Unit 3, Lesson 8

Ratios and Rates with Fractions

Accelerated 6

8.1

Warm-up

Find each answer mentally.

How many s are there in 5?
What is ?
What is ?
What is ?

8.2

Activity

Calculate at least four quotients. Show your reasoning.

8.3

Activity

Lin ran miles in of an hour. Noah ran miles in of an hour.

Who ran faster, Noah or Lin? Explain or show your reasoning.

Student Lesson Summary

There are 12 inches in 1 foot, so we can say that for every 1 foot, there are 12 inches, or the ratio of feet to inches is . We can find the unit rates by dividing the numbers in the ratio:

,
so there is foot per inch.

,
so there are 12 inches per foot.

When the numbers in a ratio are fractions, we calculate the unit rates the same way: by dividing the numbers. For example, if someone runs mile in minutes, the ratio of minutes to miles is .

, so the person’s
pace is minutes per mile.

, so the person’s
speed is mile per minute.

A unit rate is a rate per 1.

For example, 12 people share 2 pies equally. One unit rate is 6 people per pie, because . The other unit rate is of a pie per person, because .

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Ratios and Rates with Fractions

Warm-up

Activity

Activity

Student Lesson Summary