4-7 Dimensional Analysis Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes.

4-7 Dimensional Analysis

Warm UpWarm Up

Lesson Presentation

Problem of the Day

Lesson Quizzes

4-7 Dimensional Analysis

Warm UpFind each unit rate.

1. jump rope 192 times in 6 minutes

2. four pounds of bananas for $2.36

3. 16 anchor bolts for $18.56

4. 288 movies on 9 shelves

32 jumps/min

$0.59/lb

$1.16/bolt

32 movies/shelf

4-7 Dimensional Analysis

Problem of the Day

The sum of four consecutive integers is 182. What are the four numbers?

44, 45, 46, and 47

4-7 Dimensional Analysis

MA.7.G.4.4 Compare, contrast, and convert units of measure between different measurement systems (US customary or metric (SI)), dimensions, and derived units to solve problems.

Sunshine State Standards

4-7 Dimensional Analysis

Vocabulary

unit conversion factor

4-7 Dimensional Analysis

A unit conversion factor is a fraction in which the numerator and denominator represent the same quantity in different units.

4-7 Dimensional Analysis

The average American uses 580 pounds of paper per year. Find this rate in pounds per month, to the nearest tenth.

Additional Example 1: Using Conversion Factors to Solve Problems

The problem gives the ratio 580 pounds to 1 year and asks for an answer in pounds per month.

580 lb 1 yr

1 yr 12 mo

580 lb 12 mo

=

= 48.3 lb per month

Multiply the ratio by the conversion factor.

Divide 580 by 12.

The average American uses 48.3 pounds of paper per month.

Cancel yr units. •yrmo= lb

molbyr

4-7 Dimensional Analysis

Check It Out: Example 1

Sam drives his car 23,040 miles per year. Find this rate in the number of miles driven per month, to the nearest mile.

23,040 miles 1 yr

1 yr 12 mo

= 1,920 mi/mo

4-7 Dimensional Analysis

One mile is about 1.6 kilometers. What is the length in miles of a 10 kilometer race? Round to the nearest tenth of a mile.

Write a proportion using 1 mi. = 1.6 km.

= miles kilometers

1 1.6

Additional Example 2: Converting Between Metric and Customary Units

x 10

1 · 10 = 1.6 · xThe cross products are equal.

10 = 1.6x Multiply. ___ ___ 1.6 1.6 Divide each side by

1.6.6.25 = x

A 10 kilometer race is about 6.3 miles.

4-7 Dimensional Analysis

One inch is equal to 2.54 centimeters. How many inches are there in 12 centimeters? Round to the nearest tenth.

Check It Out: Example 2A

; 2.54 1

12 x

2·54x = 12; x ≈ 4.7; 4.7 in. =

4-7 Dimensional Analysis

One gallon is equal to about 3.875 liters. How many liters are there in 6 gallons? Round to the nearest tenth.

Check It Out: Example 2B

; 3.875 1

x 6

x= 6 3.875 = 23.25; 23.3 L =

4-7 Dimensional Analysis

Additional Example 3: Application

A tennis pro serves a ball that travels the length of the court, 78 feet, in 0.75 second. How fast is the ball moving in feet per second? Check your answer for reasonableness.

4-7 Dimensional Analysis

Additional Example 3 Continued

The ball’s speed is 104 ft/s.

Convert ft/s to mi/h to see if the answer is reasonable.

The ball’s average speed is 71 mi/h, which is a reasonable speed for a serve.

4-7 Dimensional Analysis

Check It Out: Example 3

Gary travels 1,320 ft in 1.5 min on his bicycle. How fast is he traveling in feet per min? Check your answer for reasonableness.

1,320 ft1.5 min

= 1,320 ft ÷ 1.51.5 min ÷ 1.5

= 880 ft1 min

4-7 Dimensional Analysis

Check It Out: Example 3 Continued

Convert to mi/hr:

880 ft1 min

880 ft1 min

= 60 min1 hr

1 min5280 ft

= 10 minhr

This is a reasonable speed for a bicycle.

4-7 Dimensional Analysis

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

4-7 Dimensional Analysis

Lesson QuizFind the appropriate factor for each conversion.

1. You drive 136 miles from your house to your aunt’s

house at the lake. You use 8 gallons of gas. How

many yards does your car get to the gallon?

2. One ounce is about 28.3 grams. A box of cereal has a

mass of 400 grams. What is the weight of the box in

ounces? Round to the nearest tenth of an ounce.

29,920 ydgal

14.1 oz

4-7 Dimensional Analysis

Lesson Quiz

Find the appropriate factor for each conversion.

3. A cheetah was timed running 200 yards in 6

seconds. What was the average speed in miles per

hour?

≈ 68 mi/h

4-7 Dimensional Analysis

1. A recipe for lemonade requires diluting the lemonade concentrate with 6 quarts of water. How many gallons of water are required to dilute the concentrate?

A. 1 gallon

B. 1.5 gallons

C. 2 gallons

D. 2.5 gallons

Lesson Quiz for Student Response Systems

4-7 Dimensional Analysis

2. There are about 400 jelly beans in a pound. There are 2.2 pounds in a kilogram. About how many grams does a jelly bean weigh?

A. 0.85 g

B. 0.98 g

C. 1.06 g

D. 1.14 g

Lesson Quiz for Student Response Systems

4-7 Dimensional Analysis

3. A sea horse swims at about 0.01 miles per hour. What is the swim speed in inches per second?

A. 10.56 inches per second

B. 10.75 inches per second

C. 11.24 inches per second

D. 11.5 inches per second

Lesson Quiz for Student Response Systems