Simplify each complex fraction. See Examples 5 and 6.

5⁄8 + 2⁄3...

Question

Simplify each complex fraction. See Examples 5 and 6.

5⁄8 + 2⁄3
————
 7⁄3 - 1⁄4

Accepted Answer

Hello, everyone. We are asked to simplify the following rational expression. We have 3/4 plus nine fifths in the numerator divided by five halves minus 2/11. As our denominator, our answer choices are a 7/11 B, 5/12 C 11 10th, D 4/11. So we're gonna start by rewriting this. And as I have fractions in both my numerator and my denominator, I'm gonna simplify them independently and then bring them back together. So we have 3/4 plus nine fifths in our numerator and our denominator, we have five halves minus 2/ starting with the numerator. I want to create a common denominator to be able to add those two fractions together. Looking at the numbers four and five, I think my least common denominator will be 20. So that's the smallest number that they both divide evenly into. So to get four to be 20 I had to multiply it by five. So I multiply my numerator of that fraction also by five, three, multiplied by five is 15. And in the second fraction I multiplied five by four to get 20. So I multiply my num reader of nine by four and we get 36. So right now, our numerator is 15/20 plus 36 20th. And as I said, I'm not touching my denominator just yet. I'm gonna finish up this numerator and then go back to it. So now adding these together 15 plus 36 would give me 51 divided by 20 is our new numerator. I have nothing there. I think I can reduce. So I'm gonna leave it as 51 divided by 20 for now. So going back to the five halves minus 2/11 in our denominator, I again need to create a common denominator like I did previously. So for two and 11, the smallest number that they both go evenly into appears to be and I multiplied two by 11 to get 22. So I'm gonna multiply its numerator of five by 11. I'll have 55 divided by 22 is my first fraction. And then for my second fraction, I multiplied 11 in the denominator by two to get 22. So I multiply two in the numerator by two and I have four. So right now I have 55 divided by 22 minus four, divided by 22. So I'm gonna do that operation. Keep my common denominator of 22 and I'll have 51 divided by 22 as my denominator. So now I have a complex fraction, 51 divided by 20 divided by 51 divided by 22. At this point, I want to rewrite this as a division sentence. I don't like having a complex fraction. So I'm gonna rewrite this as 51 divided by 20. And then my classic division sign 51 divided by 22. And I recall when I divide fractions, I actually multiply by the reciprocal. So we have 51 divided by 20 multiplied by the reciprocal of 51 divided by 22 which is 22 divided by 51. So in multiplication of fractions, we can cross reduce. So I'm gonna do that before I do any other steps, cross reducing means I can reduce any numerator with any denominator as long as they have something in common. So I'm gonna start out by reducing my 51. They both become one and going in the other diagonal, I can reduce 2022 both by two. So 22 becomes 11, 20 becomes 10. Now multiplying straight across one, multiplied by 11 is 11 10, multiplied by one is 10 and this cannot get any more simplified. So 11 10th is our answer and it is answer choice. C have a nice day.

Simplify each complex fraction. See Examples 5 and 6. 5⁄8 + 2⁄3 ———— 7⁄3 - 1⁄4

Key Concepts

Complex Fractions

Common Denominator

Order of Operations

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