Simplify the Complex Fraction

Question

I am having trouble with the following complex fraction. I have simplified everything for the most part, but I am stuck on the last part and need to know what I have to do next.

$$\frac{\frac{2}{3}+\frac{4}{5}}{\frac{5}{6}-\frac{1}{2}}$$

(I hope this converts over to the way it needs to be displayed.

I have simplified it to $\frac{\frac{10}{15}+\frac{12}{15}}{\frac{10}{12}-\frac{6}{12}}$

which equals to $\frac{\frac{22}{15}}{\frac{4}{12}}$

simplified to

$\frac{4}{12}×\frac{15}{22}$

At this point do I cross multiply and then add the two results? I can't figure out what to do next. Please help me.

Answer 1

You will get $\frac{12*22}{15*4} = \frac{22}{5}$.

Answer 2

(5/6)-(1/2) <- for this one you could just multiply the numerator and denominator of the second fraction by 3 instead of 6 and it'll be (5/6)-(3/6)

Then you'll get (22/15)/(2/6) , Then, to divide two fractions you take the second one and flip it then multiply. So, this (22/15)/(2/6) becomes this (22/15)*(6/2)

To make your life easier see if you can simplify before multiplying. Well, in this case we certainly can. 22 is divisible by 2 and 2 is divisible by 2. Also, 6 is divisible by 3 and 15 is divisible by 3. After simplifying it'll be (11/5)*(2/1) at this point there isn't anymore simplification you can make so the answer is:

22/5

Answer 3

The correct answer is $22/5$: $$ \frac{\frac{2}{3}+\frac{4}{5}}{\frac{5}{6}-\frac{1}{2}}= \frac{\frac{10+12}{15}}{\frac{5-3}{6}}= \frac{\frac{22}{15}}{\frac{2}{6}}= \frac{\frac{22}{15}}{\frac{1}{3}}= \frac{22}{15}\cdot \frac{3}{1}=\frac{22}{5}. $$