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BELL Ringer 10-30 – 5 minutes

1 . What is the Title of Lesson 2-6? 2. What is a ratio? 3. What is a proportion? 4. What is the difference between a rate and a unit rate? 5. What are means and extremes?. BELL Ringer 10-30 – 5 minutes. Objectives: By the end of the next class, students will be able to:

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BELL Ringer 10-30 – 5 minutes

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  1. 1. What is the Title of Lesson 2-6? 2. What is a ratio? 3. What is a proportion? 4. What is the difference between a rate and a unit rate? 5. What are means and extremes? BELL Ringer 10-30 – 5 minutes

  2. Objectives: By the end of the next class, students will be able to: • Analyze and compare ratios and rates. • Solve proportions using equivalent ratios (fractions) and rates. • Find the means and extremes of a proportion with 85% or above mastery. Lesson 2-7 objectivesRatios and Proportions

  3. A ratio is a comparison of two numbers by division. The ratio of x to y can be written in 3 different ways. x: y x to y or x y An equation that has 2 equal ratios (fractions) is called a proportion. Example: 2: 5 = 6: 15 2 = 6 5 15 p. 111

  4. To determine if 2 ratios (fractions) are equivalent, you can write them in simplest form. See Example 1: Another way to determine if 2 ratios are equal is by using cross products. If cross products are =, then the ratios form a proportion. (This means that the product of the means must equal the product of the extremes.) In 2: 5 = 6:15 2 = 6 5 15 5 and 6 are called the means (the middle terms of the proportion). 15 and 2 are called the extremes (the first and last terms of the proportions). Does 5  6 = 15  2 30 = 30

  5. So, 2 = 6 5 15 1. 3 , 9 7 14 Are these fractions equivalent? 7  9 = 3  14 Put a ? over the = sign 63  42 So 39 7 14 Individual Practice – p. 114 2, 3 p. 114

  6. Solve each proportion. If necessary round to the nearest tenth. 4. n = 6 9 27 27(n) = 9(6) 27n = 54 27 27 n = 2 Solving Proportions

  7. The ratio of 2 measurements having different units of measure is called a rate. For example, 45 miles in 5 hours is called a rate. miles hour A rate that tells how many of one item is being compared to 1 of another item is called a unit rate. In the example above 9 miles per hour. 7. Jennie ran the first 6 miles of a marathon in 58 minutes. If she is able to maintain the same pace, how long will it take her to finish the 26.2 miles? What units of measure are we comparing?

  8. miles minutes How will this proportion be setup? 6 miles = 26.2 58 minutes x minutes 6x = 58(26.2) 6x = 1519.6 6 6 x = 253.3 minutes How many hours and minutes would this be? It would take her 4 hours and 13.3 minutes to finish the race.

  9. 8. Maps: On a map, North Carolina, Raleigh and Asheville are about 8 inches apart. If the scale is 1 inch = 12 miles, how far apart are the cities? The rate will be inches miles 1inch = 8 inches 12 miles m miles 1m = 96 Cross Products m = 96 miles Simplify The cities are about 96 miles apart. Scale Model #8

  10. 33. Menu: On Monday, a restaurant made $545 selling 110 hamburgers. If they sold 53 hamburgers on Tuesday, how much did they make? The rate will be cost hamburgers cost545 = x Hamburgers 110 53 110x = 28, 885 Cross products 110 110 Divide both sides by 110 x = 262.59 Simplify

  11. The made about $262.59 on Tuesday for selling 53 hamburgers. Proportions Using the Distributive Property. 27. x – 3 = 6 5 10 10(x – 3) = 30 Cross products 10x – 30 = 30 Distributive Property +30 +30Add 30 to both sides 10x = 60Simplify 10 10 Divide 10 on both sides x = 6 Simplify

  12. Shared Practice: Now try 29, 31 and 35

  13. 37. 4v + 7 = 6v + 2 15 10 15(6v + 2) = 10(4v + 7) 90v + 30 = 40v + 70 Try 39 Proportions and Variables on both sides

  14. 44. Diaries: In a survey, 36% of the students said that they kept an electronic diary. There were 900 students who kept an electronic diary. How many students were in the survey? What units of measure are we using? students keeping an electronic diary total students 36 = 900 100 x 36x = 90,000 36 36 x = 2,500

  15. There were 2500 total students in the survey.

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