Unit 4 RATIO AND PROPORTION

2 RATIOS  A ratio is the comparison of two like quantities The terms of a ratio must be compared in the order in which they are given The first term is the numerator of a fraction, and the second term is the denominator A ratio should be expressed in lowest fractional terms

3 RATIOS  Express 3 feet to 18 inches as a ratio in lowest terms Change the quantities to a common unit We will change the 3 feet to 36 inches Then write the ratio as a fraction and reduce

4 PROPORTIONS  A proportion is an expression that states the equality of two ratios The product of the means equals the product of the extremes In the proportion or 3:4 = 9:12 3 and 12 are the extremes, 4 and 9 are the means

5 1.2A = (14.8)(2.4) Divide both sides by 1.2 A = 29.6 Ans PROPORTIONS  Solve the proportion below for A: Cross Multiply

6 DIRECT PROPORTIONS  Two quantities are directly proportional if a change in one produces a change in the other in the same direction  When setting up a direct proportion in fractional form Numerator of the first ratio must correspond to numerator of the second ratio Denominator of the first ratio must correspond to the denominator of the second ratio

7 DIRECT PROPORTION EXAMPLE  If reducing calorie intake by 2,000 calories results in a weight loss of one pound, how many pounds would a person lose if he/she ate 14,500 fewer calories? Since an increase in calorie reduction will result in an increase in weight loss, the proportion is direct Set calories as the numerator and pounds as the denominator in both ratios

8 EXAMPLE (Cont)  Solve by cross multiplication x = 7.25 pounds Ans

9 INVERSE PROPORTIONS  Two quantities are inversely or indirectly proportional if a change in one produces a change in the other in the opposite direction  The two quantities are inversely proportional if An increase in one produces a decrease in the other A decrease in one produces an increase in the other

10 INVERSE PROPORTIONS  When setting up an inverse proportion in fractional form Numerator of first ratio must correspond to the denominator of the second ratio. Denominator of first ratio must correspond to the numerator of second ratio

11 INVERSE PROPORTION EXAMPLE  It takes 3.5 hours for the 12 workers at Betty’s Bakery to prepare the baked goods sold each day. How many hours would it take 15 workers to produce the same goods? Since more workers would require less time to bake the goods, this problem is an inverse proportion Set numerator of first ratio equal to 3.5 hours and set corresponding 12 workers equal to denominator of second ratio.

12 EXAMPLE (Cont)  Denominator of first ratio will be the variable (x hours)  Numerator of second ratio will be the corresponding 15 workers  Solve by cross multiplication x = 2.8 hours Ans

13 PRACTICE PROBLEMS  Express the following ratios in lowest terms: 1. 16: /5 to 1/ min to 1 hour

14 PRACTICE PROBLEMS (Cont) 7. The fifteen workers in the Fly-By- Night Machine Shop produce 1200 keyboards daily. How many keyboards would twenty workers produce daily? 8. The scale on a given map is 1 inch = 32 miles. How many miles would there be between two cities that are 3 inches apart on the map?

15 PRACTICE PROBLEMS (Cont) 9. Two gears are in mesh. The driver gear has 30 teeth and revolves at 250 revolutions per minute. Determine the number of revolutions per minute of a driven gear with 12 teeth. 10. If six identical machines can produce 1000 parts in 7 hours, how many hours will it take four of these machines to produce the same 1000 parts?

16 PRACTICE PROBLEMS (Cont) 11. You drive to school through a construction zone so it is 35 mph and takes you 75 minutes. When the construction is done, you can go 55mph, how long will it take you to get to school? Round to the nearest minute. 12. You moved a year ago and it took you and 3 friends (4 people) 6.5 hours. If you get 5 more friends and have not gained any items over the year, how long will it take the 9 people to move you? Round to the tenth of an hour.

17 PROBLEM ANSWER KEY 1. 4/7 2. 6/5 3. 1/ keyboards miles rpm hours minutes hours