estimate a rate

Look for mile marker signs like the one at the right. How fast is this vehicle going?

identify rates

Write a unit rate to describe the relationship between distance and time in this situation:

Jocelyn and her mom drove 78 miles to a soccer tournament. The trip took them 1.5 hours.

Write the ratio comparing distance to time.
This is a rate:

miles : hours

Divide both terms of the rate by the same number so that one of the numbers is 1. This is the unit rate.

\(\frac{\FormInput[][math_wrap][]{partial3_wrap}\FormInput{partial3}}{\FormInput[][math_wrap][]{partial4_wrap}\FormInput{partial4}}\) \(\div\) \(\frac{\FormInput[][math_wrap][]{partial5_wrap}\FormInput{partial5}}{\FormInput[][math_wrap][]{partial6_wrap}\FormInput{partial6}}\) = miles : 1 hour

Think about what the result means.

Jocelyn and her mom drove at a rate of miles
per hour to the soccer tournament.

use unit rates involving money

What would you pay for 6 pounds of these apples? How many pounds would you get for $1?

Write the price of the apples as a unit rate.

dollars : pound = \(\frac{\FormInput[][math_wrap][]{partial11_wrap}\FormInput{partial11}}{\FormInput[][math_wrap][]{partial12_wrap}\FormInput{partial12}}\)

Multiply both the numerator and denominator by 6 to get the price for 6 pounds. (Estimate first. It's going to be close to 6 × 2, right?)

\(\frac{\FormInput[][math_wrap][]{partial13_wrap}\FormInput{partial13}}{\FormInput[][math_wrap][]{partial14_wrap}\FormInput{partial14}}\) \(\times\) \(\frac{\FormInput[][math_wrap][]{partial15_wrap}\FormInput{partial15}}{\FormInput[][math_wrap][]{partial16_wrap}\FormInput{partial16}}\) = $ : 6 pounds

Divide both the numerator and denominator of the unit rate by 1.99 to see how much of a pound you can get for $1. Round to the nearest tenth. (Estimate first. It's going to be close to 1 ÷ 2, or about 0.50, right?)

\(\frac{\FormInput[][math_wrap][]{partial18_wrap}\FormInput{partial18}}{\FormInput[][math_wrap][]{partial19_wrap}\FormInput{partial19}}\) \(\div\) \(\frac{\FormInput[][math_wrap][]{partial20_wrap}\FormInput{partial20}}{\FormInput[][math_wrap][]{partial21_wrap}\FormInput{partial21}}\) = $1 : pound

identify unit rates to solve problems

About how much did this person pay per gallon for gas? Round to the nearest cent.

Write the dollars to gallons as a rate (nearest tenth for gallons). Then simplify to a unit rate.

\(\frac{\FormInput[][math_wrap][]{partial23_wrap}\FormInput{partial23}}{\FormInput[][math_wrap][]{partial24_wrap}\FormInput{partial24}}\) ≈ \(\frac{\FormInput[][math_wrap][]{partial25_wrap}\FormInput{partial25}}{\FormInput[][math_wrap][]{partial26_wrap}\FormInput{partial26}}\)

Write the result as a sentence.

This person paid $ per gallon for gas.

think flexibly with unit rates

Look back at the worked examples to complete these sentences. Round to the nearest hundredth.

Jocelyn and her mom drove at a rate of about hour per mile.

In "At the Pump," the person got about gallon of gas per dollar.