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?

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Answer 1 · 2017-07-07T16:16:13

50 boxes with 9 books left over.

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#