Distributive property exercise examples (Khan Academy)

[One speaker] 

[Video opens to a math problem on a computer with an area to enter your answer and a button to check your answer.]

Narrator: We’re asked to rewrite the expression 7 · (5 + 11) 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 · the quantity 5 + 11. Now this is easy to calculate you just say 5 + 11 is 16 and then 16 · 7 is what? That’s 70 + 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 see if we can get a sum of 35 and another whole number. So 7 · (5 + 11), that’s the same thing as 7 · 5 + 7 · 11. And you can see with this expression editor 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 · 5+ 7 · 11. Well, 7 · 5 is 35 and 7 · 11 is 77. Now have we done what they’re asking us? They said rewrite this expression as a 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 we got the right answer. [Clicks Check Answer] Yes we did. Let’s do one more of these.

Rewrite the expression 12 + 75 in the following form: a · (4+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.

 [Highlights 12 + 75]

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 is the same thing as 3 · 4 and 75 is the same as 3 · 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 · 4 + 3 · 25, that’s the same thing as 3 · (4 + 25). And it actually looks like we’ve put it in the form that they want us to put it in, where 3 is a and 4 is right there and c is 25. So we’ve put it in the right form. Let’s check our answer [Clicks Check Answer] We got it right.

[end of video.]