Topic 3

Unit Rates and Conversions

Name  Date

I.  Converting Within Systems

A.  Complete each customary measurement conversion.

1. There are 4 quarts in 1 gallon. How many 2. There are 16 ounces in 1 pound.
quarts are in 4 gallons? How many pounds are in 48 ounces?

3. There are 12 inches in 1 foot. How many 4. There are 3 feet in 1 yard. How many
feet are in 174 inches? yards are in 12 feet?

5. There are 5280 feet in 1 mile. How many 6. There are 2000 pounds in 1 ton.
feet are in 3.5 miles? How many tons is 7500 pounds?

B.  Complete each metric measurement conversion.

1. There are 10 meters in 1 dekameter. 2. There are 100 dekameters in 1 kilometer.

How many meters are in 5 dekameters? How many dekameters are in
8.5 kilometers?

3. There are 10 centimeters in 1 decimeter. 4. There are 100 meters in 1 hectometer.

How many decimeters are in How many hectometers are in 201 meters?
37 centimeters?

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5. There are 1000 milligrams in 1 gram. 6. There are 1000 millimeters in 1 meter.
How many grams is 25 milligrams? How many meters are in 350 millimeters?

C.  Multiply by a unit rate to determine each measurement conversion using unit analysis.

1. How many feet are in 3 miles? 2. How many pounds are in 5 tons?

3. How many fluid ounces are in 8 cups? 4. How many yards are in 504 inches?

5. How many pounds are in 480 ounces? 6. How many gallons are in 200 quarts?

7. How many ounces are in 1 ton? 8. How many yards are in 2 miles?

9. How many inches are in 1 mile? 10. How many fluid ounces are in 2 pints?

11. How many pints are in 3 gallons? 12. How many fluid ounces are in 4 quarts?

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Percents
Unit Rates and Conversions

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Name  Date

II.  Converting Between Systems

A.  Use the table to complete each measurement conversion.

Length Mass Capacity

1 ft 5 30.48 cm 1 lb 5 0.45 kg 1 mL 5 0.034 fl oz

1 mi 5 1.61 km 1 kg 5 2.2 lb 1 pt 5 0.473 L

1 km 5 0.62 mi 1 kg 5 35.27 oz 1 L 5 0.264 gal

1 m 5 39.37 in.

1 in. 5 0.0254 m

1 m 5 1.09 yd

1. How many inches are in 32 centimeters? 2. How many feet are in 26 meters?

3. How many kilometers are in 57 yards? 4. How many ounces are in 26 grams?

5. How many liters are in 19 quarts? 6. How many grams are in 5 pounds?

7. How many cups are in 40 liters? 8. How many gallons are in 800 milliliters?

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B.  Use the table and scale up or down to calculate each measurement conversion. Round your
answer to the nearest hundredth, if necessary.

1. Rosa drove 175 miles to visit her 2. Franco weighs 165 pounds. What is his
grandparents. How many kilometers did mass in kilograms?
she travel?

3. Ronna is making dinner for her family. The 4. Hector needs to refill his lawn mower gas
recipe she is using calls for 0.5 kilogram tank. The tank holds 4.2 liters of gas. How
of ground chicken. How many pounds of many gallons of gas does the tank hold?
ground chicken does she need?

5. Lee is going to compete in a 5000 meter 6. Lavon’s favorite basketball player is

Race Walk. How long is the race in yards? 2.1 meters tall. How tall is Lavon’s favorite
basketball player in feet?

III.  Fractional Rates

A.  A common error in advertising occurs when announcing prices less than $1.00.
Read the scenario and then answer each question.

1. Sue’s Stop-n-Shop advertises that 2. Wesley’s Wings and More advertises

12-ounce sodas are “0.99 cents” each and a wing special on Monday nights. The
programs this price into her cash registers. advertisement states that wings are
Using the advertised price, determine the “0.25 cents” each. Elias and his two
income generated by selling 500 sodas. friends each ordered 20 wings. Using the
advertised price, determine how much
Elias and his two friends should pay.

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Percents
Unit Rates and Conversions

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Name  Date

3. A cell phone company advertises that 4. A carnival game advertises “0.50 cents
their data plan costs “0.02 cents” for for a ring toss”. Sarah wants to toss the
every kilobyte of data. Corinne used ring 12 times. Using the advertised price,
1000 kilobytes of data. Using the determine how much Sarah should pay for
advertised price, determine how much her ring tosses.
Corinne owes on the data plan.

5. At a yard sale, Enzo sees a sign that 6. School Supplies R Us is having a back-
advertises “0.05 cents per used book.” to-school sale and advertises in the local
Using the advertised price, determine the paper that pencils are “0.88 cents a pack.”
cost of 40 used books. Using the advertised price, determine the
income generated by selling 200 packs of
pencils.

IV.  Comparing Rates

A.  Solve each problem by determining and then comparing the rates in each situation.

1. Kordell is able to complete 14 math 2. Bashir drove 64 miles and used 2 gallons
problems in 21 minutes. Gabriel is able to of gas. Rebecca drove 36 miles and used
complete 6 math problems in 10 minutes. 1 gallon of gas. Determine how many
Determine how many problems each miles each person drove per 1 gallon of
student can complete per minute. Who gas. Who drove more fuel-efficiently?
can complete problems more quickly?

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3. Pia’s home computer downloads a 4. Howard went fishing and caught 28 fish
3-megabyte program in 10 seconds. in 7 hours. Santo went fishing for 9 hours
Estelle’s home computer takes 42 seconds and caught 27 fish. Determine how many
to download a 10-megabyte program. fish each person caught per hour. Who
Determine how many megabytes each caught fish more quickly?
computer downloads per second. Whose
computer downloads faster?

5. Lydia travels for 81 minutes to visit a friend 6. Margarita baked 49 cookies in 4 hours.
who lives 6 miles away. Tonya travels 5 Edward was baking for 5 hours and
miles to visit a friend. It takes 81 minutes made 63 cookies. Determine how many
to get there. Determine how many miles cookies each person baked per hour.
each person travels in one minute. Who Who baked cookies faster?
travels more rapidly?

7. Chelsea and Justin have a reading 8. Darius biked for 2 hours and traveled
assignment for English class. Chelsea takes 21 miles. Kala biked 42 miles in 5 hours.
54 minutes to read 27 pages. Justin takes Determine how many miles each person
16 minutes to read 8 pages. Determine biked in one hour. Who biked more
how many pages each student can read quickly?
per minute. Who can read more quickly?

9. During the basketball season, Terrell 10. Alvin is able to complete 6 math
scored a total of 54 points in 9 games. problems in 15 minutes. Fernando
Marvin scored a total of 45 points in takes 49 minutes to complete
6 games. Determine how many points 14 math problems. Determine how many
each player scored per game. Which problems each student can complete
player scored more points per games? per minute. Who can complete problems
more quickly?

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Percents
Unit Rates and Conversions

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Name  Date

11. Vivian drove 84 miles and used 7 gallons 12. Emily went fishing and caught 36 fish in
of gas. Pauline used 3 gallons of gas to 5 hours. Juan went fishing for 8 hours
drive 45 miles. Determine how many and caught 48 fish. Determine how many
miles each person drove per 1 gallon of fish each person caught per hour. Who
gas. Who drove more fuel-efficiently? caught fish more quickly?

Unit Rates and Conversions: Skills Practice • 55