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2.6 Write Ratios and Proportions

9-16-14. 2.6 Write Ratios and Proportions. Warm-up:. Common Core CC.9-12.A.CED.1 Create equations and in one variable and use them to solve problems. Solve the equation 5/6x = 25 2/3(6x + 3) = 14 g/5 – 7 = 12

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2.6 Write Ratios and Proportions

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  1. 9-16-14 2.6 Write Ratios and Proportions Warm-up: Common Core CC.9-12.A.CED.1 Create equations and in one variable and use them to solve problems. Solve the equation 5/6x = 25 2/3(6x + 3) = 14 g/5 – 7 = 12 You buy three identical polyester film balloons and a birthday card. The card costs $3.95. Find the cost of each balloon if your total bill before tax was $33.80 Essential Question: How do you find ratios and write and solve proportions?

  2. Ratios • A ratio uses division to compare two quantities. You can write the ratio of two quantities a and b, where b is not equal to 0, in three ways. • a to b a:b a/b • Each ratio is read “the ratio of a to b.” Ratios should be written in simplest form.

  3. SOLUTION 14 14 10 14 + 10 a. = = 14 7 7 12 5 24 home matches home matches b. = = = all matches away matches EXAMPLE 1 Write a ratio VOLLEYBALL A volleyball team plays 14 home matches and 10 away matches. a.Find the ratio of home matches to away matches. b.Find the ratio of home matches to all matches.

  4. ANSWER 11 11 13 24 ANSWER EXAMPLE 1 for Example 1 GUIDED PRACTICE Derek and his brother decide to combine their CD collections. Derek has 44 CDs, and his brother has 52 CDs. Find the specified ratio. 1.The number of Derek’s CDs to the number of his brother’s CDs. 2.The number of Derek’s CDs to the number of CDs in the entire collection.

  5. Proportions • A proportion is an equation that states that two ratios are equivalent. The general form of a proportion is given below: where b

  6. 330 . x 11 x x Solve the proportion = = 30 30 30 6 6 x = 11 11 6 6 30 30 = EXAMPLE 2 Solve a proportion Write original proportion. Multiply each side by 30. Simplify. 55= x Divide.

  7. = 4 w 7 35 3. ANSWER 20 EXAMPLE 2 for Example 2 GUIDED PRACTICE Solve the proportion. Check your solution.

  8. = m 9 12 2 4. ANSWER 54 EXAMPLE 2 for Example 2 GUIDED PRACTICE Solve the proportion. Check your solution.

  9. = 5 z 9 54 5. ANSWER 30 EXAMPLE 2 for Example 2 GUIDED PRACTICE Solve the proportion. Check your solution.

  10. EXAMPLE 3 Solve a multi-step problem ELEVATORS The elevator that takes passengers from the lobby of the John Hancock Center in Chicago to the observation level travels150feet in 5 seconds. The observation level is located on the 94th floor, at 1029 feet above the ground. Find the time it takes the elevator to travel from the lobby to the observation level.

  11. 5 Seconds x = 150 1029 feet STEP 2 Solve the proportion. EXAMPLE 3 Solve a multi-step problem SOLUTION STEP 1 Write a proportion involving two ratios that compare the amount of time the elevator has ascended with the distance traveled.

  12. 1029 = 1029 5 150 5145 x = 150 ANSWER The elevator travels from the lobby to the observation level in 34.3 seconds. x x 5 = 1029 1029 150 EXAMPLE 3 Solve a multi-step problem Write proportion. Multiply each side by1029. Simplify. 34.3 =x Use a calculator.

  13. EXAMPLE 3 Solve a multi-step problem CHECK You can use a table to check the reasonableness of your answer. The solution, 34.3 seconds, is slightly less than 35 seconds, and 1029 feet is slightly less than 1050 feet. So, the solution is reasonable.

  14. 6. WHAT IF? In Example 3, suppose the elevator travels 125 feet in 5 seconds. Find the time it will take for elevator to travel from the lobby to the observation level. ANSWER 41.16 sec GUIDED PRACTICE for Example 3

  15. 7. When two full moons appear in the same month. The second full moon is called a blue moon. On average, 2 blue moons occur every 5 years. Find the number of blue moons that are likely to occur in the next 25 years. ANSWER 10 blue moons GUIDED PRACTICE for Example 3 ASTRONOMY

  16. Classwork/Homework 2.6 Exercises 2-54 even pages 117 to 119

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