Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Warm Up Find 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

Problem of the Day The sum of four consecutive integers is 182. What are the four numbers? 44, 45, 46, and 47

Learn to use dimensional analysis to make unit conversions.

Vocabulary unit conversion factor

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

Be sure to put the units you are converting to in the numerator and the units you are converting from in the denominator. Caution!

Additional Example 1: Using Conversion Factors to Solve Problems The average American uses 580 pounds of paper per year. Find this rate in pounds per month, to the nearest tenth. 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 Multiply the ratio by the conversion factor. Cancel yr units. • yr mo = lb 580 lb 12 mo = = 48.3 lb per month Divide 580 by 12. The average American uses 48.3 pounds of paper per month.

Multiply the ratio by the conversion factor. Check It Out: Example 1 Sam drives his car 23,000 miles per year. Find the number of miles he drives per month, to the nearest mile. The problem gives the ratio 23,000 miles to 1 year and asks for an answer in miles per month. 23,000 mi 1 yr 1 yr 12 mo Multiply the ratio by the conversion factor. Cancel yr units. • yr mo = mi 23,000 mi 12 mo = = 1916.6 per month Divide 23,000 by 12. Sam drives his car about 1917 miles per month.

Additional Example 2: Converting Between Metric and Customary Units 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. miles kilometers Write a proportion using 1 mi. = 1.6 km. 1 1.6 x 10 = The cross products are equal. 1 · 10 = 1.6 · x 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.

Check It Out: Example 2 1 hour is equal to 60 minutes. What is the time in hours for a 165 minute movie? Round to the nearest hour. hour minutes Write a proportion using 1 hour = 60 min 1 60 x 165 = The cross products are equal. 1 · 165 = 60 · x 165 = 60x Multiply. ___ ___ 60 60 Divide each side by 60. 2.75 = x A 165 minute movie is about 3 hours.

Additional Example 3: Physical Science Application A strobe lamp can be used to measure the speed of an object. The lamp flashes every of a second. A camera records the object moving 52 cm between flashes. How fast is the object moving in m/s? 1 100 52 cm 1 100 s distance . time Use rate =

Additional Example 3 Continued 1 100 It may help to eliminate the fraction first. 52 cm 1 100 s = 100 • 52 cm 1 100 s 100 • Multiply top and bottom by 100. 5200 cm 1 s =

Additional Example 3 Continued Now convert centimeters to meters. 5200 cm 1 s 5200 cm 1 s = • 1 m 100 cm Multiply by the conversion factor. 5200 m 100 s = 52 m 1 s = The object is traveling 52 m/s.

Check It Out: Example 3 A strobe lamp can be used to measure the speed of an object. The lamp flashes every of a second. A camera records the object moving 65 cm between flashes. How fast is the object moving in m/s? 1 100 65 cm 1 100 s distance . time Use rate =

Check It Out: Example 3 Continued 1 100 It may help to eliminate the fraction first. 65 cm 1 100 s = 100 • 65 cm 1 100 s 100 • Multiply top and bottom by 100. 6500 cm 1 s =

Check It Out: Example 3 Continued Now convert centimeters to meters. 6500 cm 1 s 6500 cm 1 s = • 1 m 100 cm Multiply by the conversion factor. 6500 m 100 s = 65 m 1 s = The object is traveling 65 m/s.

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

Lesson Quiz Find 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 yd gal 14.1 oz

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

Lesson Quiz for Student Response Systems 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 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 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