Question

Can someone plz explain this to me i would appreciate the help!

Answer 1

Answer: $\frac{6}{65}$

Step-by-step explanation:

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

Let's solve each separately.

$\frac{1}{2}-\frac{2}{5}=\frac{(1)(5)-(2)(2)}{(2)(5)} =\frac{5-4}{10} =\frac{1}{10}$

$\frac{1}{3}+\frac{3}{4}=\frac{(1)(4)+(3)(3)}{(3)(4)} =\frac{4+9}{12} =\frac{13}{12}$

This leaves the fraction as;

$\frac{\frac{1}{10} }{\frac{13}{12} }$

To get rid of the fraction in the denominator, multiply by its reciprocal. The reciprocal of a fraction is the same fraction but inverted.

$\frac{\frac{1}{10} }{\frac{13}{12} }*\frac{12}{13}$

This will eliminate the denominator, leaving the fraction like;

$\frac{1}{10}*\frac{12}{13}$

12 and 10 can be simplified.

12/2=6

10/2=5

Our new fraction would be;

$\frac{1}{5}*\frac{6}{13}$

Multiply;

$\frac{6}{65}$