# How do you simplify 3/4 div 1/8?

Aug 13, 2018

$6$

#### Explanation:

$\text{to perform the calculation}$

• " leave the first fraction"

• " change division to multiplication"

.• " turn the second fraction upside down"

• " perform any cancelling"

$\frac{3}{4} \times \frac{8}{1} = \frac{3}{\cancel{4}} ^ 1 \times {\cancel{8}}^{2} = 3 \times 2 = 6$

Aug 13, 2018

$\frac{3}{4}$ is the same as $\frac{6}{8}$

So how many $\frac{1}{8}$ are in $\frac{6}{8}$ obviously 6 of them.

This only works because the fractions are 'nice' ones. The method to use for every division with fractions is
color(red)Kcolor(blue)Fcolor(purple)C (color(red)Keep color(blue)Flip color(purple) Change)

You $\textcolor{red}{K}$eep the first fraction the same
You $\textcolor{b l u e}{F}$lip the second fraction
You $\textcolor{p u r p \le}{C}$hange the divide to a multiply sign.

$\frac{3}{4} \div \frac{1}{8} = \textcolor{red}{\frac{3}{4}}$$\textcolor{p u r p \le}{\times}$$\textcolor{b l u e}{\frac{8}{1}} = \frac{24}{4} = 6$

Aug 13, 2018

$6$

#### Explanation:

Despite what we are always taught about having to flip the second fraction when we are dividing, it is possible to just divide straight across as we do in multiplication.

However, the divisions often lead to uncomfortable numbers, so we choose not to do divisions that way.

For example: $\frac{8}{15} \div \frac{2}{5} = \frac{8 \div 2}{15 \div 5} = \frac{4}{3}$

This is exactly the same answer as is obtained from:

$\frac{8}{15} \times \frac{5}{2} = {\cancel{8}}^{4} / {\cancel{15}}_{3} \times \frac{\cancel{5}}{\cancel{2}} = \frac{4}{3}$

or $\frac{40}{30} = \frac{3}{4}$

In this case, we have $\frac{3}{4} \div \frac{1}{8}$

$\frac{3 \div 1}{4 \div 8} = \frac{3}{\frac{1}{2}} = \frac{3 \times 2}{1 \times 1} = 6$

But consider that $\frac{3}{4} = \frac{6}{8}$

$\frac{6}{8} \div \frac{1}{8} = \frac{6 \div 1}{8 \div 8} = \frac{6}{1} = 6$

There are times when this direct method is the easiest and quickest - look out for them!

eg: $\frac{21}{16} \div \frac{3}{4} = \frac{7}{4}$