Understanding UNIT RATES 6.RP.A.2

Understanding UNIT RATES

6.RP.A.2

6.RP.A.2

Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.

Note: Expectations for unit rates in this grade are limited to non-complex fractions.

Examples of Unit Rates

• This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.

• We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.

Unit Rates

• have denominators equal to one

• labeled units

• Ex. $2/1 ticket, $2 per ticket, $2:1 ticket

• Ex. 

   $\frac{30\ students}{teacher}$  or 30 students/teacher

Let’s find the unit rate of each real-world situation! Ex. Kenny goes to the grocery store and buys 5 pounds of apples for $8.40

Step 1: Write a rate in fraction form.
Step 2: Divide to find the unit rate.

 $\frac{\text{}\text{8.40 dollars}}{5\ pounds}$  ---> $8.40 ÷ 5 pounds = $1.68 per pound

Example Problem

On a bicycle you can travel 20 miles in 4 hours. What is the distance you can travel in 1 hour and the amount of time required to travel 1 mile? HINT: Set and solve using a table with equal measures or a proportion.

Solution:

 You can travel 5 miles in 1 hour written as 

 $\frac{5\ miles}{1\ hour}$  and it takes  $\frac{1}{5}$   of an hour to travel each mile. 

Multiple Choice

A simple modeling clay recipe calls for 1 cup corn starch, 2 cups salt, and 2 cups boiling water. How many cups of corn starch are needed to mix with each cup of salt?

• 1

• 2

• $\frac{1}{2}$

Multiple Choice

Lin rode a bike 20 miles in 150 minutes. If she rode at a constant speed, how far did she go in 15 minutes? HINT: Set up and solve a PROPORTION.

• 2

• 10

Multiple Choice

Lin rode a bike 20 miles in 150 minutes. If she rode at a constant speed, how long did it take her to ride 6 miles? HINT. Set up and solve a proportion.

• 45

• 10

• 50

Multiple Choice

Lin rode a bike 20 miles in 150 minutes. If she rode at a constant speed, how fast did she ride in miles per hour? (This represents a UNIT RATE.)

• 8 miles per hour

• 10 miles per hour

• 15 miles per hour

• 8 miles in 60 minutes

Multiple Choice

Lin rode a bike 20 miles in 150 minutes. If she rode at a constant speed, what was her pace per minute? HINT. Set up and solve a proportion.

• $\frac{4}{30}$ mile per minute

• $\frac{5}{6}$ mile per minute

• $\frac{7}{8}$ mile per minute

Another was to solve the problem is to set up a table.

Multiple Choice

Michelle is computer programmer who designs video games.

She works 30 hours each week and makes $2,535. How much does she make per hour?

• $2,535 ÷ 30 hours = $84.50 per hour

• 30 hours ÷ $2,535 = $84.50 per hour
  

Multiple Choice

Cameron has 2 jobs offers as a camp counselor. At the YMCA, he will be paid $90 for working 8 hours. At the school’s day camp, he will be paid $78 for working 6.5 hours. Which job pays the most?

• YMCA

• School Job

SUMMARY

• Today, we learned that to compare rates, we can first find the __UNIT_ _RATE____ .

• A unit rate is a comparison of 2 different quantities where one measurement has only _1_ unit.

• We can use unit rates to find things like how much a job pays per hour.