Rates & Unit Rates

What is a rate? A rate is a ratio that is used to compare measurements with different units.

What is a unit rate? A Unit Rate - is a rate with a denominator of 1.

Rate Unit Rate$32 in 4 hours = $8 in 1 hour36 students at 9 tables = 4 students at 1 table120 miles in 2 hours = 60 miles in 1 hour$5.94 for 6 sodas = $0.99 for 1 soda

Read this slide, then talk about it with a partner!

There are 672 students in a school and there are 28 teachers. How many students per teacher?

To find the unit rate (or students per 1 teacher) divide both the numerator and the denominator by the denominator.

students 672 ÷ 28 = 24teachers 28 ÷ 28 1

There are 24 students per teacher.

Read this slide, then talk about it with a partner!

Try these.Find the unit rates.

20 toys for 5 dogs = 4 toys for 1 dog

$735 per week = $147 per week(Hint: 5 day work week)

For every 12 laps Evan Evan runs 3 laps runs Lucas runs 4 Lucas runs 1

Richard read 27 pages Richard read 9 in 3 hours pages in 1 hour

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For each of the following questions,

answer on a whiteboard or in your journal

BEFORE you check the answer

Emily drove 825 miles in 15 hours. How many miles per hour (mph) did she drive?

A 815 miles per hour

B 60 miles per hour

C 55 miles per hour

D 15 miles per hour

Answer: C 55 miles per hour

Emily's brother drove 340 miles and used 17 gallons of gas. How many miles per gallon (mpg) did he get?

Answer: 20 miles per gallon or 20 mpg

Margot bought 16 oranges for $4. How much does 1 orange cost? (Read carefully!!)

Answer:

We need to find the rate of DOLLARS per ORANGE (not oranges per dollar )

$4 ÷ 16 = $0.25 per orange

Brian bought 3 pounds of chicken for $10.47. How much was one pound of chicken?

Answer:

Again, we need to find the rate of DOLLARS per POUND of chicken

$10.47 ÷ 3 = $3.49 per pound

150 ÷ 20 = 7.5 min per mile so 7.5 x 6 = 45 minutes to run 6 miles

20 ÷ 150 = 0.13 mile per min so 0.13 x 15 = about 2 miles in one minute

20 ÷ 150 = 0.13 mile per min then 0.13 x 60 = 7.8 miles per hour

150 ÷ 20 = 7.5 min per mile

Tim ran 1 mile in 11 minutes, Bob ran 4 miles in 43 minutes, Rosana ran 15 miles in 2 hours 38 minutes and Carrie ran 23 miles in 3 hours 50 minutes. Who ran the fastest?

A Tim

B Bob

C Rosana

D Carrie

Answer:

A 11 min ÷ 1 mi = 11 min per mileB 43 min ÷ 4 mi = 10.75 min per mileC 158 min ÷ 15 mi = 10.5 min per mileD 230 min ÷ 23 mi = 10 min per mile

Now create an example of your own and share with your math buddy.

What type of unit rate question will you create?1- Multiple Choice2- Short Answer3-Statement and decide who is correct? 4-Open ended