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Chapter 4

Chapter 4. Rates, Ratio, and Proportions. Ratio-. Is the comparison of two quantities that have the same units, often written in fraction form. The first quantity mentioned is the numerator and the second quantity is the denominator.

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Chapter 4

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  1. Chapter 4 Rates, Ratio, and Proportions.

  2. Ratio- • Is the comparison of two quantities that have the same units, often written in fraction form. • The first quantity mentioned is the numerator and the second quantity is the denominator. • Always reduce the fraction to lowest terms. Leaving improper fractions as improper.

  3. Examples of a Ratio The ratio of 15 hours to 20 hours. 15 hours 20 hours = 3 hours 4 hours Penny’s Kennel has 57 golden retriever puppies. Thirty- eight are females. What is the ratio of female puppies to male puppies? = 38 19 Female puppies Male puppies

  4. Rates • is the comparison of two quantities with different units. Unit Rate- is the rate whose denominator value equals one. (Divide)

  5. Examples of Unit Rates A car traveled 301 miles in 7 hours. Find the unit rate. 301 / 7 = 43 miles per hour

  6. Example 2- Unit Rate You spend $4.00 for 15 tablets. Find the unit rate. 4.00 / 15 = .2666 repeats = $ 0 .27 per tablet

  7. Example 3- Unit Rate You spend $6150 on 150 shares. Find the unit rate. 6150 / 150 = $41 per share

  8. Proportions • states that two rates or two ratios are equal. • Important- When you write a proportion, order is important. Be sure you match up the rates • To find out if it is true proportion cross multiply, and make sure they equal.

  9. Example 1 Determine if the two ratios form a proportion • = 35 • 2 10 2 x 35 = 70 YES 7 x 10 = 70

  10. Example 2 3 ½ = 5 ¼ 8 12 3 ½ x 12 = 42 YES 5 ¼ x 8 = 42

  11. Example 3 2.5 = 4.3 3 5 2.5 x 5 = 12.5 NO 4.3 x 3 = 12.9 Validation is not required

  12. Solving Proportions • You cross multiply and divide. • Validate- by cross multiplying to make sure they are equal. 9 x 16 = 144 • = 9 • 16 n 144 / 36 = 4

  13. Example 2 • = N • 12 144 144 x 5 = 720 720 / 12 = 60

  14. Example 3 6.5 = n 10 4.3 6.5 x 4.3 = 27.95 27.95 / 10 = 2.795

  15. Application Problems Example 1 In the manufacturing process, it has been found that for every 192 items assembled, 3 are defective. At this rate, if 6400 items are assembled, how many will be defective? 6400 x 3 = 19200 6400 N 192 3 = 19200 / 192= 100

  16. Example 2 If 2 ½ inches on a map represent 48 miles, what distance does 6 inches represent? 2 ½ 48 6 N 6 x 48 = 288 = 288 / 2 ½ = 115.2

  17. Example 3 During a sunset, a pole barn casts a shadow 7 ½ feet long while the 3 foot tall evergreen tree growing next to it casts a shadow 2 feet long. To the the nearest foot, how tall is the pole barn? 7 ½ N 2 3 7 ½ x 3 = 22.5 = 22.5 / 2 = 11.2 Round to 11 feet

  18. Example 4 The school volunteers used 3 gallons of paint for two rooms. How many gallons would they need to paint 10 rooms of the same size? 3 x 10 = 30 3 2 N 10 = 30 / 2 = 15

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