# How do you multiply mixed rational numbers like a decimal and a fraction?

Apr 1, 2018

See explanation below.

#### Explanation:

To multiply two rational numbers without a calculator, it is easiest to express them both as fractions, then multiply their numerators and denominators.

For example, if you have

1.6xx5/9=?

You can express $1.6$ as $\frac{8}{5}$, so it becomes

$\frac{8}{\cancel{5}} \times \frac{\cancel{5}}{9} = \frac{8}{9} = 0.88888 \ldots$

How did I know that $1.6 = \frac{8}{5}$?

Try to see that 1.6 can be expressed as:

$\textcolor{red}{1.6}$

$= 1 + \frac{6}{10}$

$= \frac{10}{10} + \frac{6}{10}$

$= \frac{16}{10}$

$= \frac{\cancel{2} \times 8}{\cancel{2} \times 5}$

$= \textcolor{red}{\frac{8}{5}}$

Similarly, if we had a really weird number like 1.234, we can do the same thing:

$\textcolor{red}{1.234}$

$= 1 + \frac{2}{10} + \frac{3}{100} + \frac{4}{1000}$

$= \frac{1000}{1000} + \frac{200}{1000} + \frac{30}{1000} + \frac{4}{1000}$

$= \frac{1234}{1000}$

$= \frac{\cancel{2} \times 617}{\cancel{2} \times 500}$

$= \textcolor{red}{\frac{617}{500}}$

Using this method, ANY rational number, by definition, can be expressed as a fraction.

Hope this helps!