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.