For every 1/2 mile that Sira jogs, she walks 3/4 mile. What unit rate gives the number of miles Sira jogs for every mile she walks?

Nov 12, 2016

The unit rate is $\frac{2}{3}$

With units of measurement we have:$\text{ } \frac{2}{3}$ miles jogged per mile walked

Explanation:

The clue is the wording part: "the number of miles jogged for every mile she walks".

What is on each side of the word 'for' tells you which way round the format is.

So we have $\left(\text{something")/("miles walked = 1}\right)$

The 'something' is miles jogged.

So initial condition $\to \left(\frac{1}{2} \text{ mile jogged")/(3/4"miles walked}\right)$

To make this 'unit rate' we need to change $\frac{3}{4}$ miles walked into 1 mile walked (unit->1)

To change $\frac{3}{4}$ into 1 multiply by $\frac{4}{3}$

What we do to the bottom we also do to the top for multiply or divide giving:

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

So the unit rate is $\frac{4}{6} \equiv \frac{2}{3}$