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# November 29

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### November 29

1. 1. November 29, 2012 Today: Fast 15 Warm-Up (5 Questions) Vocabulary Proportions Ratios/Rates/Unit Rates Make-Up Tests
2. 2. Warm-Up Questions1. A student scored 96% on a test with 50 questions. How many questions were missed?2. Ramon spent 40% of his savings on new shoes. He has saved \$275. How much were the shoes?3. In a survey, people were asked to name their favorite sport. 30 said Baseball, 42 football, and 8 soccer. What percent like baseball best?4. Minimum wage in the CNMI has increased from \$4.60 to \$5.55 in the past two years. What is the percent increase?5. You are 15 years old and have lived 18% of your life. At what age will you die?
3. 3. Ratios, Proportions, & RatesA Ratio is a comparison of two numbers by division. Ratios canbe expressed by: 4:3, or 4 to 3, or 4/3.A Proportion is an equation that two ratios are equal. Todetermine if ratios are equal, cross-multiply and check forequality. 2/5 and 6/15 are proportional ratios.A Rate is the comparison (ratio) of two different units ofmeasure. Ex: miles per hour, gallons an hour, dollars a poundWe have used the Percent Proportion to solve percent problems,but there are other problems which do not involve percents.
4. 4. Solving Proportions Example 1: Ben runs 4 miles in 45 minutes. If he only has 30 minutes, how far can he run? Set up a proportion and solve: 4 (miles) = x (miles) 45 (min.) 30 (min.)Example 2: Jill can jump rope 420 times in 2.5 minutes. At thisrate, how many can she do in 30 minutes?Set up a proportion and solve: 402(jumps) = x (jumps) 2.5 (min.) 30 (min.)
5. 5. Proportions and Similar Figures. You can use proportions to find dimensions of objects that are difficult to measure directly…In the Figure below, ABC ~ (is similar) DFE. Find DE. C E Set up the 18 cm proportion: 21 cm x 15 = 21 D F 10 x 10 cm A B 15 cm
6. 6. Example 1: Writing Ratios in Simplest FormWrite the ratio 15 bikes to 9 skateboards in simplestform. bikes = 15 Write the ratioskateboards 9 as a fraction. 15 ÷ 3 = = 5 Simplify. 9÷3 3 The ratio of bikes to skateboards is 5 , 5:3, or 5 to 3. 3
7. 7. Example 1: Using RatiosThe ratio of the number of bones in a human’s ears to thenumber of bones in the skull is 3:11. There are 22 bones inthe skull. How many bones are in the ears? Write a ratio comparing bones in ears to bones in skull. Write a proportion. Let x be the number of bones in ears. Since x is divided by 22, multiply both sides of the equation by 22. There are 6 bones in the ears.
8. 8. The ratio of games lost to games won for a baseball teamis 2:3. The team has won 18 games. How many gamesdid the team lose? Write a ratio comparing games lost to games won. Write a proportion. Let x be the number of games lost. Since x is divided by 18, multiply both sides of the equation by 18. The team lost 12 games.
9. 9. The ratio of left handed to right handed students atNorth High is 2:21. North High has an enrollment of1058 students. How many left handers are at theschool?
10. 10. Solving Rate ProblemsA rate is a ratio of two quantities with different units, such asRates are usually written as unit rates. A unit rate is a rate with asecond quantity of 1 unit, such as or 17 mi/gal. You canconvert any rate to a unit rate.
11. 11. Class Work: Problem 16; side Z should be 9.
12. 12. Class Work:
13. 13. (1) Mindy has 72 candy bars. If the ratio of Mars to Snickers is 8:4, Find the number of each type of candy.(2) Explain what this ratio tell us.
14. 14. Rate Problems: Example 1Cory earns \$52.50 in 7 hours. Find the unit rate. Write a proportion to find an equivalent ratio with a second quantity of 1. Divide on the left side to find x. The unit rate is \$7.50.
15. 15. Converting Rates of Different UnitsA cheetah can run at a rate of 60 miles per hour in shortbursts. What is this speed in feet per minute? Step 1 Convert the speed to feet per hour. Step 2 Convert the speed to feet per minute. To convert the first quantity in a rate, multiply by a conversion factor with that unit in the first quantity. The speed is 5280 feetfeet per hour. 316,800 per minute.
16. 16. Example 2A cyclist travels 56 miles in 4 hours. What is the cyclist’s speedin feet per second? Round your answer to the nearest tenth,and show that your answer is reasonable. Step 1 Convert the speed to feet per hour. Change to miles in 1 hour. To convert the first quantity in a rate, multiply by a conversion factor with that unit in the second quantity. The speed is 73,920 feet per hour.
17. 17. (1) You have 150 different shirts. The ratio ofblue to black shirts is 20 . How many blackshirts do you have? 30