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?

Question

Kennedy Adams · Accepted Answer

The unit rate is #2/3#

With units of measurement we have:#" "2/3 # miles jogged per mile walked

The phrase "the number of miles jogged for every mile she walks" is the clue. The word "for" and what's on either side of it indicate which way around the format is. So we have #("something")/("miles walked = 1")# The'something' is the miles-jogged. So initial condition #->(1/2" mile jogged")/(3/4"miles walked")# To make this 'unit rate' we need to change #3/4# miles walked into 1 mile walked (unit->1) To change #3/4# into 1 multiply by #4/3# For multiply or divide giving, we do the same thing to the top as we do to the bottom: #(1/2xx4/3)/(3/4xx4/3) = (4/6)/1# So the unit rate is #4/6-=2/3#

Eva Abramson · Answer

undefined To find the unit rate of miles Sira jogs for every mile she walks, divide the distance she jogs by the distance she walks.

$ \frac{\frac{1}{2} \text{ miles jogged}}{\frac{3}{4} \text{ mile walked}} $

To divide fractions, multiply the first fraction by the reciprocal of the second fraction:

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

Simplify the fraction:

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

So, the unit rate is $ \frac{2}{3} $ miles jogged for every mile walked.