GCF Distributive Property rewrite 60 - 50
Math
rewriting the Distributive Property
To rewrite this problem using the distributive property, we first need to prime factorize the two numbers 60 and 50. Prime factorize means breaking them down from composite, which they currently are into primes, which you have a list in your notes of. So let's break down the 60. What times what is 60? Well, 6 times ten is 60. Our 6 and ten on your prime number notes, no they're not. So we can keep breaking them down. 6 can break down into three times two. Since three and two are prime, we're going to circle those. Ten can break down to 5 times two. And we'll circle both of those as well. Now let's break down the 50. So 50 can break down to 5 times ten. Circling the 5 and the ten breaks down to two times 5 circling both of those.
So now we're going to make a van diagram. This left and diagrams for our left number 60, the right fin diagrams for our right number 50. What do they have in common? Well, I noticed that they each share a two, so they'd share one, two. I'm going to put one, two in the middle, and they each share one, 5. So we'll put one 5 in the middle. Anything left over, see the leftover in the 50 side 5 goes over there. The leftover and 60 side to three and the two goes over there. Now our notes tell us that the GCF is found by multiplying the middle. So the GCF will be two times 5. The GCF is ten. To write it like a distributive property, the ten is going to go outside the parentheses. Now, there was a subtraction symbol at the start of the problem. So we'll put the subtraction symbol back in. And now the right side here, we'll go to the right side there. And the left side here will go over here. So three times two is 6. So the 6 will go over