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# December12, 2013

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### December12, 2013

1. 1. Make-Up Tests? K. Academy Topics Warm-Up: (0 Questions) Ratios/Rates/Unit Rates Measurement Ratios Class Work
2. 2. 1. Ratio Word Problems 2. Rate Problems .5 3. Rates & Proportional Relationships Topics are due by December 20 for online and Alt.Khan. **Waaaaay too many people have a grade of zero for their homework grade (Khan), which is 20% of your overall grade.
3. 3. A fraction is a 'part over the whole' comparison of one number. Remember the root comes from the Latin "to break up". We are taking one number and breaking it up. A ratio is the comparison of two different numbers. Therefore, we must solve ratio problems differently.
4. 4. Class Notes Section of Notebook. please
5. 5. A Ratio is a comparison of two numbers by division. Ratios can be expressed by: 4:3, or 4 to 3, or 4/3. A Proportion is an equation that two ratios are equal. To determine if ratios are equal, cross-multiply and check for equality. 2/5 and 6/15 are proportional ratios. A Rate is the comparison (ratio) of two different units of measure. Ex: miles per hour, gallons an hour, dollars a pound We have used the Percent Proportion to solve percent problems, but there are other problems which do not involve percents.
6. 6. 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 this rate, how many can she do in 30 minutes? Set up a proportion and solve: 402(jumps) = x (jumps) 2.5 (min.) 30 (min.)
7. 7. 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) C E 18 cm 21 cm A 15 cm B Set up the proportion: 15 = 21 10 x x D 10 cm DFE. Find DE. F
8. 8. Example 1: Writing Ratios in Simplest Form Write the ratio 15 bikes to 9 skateboards in simplest form. bikes = 15 skateboards 9 15 ÷ 3 = 5 = 9÷3 3 Write the ratio as a fraction. Simplify. The ratio of bikes to skateboards is 5 , 5:3, or 5 to 3. 3
9. 9. Example 1: Using Ratios The ratio of the number of bones in a human’s ears to the number of bones in the skull is 3:11. There are 22 bones in the 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.
10. 10. The ratio of games lost to games won for a baseball team is 2:3. The team has won 18 games. How many games did 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.
11. 11. The ratio of games lost to games won for a baseball team is 2:3. The team has played 45 games. How many games did the team lose? Write a ratio comparing games lost to total games Write a proportion. Let x be the number of games lost.
12. 12. Rate: 90 miles 3 hours Read as “90 miles per 3 hours.”