# How do you simplify 1.6 div 0.336?

Oct 3, 2016

$1.6 \div 0.336 = 4.76$

#### Explanation:

When you are dividing BY a decimal, it is possible to make the decimal into a whole number by multiplying by 10, 100 or 1000. etc

$\frac{1.6}{0.336} \times \frac{1000}{1000} = \frac{1600}{336}$

This can now be divided by long division, double division or any similar method

$\textcolor{w h i t e}{\times x . . x} 4.76$
336)bar(1600.00)
$\textcolor{w h i t e}{\times .} \underline{1344} \downarrow$
$\textcolor{w h i t e}{\times \ldots .} 2560$
$\textcolor{w h i t e}{\times \ldots .} \underline{2352} \downarrow$
$\textcolor{w h i t e}{\times x \ldots .} 2080$
$\textcolor{w h i t e}{\times x \ldots .} \underline{2016}$
$\textcolor{w h i t e}{\times \times x \ldots .} 64$

Oct 3, 2016

$\frac{100}{21}$

#### Explanation:

Assuming you can't simply use a calculator, the only way I see to simplify this expression is translating everything to fractions: we have

$1.6 = \frac{16}{10} = \frac{8}{5}$

and

$0.336 = \frac{336}{1000} = \frac{42}{125}$

Now, if you want to divide by a fraction, you have to multiply for the inverse of that fraction: dividing by $\frac{3}{5}$ is the same thing as multiplying by $\frac{5}{3}$, so

$1.6 : 0.336 = \frac{8}{5} : \frac{42}{125} = \frac{8}{5} \cdot \frac{125}{42}$

And now we can do cross canceling:

$\frac{8}{5} \cdot \frac{125}{42} = 4 \cdot \frac{25}{21} = \frac{100}{21}$