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?

3 Answers
Feb 22, 2018

13

Explanation:

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.

Feb 22, 2018

13.5 pieces

Explanation:

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

Feb 22, 2018

13 shelves can be cut.

Explanation:

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