Question

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?

Answer 1

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.

`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).

`909/18 = (909-:2)/(18-:2)=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.

`" "454.5`
`color(magenta)(50)xx9->ul(450.0)larr" Subtract"`
`" "4.5larr" This is less than 9"`

Note that `4.5` is the same as `color(green)([45xx1/10])` and 45 is more than 9

So to divide by `color(blue)(9)` we have

`color(green)([45xx1/10])color(blue)(xx1/9)" "=" "45/9xx1/10" "=" "5xx1/10=color(magenta)(0.5)`

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

So we have 50 boxes + `1/2` a box left over.

`1/2` a box is `[1/2xx18]=9`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check:

`[50xx18]+9 = 909`