Question

Jimmy walked one 3/4 miles to school if you took a break every 1/8 of a mile how many breaks did he take?

Answer 1

He took 5 breaks

Explanation:

If a break was taken every `1/8` of a mile the question is really asking: how many `1/8` can you fit in the distance walked. There is a trap in this and I did fall into it.

`=> 3/4 -:1/8" "->" "3/4xx8/1`

`3/(cancel(4)^1)xx(cancel(8)^2)/1 = 3xx2=6`

As Ez as pi correctly pointed out. The end point is not a break but a stop so is has to be removed from the count.

`3/4 = 6/8` so lets look at this as a distance line diagram

This shows that if you can draw one a quick sketch pays off in the end.

The count of breaks is `(3/4-:1/8) -1 = 6-1 =5`

Answer 2

`5` breaks on a `3/4` mile walk.
`13` breaks on a `1 3/4` mile walk.

Explanation:

The question is not clear -whether Jimmy walked `1 3/4` miles or whether it was just `3/4` of a mile.

Let's consider both...

He rests every `1/8` of a mile. Each quarter has two eighths in it, so it would seem that:

`3/4 div 1/8 = 6`

However, after the last `1/8`, he is at school, so he will not take a break.
He therefore he takes 5 breaks on the way to school.

The same applies if the distance is `1 3/4` miles. In the first mile he rests 8 times, and then another 5 times in the next `3/4` because then he arrives at school. He would rest 13 times.

`1 3/4 div 1/8 = 7/4 div 1/8`

=`7/4 xx8/1 = 14` times. But after the the last part he is as school.
`14-1 = 13` breaks