# A book publisher prints 909 copies of a book. He packs the books into boxes with exactly 18 books in each box. How many boxes will he be able to fill, and how many books will be left over?

##### 1 Answer
Jul 7, 2017

50 boxes with 9 books left over.

#### Explanation:

We need to see how many lots of 18 will fit into 909. Consequently this is a division.

$\frac{909}{18}$

Lets suppose you do not have a calculator.

The 18 times table is not something most people learn but there is a sort of cheat (not really).

$\frac{909}{18} = \frac{909 \div 2}{18 \div 2} = \frac{454.5}{9}$

So now we have changed it to the 9 times table.

Long division confuses some people so this is another way of approaching it.

$\text{ } 454.5$
$\textcolor{m a \ge n t a}{50} \times 9 \to \underline{450.0} \leftarrow \text{ Subtract}$
$\text{ "4.5larr" This is less than 9}$

Note that $4.5$ is the same as $\textcolor{g r e e n}{\left[45 \times \frac{1}{10}\right]}$ and 45 is more than 9

So to divide by $\textcolor{b l u e}{9}$ we have

$\textcolor{g r e e n}{\left[45 \times \frac{1}{10}\right]} \textcolor{b l u e}{\times \frac{1}{9}} \text{ "=" "45/9xx1/10" "=" } 5 \times \frac{1}{10} = \textcolor{m a \ge n t a}{0.5}$

Thus 909-:18=454.5-:9=color(magenta)(50+0.5=50.5

So we have 50 boxes + $\frac{1}{2}$ a box left over.

$\frac{1}{2}$ a box is $\left[\frac{1}{2} \times 18\right] = 9$
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Check:

$\left[50 \times 18\right] + 9 = 909$