Simplify each complex fraction. See Examples 5 and 6. [ (−4/3)...

Question

Simplify each complex fraction. See Examples 5 and 6. [ (−4/3) + 12/5 ] / [ 1 − (−4/3)(12/5) ]

Accepted Answer

Hello, everyone. We are asked to simplify the following rational expression. We are given negative 2/7 plus 14 3rd divided by one minus in parentheses, negative 2/7 multiplied by the parentheses of 3rd. Our answer choices are a 11 divided by B 92 divided by C negative 43 divided by D 31 divided by 49. So rewriting this again have negative 2/7 plus 14 3rd in the numerator. And that's divided by one minus the parentheses is negative 2/7 is multiplied by the parentheses, 14 3rd. So we have a few different simplifications we need to do here. I'm gonna start in the numerator since this is fractions that we want to add together, we need to have a common denominator and the common denominator that makes the most sense between seven and three would be 21. So that's the smallest number they both go evenly into. So to get from the denominator of seven to the denominator of 21 I have to multiply by three. So I also need to multiply my numerator by three. And when I do my new first fraction is negative 6/12. And then for the second fraction in the numerator to get from 3 to 21 I multiplied by seven. So I must al also multiply 14 by seven which gives us 98 divided by 21. Looking at the denominator, I'm going to do the multiplication first and then I'll worry about the subtraction. So I have one minus. And now looking at my multiplication, I notice I can cross reduce seven and 14, 7 goes into seven once, goes into 14 twice. So now when I multiply I have two multiplied by negative two. So negative four and divided by my denominator of one multiplied by three, which is three. So my new denominator is one minus in parentheses, negative four thirds. So I'm gonna combine my numerator into one fraction. And when I do, I have 92 divided by 21. And in my denominator, I'm going to notice that my double negative. So I'm minus a negative sign which is like adding. So I'm gonna change those to addition and I'm gonna think of one as 3/3. And when I do that, I get the fraction seven thirds. So right now I have 92 divided by 21 divided by seven thirds. Since this is a complex fraction, I'm gonna rewrite this as a fraction division sentence. So I'm going to rewrite this as 92 divided by divided by seven thirds. And then I recall that when I divide fractions, I multiply by the reciprocal of the second fraction. So this would be 92 divided by 21 multiplied by the reciprocal of seven thirds, which is 3/ from here, I can cross reduce before I multiply. So three goes into three once it goes into 21 7 times. And then I'm gonna ask myself, can seven and 92 reduce and it does not appear that they can. So I'm gonna multiply straight across the top. 92 multiplied by one is 92 straight across my denominator seven multiplied by seven is 49. And that again, does not appear to be able to be reduced any further. So 92 divided by 49 is our answer and it's answer choice B have a nice day.

Simplify each complex fraction. See Examples 5 and 6. [ (−4/3) + 12/5 ] / [ 1 − (−4/3)(12/5) ]

Key Concepts

Complex Fractions

Operations with Fractions

Order of Operations and Negative Signs

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