5. Comparing and Graphing Ratios How can ou compare two ratios? ACTIVITY: Comparing Ratio Tables Work with a partner. You make colored frosting b adding drops of red food coloring for ever drop of blue food coloring. Your teacher makes colored frosting b adding 5 drops of red food coloring for ever drops of blue food coloring. a. Cop and complete the ratio table for each frosting mixture. Your Frosting Your Teacher s Frosting Drops of Blue Drops of Red Drops of Blue Drops of Red 5 5 b. Whose frosting is bluer? Whose frosting is redder? Justif our answers. c. STRUCTURE Insert and complete a new column for each ratio table above that shows the total number of drops. How can ou use this column to answer part (b)? ACTIVITY: Graphing from a Ratio Table Ratios and Rates In this lesson, ou will compare ratios. compare unit rates. graph ordered pairs to compare ratios and rates. Work with a partner. a. Explain how ou can use the values from the ratio table for our frosting to create a graph in the coordinate plane. b. Use the values in the table to plot the points. Then connect the points and describe the graph. What do ou notice? c. What does the line represent? Drops of red 5 0 7 5 0 0 5 7 0 5 x 0 Chapter 5 Ratios and Rates Drops of blue
Math Practice Look for Patterns What patterns do ou notice in the graph? What does this tell ou about the problem? ACTIVITY: Comparing Graphs from Ratio Tables Work with a partner. The graph shows the values from the ratio table for our teacher s frosting. a. Complete the table and the graph. Your Teacher s Frosting Drops of Blue 5 Drops of Red Drops of red 5 0 7 5 0 7 5 0 0 5 7 0 5 7 Drops of blue x b. Explain the relationship between the entries in the ratio table and the points on the graph. c. How is this graph similar to the graph in Activit? How is it different? d. How can ou use the graphs to determine whose frosting has more red or blue in it? Explain.. IN YOUR OWN WORDS How can ou compare two ratios? 5. PRECISION Your teacher s frosting mixture has 7 drops of blue in it. How can ou use the graph to find how man drops of red are needed to make the frosting? Is our answer exact? Explain. Use what ou learned about comparing ratios to complete Exercises and on page. Section 5. Comparing and Graphing Ratios
Lesson 5. Lesson Tutorials One wa to compare ratios is b using ratio tables. EXAMPLE Comparing Ratios You mix tablespoons of hot sauce and cups of salsa in a green bowl. You mix tablespoons of hot sauce and cups of salsa in an orange bowl. Which mixture is hotter? Use ratio tables to compare the mixtures. Find a larger batch of each mixture in which the amount of hot sauce or salsa is the same. Green Bowl Orange Bowl Hot Sauce (tablespoons) Hot Sauce (tablespoons) Salsa (cups) Salsa (cups) The tables show that for a larger batch of each mixture using cups of salsa, the orange bowl would have = more tablespoons of hot sauce. So, the mixture in the orange bowl is hotter. EXAMPLE Comparing Unit Rates Which bag of dog food is the better bu? Use ratio tables to find and compare the unit costs. 0-Pound Bag 0 Cost (dollars) Food (pounds) 0-Pound Bag 0 7.0 0. 0 0 Cost (dollars) Food (pounds) 5.0 0. 0 0 The 0-pound bag costs $0. per pound, and the 0-pound bag costs $0. per pound. Because $0. is less than $0., the 0-pound bag is the better bu. Exercises 0. In Example, ou mix 0 tablespoons of hot sauce and cups of salsa in a red bowl. Which mixture is the mildest? Explain.. A 0-pack of paper towels costs $.0. A -pack costs $.0. Which is the better bu? Explain. Chapter 5 ms_green pe_050.indd Ratios and Rates //5 ::0 PM
EXAMPLE Graphing Values from Ratio Tables A hot-air balloon rises meters ever seconds. A blimp rises 7 meters ever seconds. a. Complete the ratio table for each aircraft. Which rises faster? Balloon Blimp (seconds) Height (meters) 7 (seconds) Height (meters) 7 Rises meters ever seconds. Ever seconds, the balloon rises meters and the blimp rises meters. So, the blimp rises faster. b. Graph the ordered pairs (time, height) from the tables in part (a). What can ou conclude? Write the ordered pairs. Balloon: (, ), (, ), (, 7), (, ) Blimp: (, 7), (, ), (, ), (, ) Stud Tip When graphing speed, ou often place time on the horizontal axis and distance on the vertical axis. Plot and label each set of ordered pairs. Then draw a line through each set of points. Height (meters) 0 Rising Speeds (, ) (, ) (, 7) (, ) Blimp (, ) (, ) (, ) (, 7) Balloon 0 0 5 7 0 x (seconds) Both graphs begin at (0, 0). The graph for the blimp is steeper, so the blimp rises faster than the hot-air balloon. Exercises and. WHAT IF? The blimp rises meters ever seconds. How does this affect our conclusion? Section 5. Comparing and Graphing Ratios
5. Exercises Help with Homework. WRITING Explain how to use tables to compare ratios.. NUMBER SENSE Just b looking at the graph, determine who earns a greater hourl wage. Explain. Earnings (dollars) You Friend (hours) x +(-)= +(-)= +(-)= +(-)= Determine which car gets the better gas mileage... Distance (miles) 5 0 Gallons Used 5 Distance (miles) 00 0 Gallons Used 0 5.. Distance (miles) 50 05 Distance (miles) 0 70 Gallons Used 5 Gallons Used 0 Determine which is the better bu. 7. Air Freshener A B. Kitten Food A B Cost (dollars) Cost (dollars) 5 Refills Cans. Ham A B 0. Cheese A B Cost (dollars) 5.70.75 Cost (dollars).5 5. Pounds 5 Slices 0. SALT WATER GARGLE Salt water gargle can temporaril relieve a sore throat. One recipe calls for teaspoon of salt in cup of water. A second recipe calls for teaspoon of salt in cups of water. Which recipe will taste saltier? Chapter 5 Ratios and Rates
Complete the ratio tables and graph the ordered pairs from the tables. What can ou conclude?. Water Tank Swimming Pool. Zoo (min) Liters Leaked (min) Liters Leaked Cost People (dollars) 0 Museum Cost People (dollars) 5 5 0 5 0. MILK In whole milk, parts out of 00 are milk fat. In % milk, part out of 50 is milk fat. Which tpe of milk has more milk fat per cup? 5. HEART RATE A horse s heart beats 0 times in 0 minutes. A cow s heart beats 0 times in minutes. Which animal has a greater heart rate?. CHOOSE TOOLS A chemist prepares two acid solutions. a. Use a ratio table to determine which solution is more acidic. b. Use a graph to determine which solution is more acidic. c. Which method do ou prefer? Explain. 7. NUT MIXTURE A compan offers a nut mixture with 7 peanuts for ever almonds. The compan changes the mixture to have peanuts for ever 5 almonds, but the number of nuts per container does not change. a. Create a ratio table for each mixture. How man nuts are in the smallest possible container? b. Graph the ordered pairs from the tables. What can ou conclude? c. Almonds cost more than peanuts. Should the compan charge more or less for the new mixture? Explain our reasoning.. The point (p, q) is on the graph of values from a ratio table. What is another point on the graph? Divide. (Section.). 5 0. 50. 5. MULTIPLE CHOICE Which of the following numbers is equal to. when ou increase it b.5? (Section.) A. B.7 C 5.7 D.7 Section 5. Comparing and Graphing Ratios 5