When do we use equivalent ratios (proportions) in everyday life? A ratio table can be used to find and organize equivalent ratios.

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1 Name: Period: Date: Pre-AP NOTES: EQUIVALENT RATIOS (PROPORTIONS) Finding Equivalent Ratios Using Ratio Tables and Graphs When do we use equivalent ratios (proportions) in everyday life? Recipe conversions (Double, halve, triple, etc.) Reading maps Speed and Distance I have a recipe that feeds four people, but I need to feed eight. How do I change the recipe? If 1 inch equals 50 miles, how far is it from Houston to San Antonio? If I can drive 60 miles in 1 hour, how long will it take me to drive 400 miles? Comparison shopping If it costs $3.65 for 5 ounces, what does 1 ounce cost? Scale drawings Example: Floor plans Measurement conversions (Feet to inches, etc.) People to people ratios If the drawing of the room is 2 by 3, how big will the actual room be? If each piece of rope is 18 inches long, how many feet do I have? If the restaurant needs 2 waiters for every 15 people, how many waiters are needed when 250 customers are in the restaurant? A ratio table can be used to find and organize equivalent ratios. A party planning guide said that three pizzas will serve about seven people. How many pizzas are needed for 350 people? # of pizzas # of people # of pizzas # of people

2 Characteristics of a Ratio Table 1. There are two or more rows and two or more columns. 2. Rows are labeled with names that indicate the meaning of the numbers (includes units if used). 3. There is no preference on what to choose as upper or lower row. 4. The ratio between the numbers in the columns is the same for all columns. 5. The numbers in an empty column can be found by multiplying or dividing a completed column by the same factor. 6. Completed columns can be added or subtracted. Let s try a few. 1. Find the cost of 6 pieces of candy if 2 pieces cost 8 cents and if the price of the candy is the same no matter how many are sold. Now solve using a proportion. 2. If 3 boxes of cereal are on sale for $6.90, and a daycare provider needs 17 boxes, how much will she pay? Now solve using a proportion.

3 3. The width of my house is 30 feet, how many inches is this? Now solve using a proportion. Graphs can also be used to find equivalent ratios. How do we know when a graph is proportional? 4. The table and graph below show Lacy s pay for different numbers of hours. Complete the table below using the graph. Time worked (hours) Pay ($) Ratio of pay to hrs 5. The graph shows the hours worked and total pay for Paul s part-time job. Use the graph to find equivalent ratios and list in the table below. Predict the pay for 25 hours.

4 Name: Period: Date: Pre-AP: Equivalent Ratios Practice Investigating Proportional Relationships 1. Here is a picture of Mr. Tall and Mr. Short. Mr. Short is six paper clips in height. If he is measured in large buttons, he is four large buttons in height. Mr. Tall is similar to Mr. Short but is six large buttons in height. Predict the height of Mr. Tall if you could measure him in paper clips. Solve as a proportion Paper clips Buttons 2. Which pitcher will have the strongest lemonade flavor or will they taste the same? Pitcher A Pitcher A Pitcher B Pitcher B Now compare the A to B ratios. If you had 8 cups of lemonade mix, how much water would be needed for pitcher A? If you had 15 cups of lemonade mix, how much water would be needed for pitcher B?

5 3. If a 7-pound weight stretches a spring a distance of 24.5 inches, how far will the spring stretch if a 12-pound weight is applied? A. 3.4 inches Solve as a proportion B inches C. 42 inches D. 294 inches 4. In Mr. Lewis s class, if you score less than a 70% on any test, you have to take the test again. The tests don t always have the same number of questions, so Mr. Lewis made a chart to help his students know how many correct answers they need to score a 70% or better. Use the ratio table below to help in fill in his chart. Number of Test Questions Number Correct Needed for 70% Correct Answers Needed Number of Questions Use a proportion to find the number of correct answers needed for 60 questions.

6 Use the mathematics chart below as needed to answer the following questions. 6. A 3 pound pork roast is cut into 10 smaller pork chops of equal weight. How many ounces does each pork chop weigh? 7. A total of 35 pints of blood were collected at a local blood drive. How many quarts of blood is this? 8. A car repair shop changed the oil of 50 cars. They 1 recovered 3 quarts of oil from each car. How 2 many gallons of oil did they recover? Solve using a proportion. 5. I have 2 pints of strawberries. A recipe calls for 5 cups of strawberries. Are 2 pints of strawberries enough? Equivalent ratios from the chart: 9. A 40-foot power boat is for sale by owner. About how long is this boat to the nearest yard? 1 pint 2 cups