# 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?

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:

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