# How do you solve \frac { 4} { 5} \div \frac { 1} { 2}?

Oct 22, 2016

$\frac{8}{5} = 1 \frac{3}{5}$

#### Explanation:

Write the problem as a complex fractions and then simplify by using the multiplicative inverse.

The fraction sign literally means to divide. So the problem is one fraction divided by a second fraction. The problem can be written

$\frac{\frac{4}{5}}{\frac{1}{2}}$ This is called a complex fraction

To simplify the fraction multiply both sides by the inverse of the bottom fraction

$\left(\frac{1}{2}\right) \times \left(\frac{2}{1}\right) = \left(\frac{2}{2}\right) = \left(\frac{1}{1}\right)$ By multiplying by the inverse the bottom term or fraction disappears.

The fairness principal states that what ever you do to one side must be done to the other side. ( The multiplication property of equality)

So both top fraction and the bottom fraction must be multiplied by the inverse $\frac{2}{1}$ This gives

$\frac{\left(\frac{4}{5}\right) \times \left(\frac{2}{1}\right)}{\left(\frac{1}{2}\right) \times \left(\frac{2}{1}\right)}$ The bottom fraction turns to $\left(\frac{1}{1}\right)$

Giving this

$\frac{\frac{4 \times 2}{5 \times 1}}{\frac{1}{1}} = \frac{8}{5}$

$\frac{8}{5} = 1 \frac{3}{5}$

The key to dividing fractions is to use the inverse of the second fraction which becomes the denominator of the complex fraction.

Oct 22, 2016

$\frac{8}{5} = 1 \frac{3}{5}$

#### Explanation:

Dividing by any number is the same as multiplying by its reciprocal.

For example, saying "10 divided by 2", is the same as "half of 10"

In Maths:

$10 \textcolor{red}{\div 2} = 10 \textcolor{red}{\times \frac{1}{2}}$

Dividing by a fraction is exactly the same. Multiply by its reciprocal.

$\frac{4}{5} \textcolor{red}{\div \frac{1}{2}}$
$\textcolor{w h i t e}{. x} \downarrow$
$\frac{4}{5} \textcolor{red}{\times \frac{2}{1}} \text{ } \leftarrow$ no cancelling to be done. Multiply across

=$\frac{8}{5}$

=$1 \frac{3}{5}$