentially factor out the 3. So this is where you could say
we're undistributing the 3. So that's the same thing. 3 times 4 plus 3
times 25, that's the same thing as
3 times 4 plus 25. And it looks like we've
actually put it in the form that they want us to put
it in, where 3 is a and 4 is right there. It's 4. And then c is 25. So we've put it
in the right form. Let's check our answer. We got it right.