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?

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Answer 1 · 2016-11-12T19:58:03

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

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

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 $\frac{something}{miles walked = 1}$ $("something")/("miles walked = 1")$

The 'something' is miles jogged.

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

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

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

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

$\frac{\frac{1}{2} \times \frac{4}{3}}{\frac{3}{4} \times \frac{4}{3}} = \frac{\frac{4}{6}}{1}$ $(1/2xx4/3)/(3/4xx4/3) = (4/6)/1$

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