LESSON Understanding Unit Rates UNDERSTAND A rate is a ratio that compares two quantities with different units of measure. A unit rate is a rate in which the second measurement or amount is unit. Three full vans, all with the same number of seats, hold a total of 6 people. The unit rate is the number of people per van. What is the unit rate? To find the unit rate, find the number of people needed to fill one van. Use drawings to find the unit rate. Draw boxes to represent the vans. Draw bars in each box to represent the people. Draw one bar in each box to represent one person per van. Draw another bar in each box. Then continue to draw one bar in each box until you have drawn 6 bars. Count the number of bars in each box to find the unit rate. Each box has bars. The unit rate is people van, or people per van. 0 Domain : Ratios and Proportional Relationships
Connect Three full vans hold 6 people. The number of people per van is the unit rate. What is the number of people per van? Write a ratio to compare the number of people to the number of vans. number of people : number of vans 6: Write the ratio in fraction form. people vans 6 Write the fraction as division. The fraction bar means division. Divide the numerator by the denominator. 6 Divide. 6 5 5 Write the unit rate. 6 5 The unit rate is people van, or people per van. DISCUSS How could you find the unit rate if full vans hold 6 people? Lesson : Understanding Unit Rates
EXAMPLE A A recipe calls for eggs to cups of milk. The unit rate is the number of eggs per cup of milk. What is the number of eggs per cup of milk? How many eggs are needed if cups of milk are used? Write a ratio to compare the number of eggs to the number of cups of milk. Write the ratio in fraction form. eggs cups of milk Write the fraction as division. Divide the numerator by the denominator. Divide. 5 6 Write the unit rate. 5 Use the unit rate to find the number of eggs needed for cups of milk. 5 6 The unit rate is 6 eggs cup milk or 6 eggs per cup of milk. Multiply to find the rate for cups of milk. 6 eggs cup milk 5 eggs cups milk eggs are needed if cups of milk are used. TRY A recipe has a ratio of cups of milk to eggs. How many eggs are needed if cups of milk are used? Domain : Ratios and Proportional Relationships
EXAMPLE B A recipe for one loaf of bread calls for cup of white flour for each cup of whole wheat flour. Rose wants to make loaves of bread. How much whole wheat flour will she need? How much white flour will she need? Identify the unit rate. The unit rate is cup of white flour per cup of whole wheat flour, to, or :. Think about the information you need. Multiply to find the amount of whole wheat flour Rose will need. The recipe for one loaf of bread calls for cup of whole wheat flour. Rose wants to make loaves of bread. So, she must multiply each ingredient by to find how much flour she will need. The recipe calls for cup of whole wheat flour. 5 Rose will need cups of whole wheat flour to make loaves of bread. Multiply to find the amount of white flour Rose will need. The recipe calls for cup of white flour. 5 5 5 Rose will need cups of white flour to make loaves of bread. MODEL In a recipe for punch, cup of pineapple juice is used for each cup of orange juice. Draw a diagram to model how many cups of pineapple juice are used with cups of orange juice. Lesson : Understanding Unit Rates
Practice Write a ratio for each rate. Then find the unit rate.. 0 miles in 5 hours. 96 words in minutes HINT Use the second term of the ratio to find the unit rate.. 08 people in buses. 6 points in 8 games 5. $.70 for goldfish 6. $ for 7 comic books Find each unit rate. 7. 8 grams of protein in servings 8.,068 miles in hours REMEMBER The second term of a unit rate is always. 9. 0 students to 5 teachers 0. $.60 for eggs. 7 strikeouts in games. 90 feet in 5 seconds. students to parents. 60 miles per 0 gallons Domain : Ratios and Proportional Relationships
Find each unit rate. Then write which is the better buy. 5. $0.90 for pens or $.75 for 5 pens 6. $.5 for tennis balls or $6. for 8 tennis balls 7. $.9 for apples or $.0 for 0 apples 8. $ for 6 pounds of cereal or $5 for 9 pounds of cereal Choose the best answer. 9. A chef uses cup of cheese per cups of milk in a casserole. How many cups of cheese are needed if the chef uses 6 cups of milk? A. cups B. cups C. 5 cups D. 6 cups 0. Javier scored 0 goals in 5 soccer games. Using the unit rate, how many goals will he score in 0 games? A. 5 goals B. 0 goals C. 5 goals D. 60 goals Solve.. The coach pays $7 for 8 hamburgers. What is the cost per hamburger?. Ayesha s puppy gained 6 pounds in 9 weeks. Using the unit rate, how many pounds did the puppy gain in 5 weeks?. ANALYSIS Compare and contrast rates and ratios. Lesson : Understanding Unit Rates 5