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

Question

Multiply or divide as indicated. Write answers in lowest terms as needed. $2 \frac{5}{8} \div 1 \frac{15}{32}$

Accepted Answer

Hello. Today we're gonna be dividing the two given mixed fractions. So what we are given is three and 2/ divided by two and 13/20. Now, before you perform any kind of operation, you always want to make sure that you change your mixed fractions into improper fractions. And in order to do that you're just going to be changing the value of the numerator in order to change the value of the numerator, you're gonna take your denominator and multiply it to the whole number, then you take that value and add it to your current numerator. And we're going to be doing this to both of the mixed fractions. So doing this five times three is going to give us 15 and 15 plus two is going to give us 17. So the numerator for the left hand improper fraction is going to be and we're going to keep the same denominator which is going to be five. So the improper fraction of three and 2/5 is going to be 17/5 and we're going to go ahead and do the same thing on the right hand side. So 20 times two is going to give us 40 and 40 plus 13 is going to give us 53 for our new numerator of the improper fraction. And again we're keeping the same denominator. So the denominator here is going to be 20. Now that we have the improper fractions. We need to go ahead and change the operation of division to multiplication because it's not possible to divide two fractions together. Well, in order to take change division to multiplication, you're going to take the reciprocal of your right most fraction. And in order to take the reciprocal you're just swapping the positions of the numerator and denominator. So the reciprocal of 53/20 is going to be 20/53. And because you're taking the reciprocal you can change the division to multiplication. So doing this, what we are left with is 17/5 times 20/53. Now that we're multiplying these fractions together, we can just go ahead and multiply the numerator with numerator and denominator with denominator. So 17 times 20 is going to give us 345 times 53 is going to give us 265. Now we want to go ahead and reduce this value while both 342 165 are divisible by five. So we can divide the numerator and the denominator by five. And doing this is going to give us 68/ And 68/53. While those two numbers don't have a common multiple that they can be divided by. So 68/53 is going to be the simplest form of the answer to this problem. And with that being said, the solution to the problem is going to be C. So I hope this video helps you in understanding how to approach this type of problem and I'll go ahead and see you all in the next video.

Multiply or divide as indicated. Write answers in lowest terms as needed. $2 \frac{5}{8} \div 1 \frac{15}{32}$

Key Concepts

Mixed Numbers and Improper Fractions

Division of Fractions

Simplifying Fractions

Watch next

Multiply or divide as indicated. Write answers in lowest terms as needed. 258÷115322\(\frac{5}{8}\) \(\div\) 1\(\frac{15}{32}\)

Key Concepts

Mixed Numbers and Improper Fractions

Division of Fractions

Simplifying Fractions

Watch next

Multiply or divide as indicated. Write answers in lowest terms as needed. $2 \frac{5}{8} \div 1 \frac{15}{32}$