Question

A strip of wood `66` inches long is is cut into `5``1/2`-inch pieces. How many pieces can be cut?

Answer 1

12

Explanation:

Let the number of pieces of length `5 1/2or11/2` inches be x
so x times of this length will be equal to total length 55 inches
i.e.
`11/2xxx=66=>x = 66xx2/11=12`

Answer 2

Do a division.
12 pieces

Explanation:

The question could be phrased as " How many times can `5 1/2` be cut from 66?"

The really long way to do this is by repeated subtraction....

`66 - 5 1/2 - 5 1/2 - 5 1/2` .... until there is not enough wood left to

cut another piece. Then count how many times you subtracted
This is just painful!

Division is a short cut for repeated subtraction.

So a better method is `66 ÷ 5 1/2`

Now it becomes division with fractions .......
1, change to improper fractions
2. change ÷ to x and invert the last fraction (use the reciprocal)
3. cancel if possible
4. simplify

`66 color(red)(÷ 11/2)`
`rArr 66/1 color(red)(xx2/11) rArr cancel66^6/1 xx 2/cancel11^1`

= 12 pieces