# 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?

Nov 17, 2016

He took 5 breaks

#### Explanation:

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

$\implies \frac{3}{4} \div \frac{1}{8} \text{ "->" } \frac{3}{4} \times \frac{8}{1}$

$\frac{3}{{\cancel{4}}^{1}} \times \frac{{\cancel{8}}^{2}}{1} = 3 \times 2 = 6$

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.

$\frac{3}{4} = \frac{6}{8}$ 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 $\left(\frac{3}{4} \div \frac{1}{8}\right) - 1 = 6 - 1 = 5$

Nov 17, 2016

$5$ breaks on a $\frac{3}{4}$ mile walk.
$13$ breaks on a $1 \frac{3}{4}$ mile walk.

#### Explanation:

The question is not clear -whether Jimmy walked $1 \frac{3}{4}$ miles or whether it was just $\frac{3}{4}$ of a mile.

Let's consider both...

He rests every $\frac{1}{8}$ of a mile. Each quarter has two eighths in it, so it would seem that:

$\frac{3}{4} \div \frac{1}{8} = 6$

However, after the last $\frac{1}{8}$, 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 $1 \frac{3}{4}$ miles. In the first mile he rests 8 times, and then another 5 times in the next $\frac{3}{4}$ because then he arrives at school. He would rest 13 times.

$1 \frac{3}{4} \div \frac{1}{8} = \frac{7}{4} \div \frac{1}{8}$

=$\frac{7}{4} \times \frac{8}{1} = 14$ times. But after the the last part he is as school.
$14 - 1 = 13$ breaks