# Question #9ddf0

Oct 1, 2016

$128$

#### Explanation:

We have: $42 \frac{2}{3} \div \frac{1}{3}$

$= \frac{42 \frac{2}{3}}{\frac{1}{3}}$

$= \frac{\frac{42 \cdot 3 + 2}{3}}{\frac{1}{3}}$

$= \frac{\frac{128}{3}}{\frac{1}{3}}$

$= \frac{128}{3} \cdot \frac{3}{1}$

$= \frac{128}{3} \cdot 3$

$= 128$

Oct 1, 2016

It is $128$

#### Explanation:

$42 \frac{2}{3} \div \frac{1}{3}$

$= 42 \frac{2}{3} \times 3$

$= 42 \times 3 + \frac{2}{3} \times 3$

$= 126 + 2$

$= 128$

I used the following properties of division and multiplication:

• division by a fraction is the same as multiplication by the fraction's reciprocal

## $a \div \frac{b}{c} = a \times \frac{c}{b}$

• distributive property:

## $a \times \left(b + c\right) = a b + a c$

Oct 1, 2016

$128$

#### Explanation:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Dividing with fractions: $\rightarrow$ In a nutshell

Step 1 . change all mixed numbers to improper fractions

Step 2 .$\div \rightarrow \times$ and flip the next fraction

Step 3 : cancel any numerator with any denominator through $\times$

Step 4 : $\left(\text{top x top")/("bottom x bottom}\right)$

Step 5 : simplify if necessary.

Step 6 : Keep improper fractions or change to mixed numbers depending on what you have been told to do.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$42 \frac{2}{3} \div \frac{1}{3}$

$= \frac{128}{3} \div \frac{1}{3} \text{ } \leftarrow$ step 1

$= \frac{128}{3} \times \frac{3}{1} \text{ } \leftarrow$ step 2

$= \frac{128}{\cancel{3}} \times \frac{\cancel{3}}{1} \text{ } \leftarrow$ step 3 and step 4

$= 128 \text{ } \leftarrow$ step 5. no further simplifying necessary

Oct 4, 2016

$42 \frac{2}{3} \div \frac{1}{3} = 128$

#### Explanation:

$\textcolor{b l u e}{\text{For a moment consider just the } 42 \frac{2}{3}}$

write this as $42 + \frac{2}{3}$

This is the same as:

$\text{ } \left[42 \textcolor{m a \ge n t a}{\times 1}\right] + \frac{2}{3}$

But we can write 1 as $\frac{3}{3}$ giving:

$\text{ } \left[42 \textcolor{m a \ge n t a}{\times \frac{3}{3}}\right] + \frac{2}{3}$

$\text{ "[126/3]" } + \frac{2}{3} = \frac{128}{3}$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Putting it all together}}$

$42 \frac{2}{3} \div \frac{1}{3} \text{ "=" } \frac{128}{3} \div \frac{1}{3}$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Shortcut method}}$
Turn the $\frac{1}{3}$ upside down and multiply

$\frac{128}{3} \times \frac{3}{1} \text{ "=" "3/3xx128/1 " "=" "1xx128" "=" } 128$

Or by cancelation (which is the same thing really):

$\frac{128}{\cancel{3}} \times \frac{\cancel{3}}{1} = \frac{128}{1} = 128$