1 / 29

HW # 58 - Ready to Go On p. 242 # 1-20 all Warm up

Week 17, Day One. HW # 58 - Ready to Go On p. 242 # 1-20 all 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.

ellema
Download Presentation

HW # 58 - Ready to Go On p. 242 # 1-20 all Warm up

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Week 17, Day One HW # 58 - Ready to Go On p. 242 # 1-20 all 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

  2. Warm Up Response 24

  3. Homework Check p. 234-235 # 6-30 even and 31, 32, 33 6) 27.5 pounds 8) 12 min 10) Yes 12) Yes 14) 24, 7th graders 16) 5 min 18) ¼ and 4/16 20) 49/182, 7/26 22)a/b, 4a/4b 24) 114 students 26) $48 28) 330 miles 30) 92 shirts 31) About 3.2 about 68 mm Hg 32) Yes; the ratio is less than 2.82:1 33) 154 and 56

  4. Goals for Today • Word problems (together) • CW: • Problem Solving 5-4 • Challenge 5-4

  5. The largest block of cheese on record weighted 920,136 oz. How many tons is this? About 28.75 tons The rate of one knot equals one nautical mile per hour. One nautical mile is 1852 meters. What is the speed in meters per second of a ship traveling at 20 knots? About 10.3 m/s The Outer Bay exhibit at the Monterey Bay Aquarium holds about 1,000,000 gallons of sea water. How many days would it take to fill the exhibit at a rate of 1 gallon per second? About 11.57 days

  6. Vocabulary conversion factor

  7. 1 ft 12 in. The process of converting from one unit to another is called dimensional analysis, or unit analysis. To convert units, multiply by one or more conversion factors. A conversion factor is a ratio of two quantities that are equal but use different units. For example, to convert inches to feet you would use the ratio as a conversion factor.

  8. 1 ft 12 in. Multiplying by a conversion factor is like multiplying by 1. 12 in. 12 in. 1 ft 1 ft = = = 1

  9. The average American uses 48.3 pounds of paper per month. 580 lb 1 yr 1 yr 12 mo yr mo lb yr lb mo = • Divide out like units. 580 lb 12 mo 48.3 lb per month 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. Convert the rate 580 pounds per year to pounds per month. To convert the second amount in a rate, multiply by the conversion factor with that unit in the first quantity. Divide 580 by 12.

  10. 23,040 mi 1 yr 1 yr 12 mo yr mo mi yr mi mo = • Divide out units. 23,040 mi 12 mo = = 1920 per month 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. Convert the rate 23,040 miles per year to miles per month. To convert the second amount in a rate, multiply by the conversion factor with that unit in the first quantity. Divide 23,040 by 12. Sam drives his car 1920 miles per month.

  11. Additional Example 2: Problem Solving Application A car traveled 60 miles on a road in 2 hours. Find this rate in feet per second.

  12. 1 Understand the Problem 1 h 60 min The problem is stated in units of miles and hours. The question asks for the answer in units of feet and seconds. You will need to use several conversion factors. List the important information: 5280 ft 1 mi • Feet to miles • Hours to minutes 1 min 60 s • Minutes to seconds

  13. Make a Plan 2 You know the conversion factor that converts miles to feet. So multiply by each conversion factor separately, or simplify the problem and multiply by several conversion factors at once.

  14. 3 Solve 1 min 60 s hours to minutes minutes to seconds 1 h 3600 s 1 h 60 min = 30 mi 1 h 5280 ft 1 mi 1 h 3600 s • • 1 h 60 min 60 mi 2 h (60÷2) mi (2÷2) h 30 mi 1 h Convert to miles per hour. = = Create a single conversion factor to convert hours directly to seconds: 1 min 60 s hours to seconds = • Set up the conversion factors.

  15. 3 1 h 3600 s 5280 ft 1 mi 30 mi 1 h • • 30 • 5280 ft • 1 1 • 1 • 3600 s 158,400 ft 3600 s = = Solve Continued Divide out like units. = 44 ft 1 s = The car was traveling 44 feet per second.

  16. 4 Look Back A rate of 44 ft/s is less than 50 ft/s. A rate of 60 miles in 2 hours is 30 mi/h or 0.5 mi/min. Since 0.5 mi/min is less than 3000 ft/ 60 s or 50 ft/s and 44 ft/s is less than 50 ft/s, then 44 ft/s is a reasonable answer.

  17. Check It Out! Example 2 A train traveled 180 miles on a railroad track in 4 hours. Find this rate in feet per second.

  18. 1 Understand the Problem 1 h 60 min The problem is stated in units of miles and hours. The question asks for the answer in units of feet and seconds. You will need to use several conversion factors. List the important information: 5280 ft 1 mi • Feet to miles • Hours to minutes 1 min 60 s • Minutes to seconds

  19. Make a Plan 2 You know the conversion factor that converts miles to feet. So multiply by each conversion factor separately, or simplify the problem and multiply by several conversion factors at once.

  20. 3 Solve 1 min 60 s hours to minutes minutes to seconds 1 h 3600 s 1 h 60 min = 45 mi 1 h 5280 ft 1 mi 1 h 3600 s • • 1 h 60 min First, convert 180 miles in 4 hours into a unit rate. 180 mi 4 h (180 ÷ 4) mi (4 ÷ 4) h 45 mi 1 h = = Create a single conversion factor to convert hours directly to seconds: 1 min 60 s hours to seconds = • Set up the conversion factors.

  21. 3 1 h 3600 s 5280 ft 1 mi 45 mi 1 h • • 45 • 5280 ft • 1 1 • 1 • 3600 s 237,600 ft 3600 s = = Solve Continued Divide out like units. = 66 ft 1 s = The train was traveling 66 feet per second.

  22. 4 Look Back A rate of 66 ft/s is more than 50 ft/s. A rate of 180 miles in 4 hours is 45 mi/h or 0.75 mi/min. Since 0.75 mi/min is more than 3000 ft/60 s or 50 ft/s and 66 ft/s is more than 50 ft/s, then 66 ft/s is a reasonable answer.

  23. 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? Use dimensional analysis to check the reasonableness of your answer. 1 100 distance . time Use rate = 52 cm 1 100 s Additional Example 3: Physical Science Application

  24. 1 100 100 • 52 cm 1 100 = s 100 • 5200 cm 1 s 52 cm 1 100 = s Additional Example 3 Continued It may help to eliminate the fraction first. Multiply numerator and denominator by 100.

  25. 1 m 100 cm 5200 cm 1 s = • 5200 m 100 s 52 m 1 s = = Additional Example 3 Continued Convert centimeters to meters to see if the answer is reasonable. 5200 cm 1 s Multiply by the conversion factor. The object is traveling 52 m/s.

  26. 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 distance . time Use rate = 65 cm 1 100 s Check It Out! Example 3

  27. 1 100 100 • 65 cm 1 100 = s 100 • 6500 cm 1 s 65 cm 1 100 = s Check It Out! Example 3 Continued It may help to eliminate the fraction first. Multiply numerator and denominator by 100.

  28. 1 m 100 cm 6500 cm 1 s = • 6500 m 100 s 65 m 1 s = = Check It Out! Example 3 Continued Convert centimeters to meters to see if the answer is reasonable. 6500 cm 1 s Multiply by the conversion factor. The object is traveling 65 m/s.

  29. Lesson Quiz 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. A cheetah was timed running 200 yards in 6 seconds. What was its average speed in miles per hour? 29,920 yd gal ≈ 68 mi/h

More Related