Bell Work:

Simplify:

x y x y

(hint: make all exponents positive)

-3 2 -1

Answer:

y

x2

LESSON 52:USING UNIT MULTIPLIERS TO CONVERT MEASURES, CONVERTING MIXED-UNIT TO SINGLE-UNIT MEASURES

Unit Multiplier*: a ratio in which the numerator and denominator are equivalent measures but different units.

Since 12 inches equal one foot, we can write these two unit multipliers for that relationship.

12 inches 1 foot

1 foot 12 inches

Each of these ratios equals 1 because the measures above and below the division bar are equivalent. Since multiplying by 1 (or a form of 1) does not change a quantity, we can multiply by a unit multiplier to convert a measure from one unit to another unit.

Example:

The sapling apple tree is 64 inches tall. Convert 64 inches to feet by multiplying 64 inches by 1foot/12inches.

Answer:

64 inches x 1ft = 64 feet

1 12in 12

= 5 1/3 feet

Practice:

A certain double feature at a theater is 270 minutes long. Use a unit multiplier to convert 270 minutes to hours.

Answer:

270 minutes x 1hr = 270 hours

1 60min 60

= 4 ½ hours

Example:

Daniel is buying refreshments for a meeting. He wonders if four quarts of juice is enough for 30 students. Is four quarts a reasonable amount of juice for the meeting? If not, suggest a more reasonable quantity.

Answer:

4 quarts = 32 oz = 128 oz

1 1 qt

128oz/30 students = 4 oz per student

4 oz is a half cup, 4 quarts will not be enough. However, 8 quarts will allow each student 1 full cup of juice.

Some units like feet and inches are used together to express a measure.

Mr. Seymour is 6ft 3in tall.

To express Mr. Seymour’s height with a single unit we could give his height in inches (75 inches) or in feet 6.25 feet.

Example:

Samantha drove 100 miles in an hour and 45 minutes. How many hours did it take for Samantha to drive 100 miles?

Answer:

45 min = 45/60 hour = ¾ hr = .75 hr

1.75 hours

Practice:

Noel ran one mile in 7 minutes and 30 seconds. Find Noel’s time in minutes. Express the result as a mixed number and as a decimal number.

Answer:

30 sec = 30/60 minutes = ½ or 0.5

7 min 30 sec = 7.5 minutes or 7 ½

Practice:

To measure a room for carpeting, Juan converts the length and width of the room from feet and inches to yards. A room that is 13 feet 6 inches long is how many yards long?

Answer:

13 ft 6 in = 13 6/12 ft = 13.5 feet

13.5 feet x 1 yard = 13.5 yards

1 3 feet 3

= 4.5 yards long

HW: Lesson 52 #1-30