Multiply or divide as indicated. Write answers in lowest terms...

Question

Multiply or divide as indicated. Write answers in lowest terms as needed. (3/20)∙(5/21)

Accepted Answer

Welcome back. I am so glad you're here. We are given this expression six, 28th times 7, 18 months and were asked to evaluate and reduce our answer to the lowest terms possible. Well, I'm going to show you two different ways to do this and you can go with which everyone feels more intuitive to you for the first one. When we're multiplying two fractions, we can multiply straight across the numerator, xyz and straight across the denominators. So six times seven, for the numerator is 42 And for the Denominators, times 18 is 504. And now we need to reduce this to the lowest terms possible. Well, sometimes when you look at a fraction, you know right away. Oh, those are both divisible by something. And then we'll just reduce by that. But sometimes you look at them and you have no idea what they're both divisible by. So when you don't know the highest factor that goes into both terms, you can build factor trees and for we know that 42 is six times seven and six reduces to two times three. So two times three times seven gives us 42 for 504. We know from over here that that is 28 times 18. 28 is seven times four and four is two times 2, 18 is three times six and six is two times three. So those are factors. And now to find out the greatest factor that goes into both of them. We look for factors that they have in common. So they both have a two, They both have a three And they both have a seven And two times three times seven when we know from right here that that is 42. So they're both divisible by 42 in the numerator, 42 divided by 42 is one in the denominator 504 divided by 42. Well you could use a calculator for that or you can look over here at your factor tree and see what's left over once you take out the seven times two times three or 42 we're left with two times two times 34 times three. This is 12. So our answer in its lowest terms is 1/12. I'm going to show you another way to do this. That I find to be easier personally, but go with whichever one is more intuitive to you. This one of voids getting big numbers like 504 and does the simplification before the multiplication, we know that when we are multiplying two fractions that we are taking all of the factors in the numerator being multiplied by each other, divided by all of the factors in the denominators, multiplied by each other. So what are all of the factors in our numerator? Well six, that is two times three and then times that 77 can be reduced 28 we know that this is seven times can be reduced but four is two times two in 18. We know that that's six times three and six is three times two and then bring down that times three. So looking at our numerator and then the second line for the denominator. If there's a factor that occurs in both the numerator and the denominator, then they cancel out. They reduce to ones. So is there anything that occurs in both? Yeah. Two occurs in both those become ones. This three occurs in both those become ones, and this seven occurs in both those become ones. And now you just multiply with what you've got left in the numerator one times one times one is one in the denominator. One times 11 times two is two times one is still two times two is four times three is 12. And there we've got our same answer, we look at our answer choices and this matches with answer choice. A well done. We'll catch you on the next one.

Multiply or divide as indicated. Write answers in lowest terms as needed. (3/20)∙(5/21)

Key Concepts

Multiplication of Fractions

Simplifying Fractions

Greatest Common Divisor (GCD)

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