VIEWS: 10 PAGES: 7 POSTED ON: 12/19/2010
Ratio Proportion Cross Rate
Ratio: A ratio is a quotient of two terms. a a to b = a : b = b Examples: 1.) Write the ratio of 8 to 28 in simplest form. 8 2 2 Answer: 8 : 28 = = final answer: or 2 : 7 or 2 to 7 28 7 7 Reduce both numerator and denominator. Divide both by 4. 2.) Write the ratio of 50 to 6 in simplest form. 50 25 25 Answer: 50 : 6 = = final answer: or 25 : 3 or 25 to 3 6 3 3 *** Do NOT change a ratio to a mixed number.*** Reduce both numerator and denominator. Divide both by 2. 3.) Write the ratio of 12 to 4 in simplest form. 12 3 3 Answer: 12 : 4 = = final answer: or 3 : 1 or 3 to 1 4 1 1 *** You must have the denominator of 1 Reduce both numerator and denominator. Divide both by 4. 4.) Write the ratio of 8 to 16 in simplest form. 8 1 1 Answer: 8 : 16 = = final answer: 1 : 2 or or 1 to 2 16 2 2 5.) Write a ratio in reduced form for each of the following. The Rocket’s baseball team has 20 wins and 8 losses. 20 5 5 a.) Write the ratio of wins to losses. 20 : 8 = = final answer: or 5 : 2 or 5 to 2 8 2 2 Reduce both numerator and denominator. Divide both by 4. b.) Write the ratio of losses to games played. There are 28 games played (losses + wins). 8 2 2 8 : 28 = = final answer: or 2 : 7 or 2 to 7 28 7 7 Reduce both numerator and denominator. Divide both by 4. Rate: A rate is a ratio of unlike quantities. For example: miles per hour (mph), miles per gallon (mpg), and feet per second. Examples: 1.) Write the rate for 30 telephone calls in 6 days in simplest form. 30 telephone calls 5 telephone calls or 5 telephone calls / day or 5 telephone calls per day 6 days 1 day Reduce both numerator and denominator. Divide both by 6. *** The units must be included as part of the answer. *** The units in this example are telephone calls and day. 2.) Write the rate for 250 calories for 10 ounces of drink in simplest form. 250 calories 25 calories or 25 calories / ounce of drink or 25 calories per ounce 10 ounces of drink 1 ounce of drink Reduce both numerator and denominator. Divide both by 10. Proportion: A proportion is when two equal ratios are set equal to each other. 1 4 8 12 Example: is a proportion. is a proportion. 2 8 12 18 8 12 Example: Is a true proportion? 12 15 To find out, you will cross multiply. If the cross products are equal, it is a true proportion. If the cross products are not equal, it is not a true proportion. 8 12 Cross multiply. 12 15 ? 12 12 8 15 144 120 8 12 Answer: No, is not a true proportion. 12 15 8 12 Example: Is a true proportion? 10 15 8 12 10 15 8 12 Answer: Yes, is a true proportion. 10 15 Solving Proportions: To solve a proportion: Cross multiply then solve the algebraic equation. Examples: 1 8 x 2 Solve: Solve: 3 6 9 5 x 1 8 x 32 Cross Multiply. Cross Multiply. 6 9 5 x This gives: 6x = 8 * 9 1 Or 6x = 72 This gives: 5*2 3x 1 Or x 10 3 6 x 72 Divide both sides by 6: 6 6 1 3 x 10 1 1 1 Divide both sides by : 3 3 3 1 Answer: x = 12 x 10 3 3 x 10* 30 1 answer: x =30 Solving Word Problems using Proportions: Example: Set up and solve a proportion for each of the following. Be sure to put the same units across from each other. 1.) If a certain plant will grow 120 cm in 6 days, how many days will it take the plant to grow 140 cm? 120 cm 140 cm Set up a proportion: 6 days x days Solve: Cross Multiply. 120 x = 6 * 140 Or 120 x = 840 120 x 840 Divide by 120 on both sides: 120 120 x=7 Answer: 7 days 2.) Mark knows his car can travel 500 miles on 20 gallons of gasoline. How many gallons can he expect to use if he travels 75 miles? 500 miles 75 miles Set up a proportion: 20 gallons x gallons Solve: Cross Multiply. 500x = 75 * 20 Or 500x = 1500 500 x 1500 Divide by 480 on both sides: 500 500 x=3 Answer: 3 gallons 3.) In Gatlinburg, double fudge sells for $48.00 for 6 pounds. If Mary buys 5 pounds, what should she expect to pay? $48.00 x dollars Set up a proportion: 6 pounds 5 pounds Solve: Cross Multiply. 6 x = 48 * 5 Or 6 x = 240 6 x 240 Divide by 6 on both sides: 6 6 x = $40.00 Answer: $40.00 Practice Ratio and Proportion: ( Answers on the next page). I. Write each as a ratio or rate in simplest form. 1.) 9 to 24 2.) 16 to 8 3.) 48 people in 8 cars 4.) 120 feet in 6 seconds II. Solve each proportion. 10 5 6 x 5.) 6.) x 4 4 6 III. Solve each of the following by setting up a proportion. Show all steps. 7.) If 8 ounces of tomato sauce is used with every 6 ounces of meat, then how many ounces of tomato sauce is needed for 9 ounces of meat. Proportion: _____________________ Answer:____________ 8.) If a certain plant will grow 9 cm in 2 days, how many cm will the plant grow in 4 days? Proportion: _____________________ Answer: _____________ 9.) If a salesman makes 50 calls in 8 hours, how many calls can he make in 4 hours? Proportion: _____________________ Answer: _____________ Answers: I. Write each as a ratio in the simplest form. 3 2 6 people 20 feet 1.) 2.) 3.) or 6 people per car 4.) or 20 feet per second 8 1 1 car 1 second II. Solve each proportion. 5.) x = 8 6.) p = 9 III. Solve each of the following by setting up a proportion. Show all steps. 8s x 8 x 7.) Proportion or Answer x = 12 6m 9m 6 9 9cm x cm 9 x 8.) Proportion or Answer x = 18 2d 4 days 2 4 50c x c 50 x 9.) Proportion or Answer x = 25 8h 4h 8 4