2. Ratios, Rates and Proportions

3. Write the ratios: Shaded to Unshaded, Unshaded to total, Total to Shaded, Shaded to Total Write equivalent ratios with 100 in the denominator

4. Ratio: Comparison of 2 quantities - fraction form. Apples to apples or oranges to oranges. It could be Granny Smith to Red delicious or Temple oranges to Navel oranges Example: 5/6 (no units)

5. Write each ratio in simplest form. REDUCE! = 220270 10 27 10 22

6. Rate: Comparison of two numbers with different units Example: Dollars to ounces Example: Miles to gallons Reduce fraction

7. Unit Rate Rate Comparison of the numerator to 1 in the denominator Divide by the denominator Example: A car traveled 600 miles in 10 hours. 600/10 = 60 mph

8. Unit Rate Examples: You purchased 5 pounds of cat food for $2.75. What was the per pound cost? $2.75 ÷ 5 pounds $ per pound

9. The Concept of Proportions The Proportion has a fraction on each side of an equal sign. The fractions have the same value.

10. Write a proportion to express the following: 5 is to 7 as 15 is to 21 Write one for: 6 is to 8 as 9 is to 12

11. Determine if a Proportion Is True or False by Multiplying diagonally across the equal sign 84=84 True Products are equa l 4/14 could have been reduced first.

12. If the cross-products are not equal, statement is false. 16(231)?21(174) 3 3 16(77) ? 7 ( 174) =16(11) ? 174 176=174 Or 16 * 231 = 369621*174=3654 3696 is not the same as 3654 = false 7

13. Solving Proportions

16. Applied Proportion Problems A car assembly line made 243 engines on Monday. 27 were defective. If that rate holds true for each day, how many of the 4131 engines made in a month are defective? Method: 1. Determine unit rate - How many engines per defective unit. Divide that into the total engines. Divide engines by engines. Method: 2. Write proportion, cross multiply and divide. You need to keep units corresponding

17. Write the proportion keeping units corresponding. Cross multiply. Divide by the coefficient of the variable

18. Create a table to keep units corresponding: 27*4131/243= x 11537/243=459 defective Or reduce first: 27*4131/243(27/27)=4131/9 27*4131=243x Never multiply the same units together. If you have, you have set up your equation wrong.

19. A 10-speed bike has a gear ratio of 3 revolutions of the pedal for every two revolutions of the bike wheel. If the bike wheel turns at 65 revolutions per minute, how many times must she pedal per minute. wheel pedal gear ratio 2 3 65 x 2x=65*3 X = 97.5 rpm

20. When there are 8500 passengers a day, Tim rents 340 bikes. The next projection is for 10,300 passengers. How many bikes should Tim plan on renting? passengers bikes 8500 340 10300 x 8500x = 340*10300 85x = 340 * 103 x = 340* 103/ 85 X = 412 bikes

21. A biologist caught 42 fish in a lake and tagged them. She returned them to the lake. After a few days, she caught 50 fish and 7 were tagged. How many fish are in the lake? caught tagged 50 7 x 42 7x = 50 * 42 x = 50 * 6 = 300 fish

22. A park ranger an Alaska forest captures and tags 50 bears. He releases them to range through the forest. Later, he recaptures 50. Four have tags. Estimate the number of bears in the forest. caught tagged 50 4 x 50 4x = 50*50 X = 2500 / 4 = 625 bears