# Question #05bea

Mar 11, 2017

$\frac{1}{\frac{2}{6}} = 1 \times \frac{6}{2} = 3$

$2$ sixths make a third

$\frac{\frac{1}{3}}{\frac{1}{6}} = 2$

#### Explanation:

For the first one and the third one, use the same concept of being able to flip the denominator if it was a fraction and change the question to multiplication.

For the second one, what you do is multiply $\frac{1}{6}$ by $2$ to get $\frac{1}{3}$

$\frac{1}{6} \times 2 = \frac{2}{6} = \frac{1}{3}$

Mar 11, 2017

$1 \div \frac{2}{6} = 3$

It takes two sixths to make $\frac{1}{3}$

$\frac{1}{3} \div \frac{1}{6} = 2$

#### Explanation:

Using the shortcut method

Part 1: $\to 1 \div \frac{2}{6}$

So that you fully understand what is going on write 1 as $\frac{1}{1}$

$\frac{1}{1} \div \frac{2}{6}$ turn the $\frac{2}{6}$ upside down and multiply

$\frac{1}{1} \times \frac{6}{2} \text{ "=" } \frac{1 \times 6}{1 \times 2} = \frac{6}{2}$

$\frac{6}{2} = \frac{6 \div 2}{2 \div 2} = \frac{3}{1} = 3$
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Part 2:$\to \text{ how many sixths make } \frac{1}{3}$

Let the unknown number be $x$

$\frac{x}{6} = \frac{1}{3}$

Multiply by 1 and you do not change the value. However, 1 comes in many forms so you can change the way a value looks without changing 'what it is worth'.

$\textcolor{g r e e n}{\frac{x}{6} = \frac{1}{3} \textcolor{red}{\times 1}}$

$\textcolor{g r e e n}{\frac{x}{6} = \frac{1}{3} \textcolor{red}{\times \frac{2}{2}}}$

$\frac{x}{6} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}$

So it takes two sixths to make $\frac{1}{3}$
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Part 3:$\to \text{What is } \frac{1}{3} \div \frac{1}{6}$

Using the shortcut method of turning upside down and multiplying

$\frac{1}{3} \div \frac{1}{6}$ gives the same answer as $\frac{1}{3} \times \frac{6}{1}$

$\frac{1 \times 6}{3 \times 1} = \frac{6 \div 3}{3 \div 3} = \frac{2}{1} = 2$