# How do you divide 5 5/8 div 2/3?

Jul 9, 2017

$8 \frac{7}{16}$

#### Explanation:

Change the mixed number to an improper fraction

$5 \frac{5}{8} = \frac{45}{8}$

Set up a complex fraction to indicate the division

$\frac{\frac{45}{8}}{\frac{2}{3}}$

eliminate the bottom fraction $\frac{2}{3}$ by multiplying by the inverse.
(Remember that what ever is done to the bottom must always be done to the top. ( fairness)

$\frac{\left(\frac{45}{8}\right) \times \left(\frac{3}{2}\right)}{\left(\frac{2}{3}\right) \times \left(\frac{3}{2}\right)}$

$\frac{2}{3} \times \frac{3}{2} = 1$ so this leaves

$\frac{45}{8} \times \frac{3}{2} = \frac{135}{16} = 8 \frac{7}{16}$

Jul 9, 2017

$= 8 \frac{7}{16}$

#### Explanation:

For division of fractions, always change mixed numbers to improper fractions:

$5 \frac{5}{8} \div \frac{2}{3}$

$= \frac{45}{8} \times \frac{3}{2} \text{ } \leftarrow$ to divide, multiply by the reciprocal

$= \frac{135}{16} \text{ } \leftarrow$ multiply straight across, nothing cancels

$= 8 \frac{7}{16}$

The question was given with mixed numbers, answer in the same form.

Jul 9, 2017

A slightly different approach.

$8 \frac{7}{16}$

#### Explanation:

$\textcolor{b l u e}{\text{An example of the method using numbers}}$

I choose: $9 \div 3$ but 9 can be written as $6 + 3$ so we may write the same thing as

$9 \div 3 \to \left(6 + 3\right) \div 3$

This is the same as: $\left(6 + 3\right) \times \frac{1}{3}$

Multiply everything inside the brackets by $\frac{1}{3}$ giving $\frac{6}{3} + \frac{3}{3} = 3$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Answering the question}}$

Writ $5 \frac{5}{8}$ as $5 + \frac{5}{8}$ so now we have: $\left(5 + \frac{5}{8}\right) \div \frac{2}{3}$

This is the same as $\left(5 + \frac{5}{8}\right) \times \frac{3}{2}$

Note that $\div \frac{2}{3}$ give the same answer as $\times \frac{3}{2}$

Multiply everything inside the brackets by $\frac{3}{2}$ giving:

$\textcolor{g r e e n}{\frac{15}{2} + \frac{15}{16} \text{ "=" } \left[\frac{15}{2} \textcolor{red}{\times 1}\right] + \frac{15}{16}}$

Multiply by 1 and you do not change the value. However 1 comes in many forms so you can change the way the fraction looks without changing its inherent value.

$\textcolor{g r e e n}{\text{ "=" } \left[\frac{15}{2} \textcolor{red}{\times \frac{8}{8}}\right] + \frac{15}{16}}$

$\text{ = "120/16 " "+15/16" "=" } \frac{135}{16}$

$\text{ "=" } 8 \frac{7}{16}$