Question

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?

Answer 1

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.`

Answer 2

`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`

Answer 3

`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