# How do you simplify 1/4+1/3div4/5?

Dec 20, 2016

$\frac{2}{3}$

#### Explanation:

We must perform the division first before adding.

To perform division follow the steps.

• Leave the first fraction

• Change division to multiplication

• Invert (turn upside down) the second fraction

• Cancel any common factors if possible

rArr1/3÷4/5=1/3xx5/4larr" multiply and invert"

There are no common factors.

$= \frac{1 \times 5}{3 \times 4} = \frac{5}{12}$

We now simplify $\frac{1}{4} + \frac{5}{12}$

To add fractions they must have a $\textcolor{b l u e}{\text{common denominator}}$

multiply the numerator and denominator of $\frac{1}{4}$ by 3 to create an equivalent fraction.

$\Rightarrow \frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$

$\text{Hence } \frac{1}{4} + \frac{5}{12} = \frac{3}{12} + \frac{5}{12} = \frac{8}{12}$

$\text{The numerator/denominator of } \frac{8}{12}$ can be divided by a common factor of 4

rArr8/12=(8÷4)/(12÷4)=2/3larr" in simplest form"

A fraction is in $\textcolor{b l u e}{\text{simplest form}}$ when no other factor but 1 will divide into the numerator/denominator.