In section 1, we learned about solving proportional relationships by multiplying by a constant. In this section, we are going to focus on a special kind of number for the constant called the unit rate. A unit rate is a ratio in which one of the values being compared is 1. Some common unit rates are miles (or kilometers) per hour, wages earned per month, meters per second, cost per item, and miles per gallon.

What do you notice about the list of common unit rates?

Interactive popup. Assistance may be required. Check Your Answer They all have the word per.

Which mathematical operation is implied by the word, "per?"

Interactive popup. Assistance may be required. Check Your Answer Division

Which mathematical operation would you use to find a unit rate from information given in a problem?

Interactive popup. Assistance may be required. Check Your Answer Division

Copy the following table in your notes and fill in the missing information.

Click here to see the completed table.

Situation	Rate			Unit Rate
Juan is training to run a long-distance race. While he trains, he keeps track of his pace in minutes per mile. On one of his training runs, he takes 36 minutes to cover 4.5 miles.	36 minutes	Per	4.5 miles	8 min/mile
Maria's dad put 7gallons of gas in the car for $24.50. What was the price per gallon?	$24.50	Per	7 gallons	$3.50 per gallon
Linda is filling out an application for a job. One of the questions on the application asks her how much she made per month at her last job. In her last job as a babysitter she made $600 in 4 months.	$600.00	Per	4 months	$150 per month
Mike reads a 495 page book for homework. It takes him 15 days to finish the book. How many pages did he read per day?	495 pages	Per	15 days	33 pages per day

You want to pay careful attention to the units when you set up your equation.

The unit rate for the first situation is 8 min/mile. We can write this as 8 minutes over 1 mile 8 minutes 1 mile

Click the ratio below to find out what happens when you multiply by a time of five minutes.

Does this answer make sense?

Interactive popup. Assistance may be required. Check Your Answer No, we don't measure in minutes times minutes per mile.

Click the ratio below to find out what happens when you multiply by a distance of five miles.

Does this answer make sense?

Interactive popup. Assistance may be required. Check Your Answer Yes

What has to be true about the units to be sure that your equation is correct?

Interactive popup. Assistance may be required. Check Your Answer The units need to cancel, or the answer won't make sense.

Take another look at the first situation in the top row of the table. Write an equation that you could use to calculate m, the number of minutes Juan runs if you know d, the distance he covers in miles. Assume that he keeps the same pace.

Interactive popup. Assistance may be required. Check Your Answer m = 8d

If the race is 3.1 miles long, how long will it take Juan to finish it?

Interactive popup. Assistance may be required. Check Your Answer m = 8d
m = 8 (3.1)
m = 24.8
It will take Juan 24.8 minutes to finish the race (about 24 minutes and 48 seconds)

Now consider the third situation with Linda and her babysitting. Write an equation that Linda could use to calculate p, the pay that Linda could expect if she were to continue babysitting for m months.

Interactive popup. Assistance may be required. Check Your Answer p = 150m

Linda decides not to take the new job and continues babysitting, how much will she earn in 7 months?

Interactive popup. Assistance may be required. Check Your Answer p = 150m
p = 150(7)
p = 1050
Linda will earn $1050 in 7 months