Fill in the Missing Numbers

1 foot = _____ inches

1 meter = _____ centimeters

1 pound = _______ ounces

1 minute = ______ seconds

1 hour = ________ minutes

1 day = __________ seconds

12

100

16

60

60

86,400

Essential Questions

• How can you use Dimensional Analysis to convert and compare simple measures using one conversion ratio?

• How can you use Dimensional Analysis to compare simple rates using one or two conversion ratios?

Vocabulary Words

• Ratio• Rate• Unit Rate• Unit Conversion Factor• Dimensional Analysis

DefinitonsA unit conversion factor is a fraction whose numerator and denominator are equivalent measures. Some common unit conversion factors are given below. You can also use the reciprocal of these.

1 ft? in.

1 yd? ft

1 mi? ft

1lb? oz

1 pt? c

1 qt? pt

1 gal? qt

1 hr? min

1 min? s

1m? cm

1km? m

DefinitionsDimensional analysis is a way to analyze and solve problems using the units, or dimensions of the measurements.

• Ratio- the indicated quotient of two mathematical expressions.

• Rate – a measure, quantity, or frequency, typically one measured against some other quantity or measure.

• Unit Rate – a comparison of two different quantities when they are combined.

Choose a unit conversion factor that…

• Introduces the unit you want in the answer

• Cancels out the original unit so that the one you want is all that is left.

“Canceling” out Words

inches feetfeet miles

seconds hoursminutes seconds

inchesmiles

hoursminutes

Practice: Choose the appropriate conversion factor.

Inches to feet 1 ft12 in.

12 in.1 ft

Minutes to hours 60 min1 hr

1 hr60 min

Meters to centimeters 1 m100 cm

100 cm1 m

inches1

minutes1

meters1

Convert 8 yards to feet…

Make a decision: What conversion factor will you use?

3 ft 1 yd or 1 yd 3 ft

Hint!Use the one that will cancel out the units you want to change

Set up the problem: Multiply the measurement by the conversion factor.

ft yd1 yd38

Solve the problem: Perform the multiplication

ft yd ft ft yd ft1 yd 1 yd3 8 3 248 24

1 1

8 yards1

A bucket holds 16 quarts. How many gallons of water will fill the bucket? Use a unit conversion factor to convert the units.

What are the two conversion factors comparing quarts and gallons?

4 qt1 gal

1 gal4 qt

Which one will “cancel” quarts?

16 qt 16 gal 4 gal

4

You Try it!One bag of apples weighs 64 ounces. How many pounds does it weigh?

1 lb 64 1 lb64 oz = 4 lb16 oz 16

Darren drank 2 liters of water. How many milliliters of water did he drink?

1000 mL 2 1000 mL2 L = 2000 mL1 L 1 L

Making Rate Conversions

Use a unit conversion to convert the units within each rate

Convert 80 miles per hour to feet per hour.

80 mi1 hr

5,280 ft1 mi

80 5280 ft

1 hr

422,400 ft

1 hr

Convert 63,360 feet per hour to miles per hour.

63,360 ft1 hr

1 mi5280 ft

63,360 ft 1 mi1 hr 5280 ft

12 mi1 hr

You Try it!Convert 32 feet per second to inches per second.

32 ft 12 in 32 ft 12 in 384 ft = 1 s 1 ft 1 s 1 ft 1 s

A craft store charges $1.75 per foot for lace. How much per yard is this?

$1.75 3 ft $1.75 3 ft $5.25 = 1 ft 1 yd 1 ft 1 yd 1 yd

Word ProblemsThe average American eats 23 pounds of pizza per year. Find the number of ounces the average American eats per year.

23 lb 16 oz 23 16 368 oz1 yr 1 lb 1 1 yr

The average American eats 368 ounces of pizza per year.

Word Problems…A car traveled 60 miles on a road in 2 hours. How many feet per second was the car traveling? Hint: Set up the words first.

mihr

ftmi

hr s

How many seconds

in an hour?60 s 60 min 3600 s

1 min 1hr 1 hr

1 hr3600 s

60 mi2 hr

5,280 ft1 mi

60 5,2802 3600

44 ft1 s

The car traveled 44 feet per second.