Section 1.5 : Ratios, Rates and Conversions

Learning Targets: N.Q.1, N.Q.2

Important Terms and Definitions

Ratio – a comparison of numbers by division. Can be written as 𝑎𝑏 ; a to b ; or 𝑎: 𝑏 (𝑏 ≠ 0).

Rate – a ratio of a to b where a and b represent quantities measured in different units of measurement.

Examples: $.7216 oz

4 miles2 gallons

$402 tickets

Unit Rate – a rate with a denominator of one

Examples: 40 miles1 hour

20 candy bars$1

Conversion Factors

Metric System Common U.S /Metric conversions

Kilo- 1 Mile = 5,280 Feet

Hecto- 1 Inch = 2.54 Centimeters

Deka- 1 Meter = 3.28 Feet

Meter/Liter/Gram 1 Pound = 16 Ounces

Deci- 1 Gallon = 3.79 Liters

Centi- 1 Kilogram = 2.2 Pounds

Milli- 1 Mile = 1.60934 Kilometers

Comparing Unit Rates

(ex 1) Trisha, Mark and Eric run in the Spartan Invitational Trisha ran 10km in 2.5 hours, Mark ran 7.5km in 2 hours and Eric ran 9.5 km in 2.25 hours. Find each unit rate and tell who had the fastest speed.

Changing Units of Measure

To change one unit of measure to another, use rates that equal one.

(ex) 60 min = 1 hr, so 60 min1 hr

= 1 and 1 hr60 min

= 1

Example: 2 qt/min = ?? gal/sec

2 qt1 min

×1 gallon4 quarts

×1 minute

60 seconds=

2 gallons 240 seconds

=1 gallon

120 seconds= .0083 gal/sec

gal-qt min-sec multiply simplify unit rate

Find the unit rates for the given situations.

(ex 2) $60 for 8 hours

(ex 3) $34 lb

Make the following conversions.

(ex 4) 17 yards into feet (ex 5) 528 hours into days

(ex 6) 1500 mL into kL (ex 7) 3 feet into centimeters

(ex 8) 8 ft 5 in into inches (ex 9) 4.5 hours into minutes

(ex 10) A sloth travels 0.15 miles per hour. Convert this speed to feet per minute.

(ex 11) Nathan Jones holds the Boardman High School record in the 100 meter dash with a time of 10.92 seconds. In miles per hour, at what speed was Nathan running when he broke that record? (Hint – you don’t need to convert meters directly to miles. Use the feet – meters conversion first, then go to miles!)

(ex 12) Which one is larger – 15 meters or 17 yards? Justify your answer.

Homework – Section 1.5 : Ratios, Rates and Conversions

Convert the given amount to the given unit.

1. 15 kg into pounds 2. 5 gallons into liters 3. 6 pounds into ounces 4. 13 miles into feet

5. In 2011, Geoffrey Mutai ran a record setting time in the Boston Marathon. He finished

the 26.2 mile course in about 2.05 hours. Find Geoffrey’s unit rate, which is his average speed.

6. Typically, a Big Mac is about 215 grams and contains 550 calories. What is the unit rate for calories per gram?

7. If Instagram decided to start charging you to have an account, and the price was $0.78 per day, what would be the cost in dollars per year?

8. Brett and Heidi are going to buy socks. Brett buys a pack of 6 pairs of socks for $10. Heidi buys 20 pairs for $35. Who paid the cheaper price for each pair of socks?

9. A brand of orange juice costs $1.56 for 48 oz. Find the unit rate. 10. The fastest recorded speed for a cheetah is about 60 miles per hour. What was the

cheetah’s speed in feet per second?