Mr: Gengel wants to make a shelf with boards that are #1 1/3# feet long. If he has an 18-foot board, how many pieces can he cut from the big board?

Well actually #13# and a half, but we are assuming he needs full pieces, so #13# shelves.

This is simple division:

Mr. Gengel needs shelves that are #1 1/3# feet long and has an #18# foot long board. In order to determine how many shelves he can make you must divide:

#18 ÷ 1 1/3#
#= 13.5#

You can't have half a shelf so you round down to #13.#

Let's convert the mixed number to an improper fraction. This is done by multiplying the whole number by the denominator (#1xx3=3#), and then adding the numerator (#3+1=4#). So now your new numerator (#4#) is replaced into the fraction, giving you #4/3#.

You can also convert whole numbers into improper fractions.
Here, we will use #54# since that is the product of #18# and #3#.*
So now you have a #54/3# foot long board, from which you want to cut #4/3# feet length boards.

Here is the division step: divide these two values. #54/3\div4/3# is also written as #54/3xx3/4# (you can flip the second fraction to multiply; this is called a "reciprocal").
Values on opposite sides of the fraction line can cancel out: #54/\cancel{3}xx\cancel{3}/4=54/4#
Simplify this and you get #54\div4=13.5#

In word problems of this type, the first decision it which operation(s) you need to do.

Questions involving fractions often sound more difficult than they are. Make a similar question with easy numbers.

How many shelves #2# feet long cut be cut from a board #12# feet long? It is clearly a division. #12 div 2 =6#

For the given question it is also a division.

#18 div 1 1/3#

#= 18/1 div 4/3" "larr# make improper fractions.

#= 18/1 xx 3/4" "larr# multiply by the reciprocal

#= cancel18^9/1 xx 3/cancel4^2" "larr# cancel by #2#

#= 27/2#

#= 13 1/2" "larr# need a whole number of shelves.

#=13# shelves