# What is 4 1/3 -: 1 1/6?

Mar 28, 2016

$3 \frac{5}{7}$

Note that the answer is given in the same format as the question.

#### Explanation:

$\textcolor{b l u e}{\text{Shortcut method}}$ Turn upside down and multiply!

$\textcolor{b r o w n}{\text{With practice you will be able to jump many steps.}}$
$\textcolor{g r e e n}{\text{Explained in detail !}}$

First note that 4 is the same as $\frac{12}{3}$ and 1 is the same as $\frac{6}{6}$

So $\text{ "4 1/3 " is the same as } \frac{12}{3} + \frac{1}{3} = \frac{13}{3}$

and$\text{ "1 1/6" is the same as } \frac{6}{6} + \frac{1}{6} = \frac{7}{6}$
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Given: $4 \frac{1}{3} \div 1 \frac{1}{6}$

Write as $\text{ } \frac{13}{3} \div \frac{7}{6}$

Turn the divisor ($\frac{7}{6}$) upside down and multiply giving

$\text{ } \textcolor{red}{\frac{13}{3}} \times \textcolor{b l u e}{\frac{6}{7}}$

You are allowed to move these number around as I will do next
Write as:

$\text{ "color(red)(13/(color(blue)(7))xx(color(blue)(6))/3)" "=" } \frac{13}{7} \times 2$

$\frac{13 \times 2}{7} \text{ "=" } \frac{26}{7}$

But $\frac{26}{7} \text{ " =" "color(magenta)( 7/7+7/7+7/7)color(blue)(+5/7)" } = \textcolor{m a \ge n t a}{3} \textcolor{b l u e}{\frac{5}{7}}$