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

Question

Multiply or divide as indicated. Write answers in lowest terms as needed. (1/8)∙(10/7)

Accepted Answer

Welcome back. I am so glad you're here. We are given the expression 2/9 times 15 11th and were asked to evaluate and reduce our answer to the lowest terms possible. And I'm actually going to show you two different ways to do that and you can go with whichever one feels more intuitive. So when we have got two fractions being multiplied, we can multiply straight across the numerator and straight across the denominator. So two times 15 is 30, divided by nine times 11 is 99. And now it's just a matter of reducing that fraction. So 30 99th. Well, sometimes it's really intuitive to know what is the highest factor that goes into both the numerator and the denominator That we could divide both of them by and reduce it. Sometimes it's not as obvious as if it's not as obvious. You can build a factor tree. 30 is three times 10 and 10 is two times five and 99. Well that's nine times 11 and nine is three times three. And then you look for any factor that occurs in both of the numbers. And here they both got a three and that's it. They don't have any other factors in common. So we can divide both of them by 3. 30 divided by three is 10 and 99 divided by three is 33. and so this reduces to 10, Now, the other way to do this whenever a factor occurs in both the numerator and the denominator of any of our fractions being multiplied. Those factors can cancel out and become once. So what are all of the factors in our numerator here? Well, we've got a two and then 15, 15 is three times five, so we've got two times three times five in our numerator in nine. Well we already know nine is three times three and then 11 doesn't reduce. So it's three times three times 11. Are there any factors that occur in both the numerator and the denominator? Yeah, that three, so three's king cancel out. And so now we're just multiplying in the numerator two times five, which is 10 divided by three times 11, which is 33. So that one essentially does the simplification. Before you do the multiplication, we look at our answer choices and this matches with answer choice D. Well done. We'll catch you on the next one.

Multiply or divide as indicated. Write answers in lowest terms as needed. (1/8)∙(10/7)

Key Concepts

Multiplication of Fractions

Simplifying Fractions

Understanding Numerators and Denominators

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