Grade 7 · Unit 1 · Lesson 1 · part 3 of 6

Now the amounts are fractions

Here is the 7th grade step.

Now the amounts are fractions

Here is the 7th grade step. The amounts can be fractions. Julia walks 12 mile every 14 hour. How far does she walk in one hour?

Ask yourself one question: what would I multiply 14 hour by to get 1 hour? Four quarter hours make an hour, so the answer is 4. That number is the reciprocal of 14: flip the fraction and you get 41, which is 4. A fraction times its reciprocal is always 1.

Now the rule: multiply the other amount by the same number. Each quarter hour, Julia walks a half mile. Four of them: 12 × 4 = 2 miles.

Four quarter hours make one hour. Each one gets a half mile. Four halves make 2 miles.

Multiply both by the reciprocal
Hours	Miles
14	12
14 × 4 = 1	12 × 4 = 2

So Julia walks 2 miles per hour. The time became 1, and the distance came along for the ride, because both amounts were multiplied by the same number.

The reciprocal method Ask: what do I multiply the time (or whatever amount comes after per) by to get 1? That number is its reciprocal. Multiply the other amount by the same number, and you have the unit rate. Use this whenever it works.

Second example, paint. A half gallon of paint covers 16 of a wall. How much paint for one whole wall? What do I multiply 16 wall by to get 1 wall? Its reciprocal, 6. So multiply the paint by 6 too: 12 × 6 = 3 gallons per wall.

Paint
Walls	Gallons
16	12
16 × 6 = 1	12 × 6 = 3

Where to go next

Next: Every ratio gives two unit ratesEvery ratio gives you two unit rates, depending on which amount you make into 1. All the partsRates with Fractions