mccoykanye

Ratios compare two quantities. A rate is a type of ratio that compares two quantities that have different units of measurement. The word “per” is often used to describe rates.

Rates can be written as fractions. The first quantity is the numerator and the second quantity is the denominator. Different rates that have the same value are equivalent rates. You can find an equivalent rate the same way you find equivalent ratios—divide or multiply the numerator and the denominator by the same number.

Look at the ratio statements below.

The car travels 15 miles per gallon.

John took 21 minutes to run 3 miles.

Karen buys 20 pencils for $4.  

These ratios are rates that compare two different units of measurements: miles to gallon, minutes to miles, and pencils to dollars.

The ratio for 15 miles per gallon as a fraction is

15 miles1 gallon.

The ratio of 21 minutes to 3 miles for John’s speed as a fraction is

21 minutes3 miles.

Find the equivalent rate for the number of minutes for each mile.

First, use the fraction and divide the numerator and denominator by 3 to find the equivalent rate for 1 mile.

21 minutes÷33 miles÷3=7 minutes1 mile

An equivalent rate of 21 minutes3 miles is 7 minutes1 mile.

John’s speed was 7 minutes per mile.

Using the Karen’s information, find the equivalent rate for the cost of 40 pencils.

First, write the rate of 20 pencils for $4 as a fraction.

20 pencils4 dollars

Next, multiply the numerator and denominator by 2 to find the equivalent rate for 40 pencils.

20 pencils×24 dollars×2=40 pencils8 dollars

An equivalent rate of 20 pencils4 dollars is 40 pencils8 dollars.

40 pencils will cost Karen $8.