# What is 9.75 divided by 1.3?

Apr 7, 2018

$9.75 \div 1.3$

$= \textcolor{red}{\frac{15}{2}} = \textcolor{red}{7.5}$

#### Explanation:

The problem is to evaluate

$9.75 \div 1.3$

To do this without a calculator, let's start by expressing each decimal as a fraction.

$9.75$

$= 9 + \frac{7}{10} + \frac{5}{100}$

$= \frac{900}{100} + \frac{70}{100} + \frac{5}{100}$

$= \frac{975}{100}$

$1.3$

$= 1 + \frac{3}{10}$

$= \frac{10}{10} + \frac{3}{10}$

$= \frac{13}{10}$

Now we want to divide $\frac{975}{100}$ by $\frac{13}{10}$.

To divide two fractions, it is easier to multiply by the reciprocal of the denominator, like so:

$\frac{\frac{975}{100}}{\frac{13}{10}} = \frac{975}{100} \times \frac{10}{13} = \frac{9750}{1300}$

This is a valid answer, but the fraction is not in its simplest form. It may be difficult to see how to simplify this, but let's try to do it step by step.

First factor out a 10:

$\frac{9750}{1300} = \frac{\cancel{10} \cdot 975}{\cancel{10} \cdot 130}$

Now factor a 5:

$\frac{975}{130} = \frac{\cancel{5} \cdot 195}{\cancel{5} \cdot 26}$

And finally factor a 13:

$\frac{195}{26} = \frac{\cancel{13} \cdot 15}{\cancel{13} \cdot 2}$

$\textcolor{red}{\frac{15}{2} = 7.5}$

This is our answer in simplest form.