Grade 7 · Unit 1 · Lesson 1

Rates with Fractions

A unit rate is how much for one. Unit means one, rate means how much of one thing for another, and per means for each. In 6th grade the numbers were whole; now they can be fractions. Ask what you would multiply the time by to get 1, its reciprocal, then multiply the distance by the same number.

About 25 minutes How much for one?

ElleMath-speak

I say it the way your test says it.

FinnPlain English

And I say it the way you would say it to a friend. Same idea, two ways.

Finn

Hi, I am Finn. I will be with you the whole way through.

Today we find how much for one, even when the amounts are fractions.

When you reach the practice, press Hint any time you are stuck. Asking is not cheating.

The big idea

Finn says

A proportional relationship always multiplies by the same number, the unit rate.

A unit rate is how much for one. Unit means one, rate means how much of one thing for another, and per means for each. To find a unit rate, ask what you would multiply the per amount by to get 1. That number is its reciprocal, and a fraction times its reciprocal is always 1. Then multiply the other amount by the same number. Written as a fraction over a fraction, a complex fraction, it is the same move: multiply top and bottom by the reciprocal of the bottom, and the bottom becomes 1. Every ratio gives two unit rates, and the question tells you which one to use. A proportional relationship always multiplies by the same number, the unit rate. This lesson finds that number.

The parts of this lesson

Each part is its own short page. Go in order, or pick the one you need.

1The Words We UseThe vocabulary for this lesson, in one place.Start here 2Unit, rate, perYou already know this one from 6th grade. 3Now the amounts are fractionsHere is the 7th grade step. 4Every ratio gives two unit ratesEvery ratio gives you two unit rates, depending on which amount you make into 1. 5Which unit rate answers the question?A ratio gives two unit rates. Pick the one that answers the question, then read why. 6Practice ProblemsTry them, get help one step at a time, then print how it went.

Printables

One page with the three words, the divide-to-find-it method, Julia's walk worked both ways, and the paint example. Plus a worksheet with an answer key and a short lesson plan for the parent or tutor.

Study guide (PDF) Worksheet and answer key (PDF) Lesson plan (PDF)

Where this goes next

Next lesson: What Makes It ProportionalChecking tables and graphs for the same multiplier. Back to the Math 7 mapEvery 7th grade lesson, in course order. Tell us what you thoughtA few quick questions about this lesson. It takes a minute, and it is how the lesson gets better.

NC Grade 7 standards in this lesson: NC.7.RP.1.