Question

Write in simplest form

Answer 1

Find the commomon denominator of 6 and 5.

It's 6 · 5 = 30.

$\dfrac{5}{6}=\dfrac{5\cdot5}{6\cdot5}=\dfrac{25}{30}\\\\\dfrac{1}{5}=\dfrac{1\cdot6}{5\cdot6}=\dfrac{6}{30}$

$\left(\dfrac{5}{6}-\dfrac{1}{5}\right)\div\dfrac{4}{5}=\left(\dfrac{25}{30}-\dfrac{6}{30}\right)\div\dfrac{4}{5}=\dfrac{25-6}{30}\div\dfrac{4}{5}=\dfrac{19}{30}\div\dfrac{4}{5}$

Divide by fraction is the same like multiply by reciprocal of this fraction:

$=\dfrac{19}{30}\cdot\dfrac{5}{4}=\dfrac{19}{6}\cdot\dfrac{1}{4}=\dfrac{19}{24}$