lesson 3 homework practice convert unit rates answer key

Unit Rates Worksheets

What Are Unit Rates? To understand rates, you must have a thorough understanding of what ratios are. Ratios is a way or comparing numbers or measurements. A special form of ration where two terms with different units are compared are what we term as rates. Rates is a very common term as is used frequently in our day to day lives. It can be about the number of working hours compared with amount earned and it can be comparison of an object with its price. Unit rates are special forms of rates. When you express rates as a quantity of one, we call them unit rates. For example, if you have been given the price of 12 tomatoes and you have to find the unit rates. You can divide the total price with 12 to find the unit rate.

Basic Lesson

Introduces the concept of converting several units to a relational rate. Example: Jan can type 80120 words in 40 minutes. How many words per minute can she type? 80120 words in 40 minutes = 80120/40 Words per minute 80120/40 = 23 minute.

Intermediate Lesson

This lesson demonstrates how to determine a unit rate from word problems. Example: 840 calories are in 7 servings of pie. How many calories are in each serving? 840 calories for 7 servings of pie = 840/7. Calories per serving = 840/7 = 120. Answer: 120 Calories.

Independent Practice 1

Students practice with 20 unit rate problems. The answers can be found below.

Independent Practice 2

Another 20 unit rate problems. The answers can be found below.

Homework Worksheet

Reviews all skills in the unit. A great take home sheet. Also provides a practice problem.

10 problems that test unit rate conversion skills.

Homework and Quiz Answer Key

Answers for the homework and quiz.

Answers for the lesson and practice sheets.

How to Measure Speed

Measuring speed requires the use of three variables. It is measured as the distance traveled divided by the amount of time the travel takes. To determine the rate of speed, divide the distance traveled by the amount of time spent traveling.

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Into Math Grade 7 Module 1 Lesson 3 Answer Key Compute Unit Rates Involving Fractions

We included H MH Into Math Grade 7 Answer Key PDF Module 1 Lesson 3 Compute Unit Rates Involving Fractions to make students experts in learning maths.

HMH Into Math Grade 7 Module 1 Lesson 3 Answer Key Compute Unit Rates Involving Fractions

I Can compute unit rates associated with ratios of fractions.

Turn and Talk How can you use the distance they each hiked in 1 hour to write a ratio for the distance they each would hike in 2 hours?

Build Understanding

1. Jessie loves to go hiking on rustic trails through trees and along rivers. One day in 20 minutes of hiking, she hiked 1 mile. If Jessie hiked at a constant rate, what would that rate be?

A. Write Jessie’s hiking rate in all the ways you can think of from the information given. Answer: One day in 20 minutes of hiking, she hiked 1 mile. The one way is The Jessie hiked at a constant rate is 20/1 minutes/mile. Another way is 1/20 miles/minute. = 1/mile/1/3 hours = 1 x 3/1 ÷ 1/3 x 3/1 = 3miles/hour.

Turn and Talk Compare the rates “minutes per mile” and “miles per minute.” Give an example of each rate. Answer: The ratio of minutes per mile = 20/1 = 20 miles per hour. The ratio of miles per hour = 1/20 hours/mile.

Step It Out

B. How can you use division to find this unit rate? ____________________ Answer: For the unite rate divide the denominator with numerator then the denominator becomes 0.

Turn and Talk How can you find the number of servings of pudding for every cup of milk?

3. Jaylan makes limeade using \(\frac{3}{4}\) cup of water for every \(\frac{1}{5}\) cup of lime juice. Rene’s limeade recipe is different. He uses \(\frac{2}{3}\) cup of water for every \(\frac{1}{6}\) cup of lime juice. Whose limeade has a weaker flavor?

A. What do you need to know to solve this problem? ____________________ Answer: Solve the unit rate of water to the lime juice in each limeade.

B. Let x represent the weight on Earth. Let y represent the weight on the moon. Write an equation for the proportional relationship. Use it to find the weight of a 20-pound dog on the moon. The equation is _____. On the moon, the dog would weigh about ____ pounds. Answer: Given that, x represents the earth y represents the moon The equation for the proportional relationship is = x/y. The weight of the moon is the 20-pound dog. Therefore the equation is x/20. On the moon, the dog would weigh about x/20 pounds

Turn and Talk What would a dog that weighs 12 pounds on the moon weigh on Earth?

Check Understanding

Question 2. Toni ran \(\frac{4}{5}\) mile in \(\frac{1}{5}\) hour. Write an equation for the distance in miles y that she ran in x hours if she ran at a constant rate. Answer: Given that, Toni ran \(\frac {4}{5} \) mile = 4/5 mile. Toni ran in hours = \(\frac {1}{5} \) = 1/5 hours The equation for the distance in miles y that she ran in x hours is y/x = 4/5 ÷ 1/5 y/x = 0.8 ÷ 0.2 y/x = 0.4 The constant rate is 0.4 miles/hour.

Question 4. Write 2\(\frac{1}{4}\) miles in \(\frac{3}{4}\) hour as a unit rate. Answer: Given that, 2\(\frac {1}{4} \) miles = 2 x 1/4 miles. \(\frac {3}{4} \) hour = 3/4 hours. Know divide miles by hours 2 x 1/4 ÷ 3/4 = 0.5 ÷ 0.75 = 0.66 miles/hours. The unit rate is 0.66 miles/hour.

On Your Own

Question 5. Health and Fitness Jorge measured his heart rate after jogging. He counted 11 beats during a 6-second interval. What was the unit rate for Jorge’s heart rate in beats per minute? _________ Answer: Given that, Jorge measured his heart rate after jogging. He counted 11 beats during a 6-second interval. The unit rate for Jorge’s heart rate in beats per minute is Divide beats by hours. 11/6 = beats/minute The unit rate for Jorge’s heart rate in beats per minute is 1.83.

Question 6. Chen bikes 2\(\frac{1}{2}\) miles in \(\frac{5}{12}\) hour, What is Chen’s unit rate in miles per hour? ____________________ Answer: Given that, 2\(\frac {1}{2} \) miles = 2 x 1/2 miles. \(\frac {5}{12} \) hour = 5/12 hours Know divide miles by hours. 2 x 1/2 ÷ 5/12 = 1 ÷ 0.416 = 2.403 miles/hours. The unit rate is 2.403 miles/hour.

Question 7. Amal can run \(\frac{1}{8}\) mile in 1\(\frac{1}{2}\) minutes.

A. If he can maintain that pace, how long will it take him to run 1 mile? _____________________ Answer: Amal run \(\frac{1}{8}\) mile in 1\(\frac{1}{2}\) minutes. 1\(\frac{1}{2}\) = 1.5 1.5 × 8 = 12 minute

B. How long would it would take Amal to run 3 miles at that pace? _____________________ Answer: It would also take him 12 minutes.

C. Naomi can run \(\frac{1}{4}\) mile in 2 minutes. Does Amal or Naomi run faster? How do you know? _____________________ Answer: Given, Amal can run \(\frac{1}{8}\) mile in 1\(\frac{1}{2}\) minutes. \(\frac{1}{8}\) ÷ 1\(\frac{1}{2}\) Convert from mixed fraction to the improper fraction \(\frac{1}{8}\) ÷ \(\frac{3}{2}\) = \(\frac{1}{12}\) mile/minute Naomi can run \(\frac{1}{4}\) mile in 2 minutes. \(\frac{1}{4}\) ÷ 2 = \(\frac{1}{8}\) mile/minute Thus Naomi runs faster than Amal.

Question 8. Open Ended When both quantities in a rate are fractions, what strategy do you use to write the rate as a unit rate? ________________________ ________________________ Answer: When both quantities in a rate are fractions, the strategy is. First, write the ratios as the fraction and divide the numerator by the denominator.

A. Show that the relationship is proportional. _____________ Answer: Yes, the relationship is proportional. The equation is y = 4x.

B. Write an equation to represent the relationship, and find the amount of peanut butter used to make 25 cracker packages. _____________ Answer: The equation to represent the relationship y = 4x Here, m = 4. Find the amount of peanut butter used to make 25 cracker packages is 25 = 4x x = 25/4 Therefore You need to use 25/4 teaspoons of peanut butter used to make the 25 cracker packages.

For Exercises 12—15, find each unit rate.

Question 12. \(\frac{5}{8}\) mile in \(\frac{1}{4}\) hour Answer: Given that, \(\frac {5}{8} \) mile = 5/8 mile. \(\frac {1}{4} \) hour = 1/4 hour. Divide mile by hour. 5/8 ÷ 1/4 = 2.5 mile/hour The unit rate is 2.5 miles/hour.

Question 13. $68 for 8\(\frac{1}{2}\) hours Answer: Given that, $68 for 8\(\frac {1}{2} \) hours $68 for 8 x 1/2. Divide dollars by hours. 68 ÷ 1/2 68 ÷ 0.5 = 136 dollars/hours. The unit rate is 136 dollars/hour.

Question 14. 1\(\frac{1}{4}\) cup of flour per \(\frac{1}{8}\) cup of butter Answer: Given that. 1\(\frac {1}{4} \) cup of flour = 1 x 1/4 \(\frac {1}{8} \) cup of butter = 1/8 Know to divide a cup of flour with a cup of butter. 1 x 1/4 ÷ 1/8 = 0.25 ÷ 0.125 = 0.25 ÷ 0.125 = 2 cups of flour/cups of butter. The unit rate is 2 cups of flour/cups of butter.

Question 15. 2\(\frac{1}{2}\) miles in \(\frac{3}{4}\) hour ____________________ Answer: Given that, 2\(\frac {1}{2} \) miles = 2 x 1/2. \(\frac {3}{4} \) hour = 3/4. Divide miles by hours. 2 x 1/2 ÷ 3/4 = 1 ÷ 0.75 = 1.33 miles/hour. The unit rate is 1.33 miles/hour.

I’m in a Learning Mindset!

What did I learn from peers when they shared their strategies with me for writing a unit rate?

Lesson 1.3 More Practice/Homework

Compute Unit Rates Involving Fractions

Question 1. STEM Density is a unit rate measured in units of mass per unit of volume. The mass of a garnet is 5.7 grams. The volume is 1.5 cubic centimeters (cm 3 ). What is the density of the garnet? Answer: Given that, The mass of the garnet is 5.7 grams. The volume is 1.5 cubic centimetres. The formula for the density is mass/volume. The density of the grant is 5.7 grams/1.5 cubic centimeters. The density of the grant = 3.8 grams/cubic centimeters.

Question 2. Math on the Spot Jen and Kamlee are walking to school. After 20 minutes, Jen has walked \(\frac{4}{5}\) mile. After 25 minutes1 Kamlee has walked \(\frac{5}{6}\) mile. Find their speeds in miles per hour. Who is walking faster? Answer: Given that, Jen and Kamlee are walking to school. After 20 minutes, Jen has walked \(\frac{4}{5}\) mile. \(\frac{4}{5}\) mile = 4/5 mile. After 25 minutes1 Kamlee has walked \(\frac{5}{6}\) mile. \(\frac{5}{6}\) = 5/6 mile. The formula for the speed = distance/time 1 hour = 60 minutes. The speed of Jan = 4/5 ÷ 20/60 = 12/5 = 2.4 miles per hour. The speed of Kamlee = 5/6 ÷ 25/60 = 2 miles per hour. Therefore Jan is 2.4 miles per hour and Kamlee is 2 hours per hour. So, Jan is walking faster.

Question 3. Reason Maria and Franco are mixing sports drinks for a track meet. Maria uses \(\frac{2}{3}\) cup of powdered mix for every 2 gallons of water. Franco uses 1\(\frac{1}{4}\) cups of powdered mix for every 5 gallons of water. Whose sports drink is stronger? Explain how you found your answer. ________________________ ________________________ ________________________ Answer: Given that, Maria uses \(\frac{2}{3}\) cup of powdered mix for every 2 gallons of water. \(\frac{2}{3}\) cup of powdered mix = 2/3. Franco uses 1\(\frac{1}{4}\) cups of powdered mix for every 5 gallons of water. 1\(\frac{1}{4}\) cups of powdered mix = 1 x 1/4. For maria the ratio of the powered mix to the water is 2/3 ÷ 2 = 1/3 cup/gallon For Franco the ratio of the powered mix to the water is 1 x 1/4 ÷ 5 = 5/4 ÷ 5 = 1/4 cup/gallon The 1/3 is bigger than the 1/4. So, Mria’s sports drink is stronger than the Franco sports drink.

Question 4. Model with Mathematics Serena estimates that she can paint 60 square feet of wall space every half-hour. Write an equation for the relationship with time in hours as the independent variable. Can Serena paint 400 square feet of wall space in 3.5 hours? Why or why not? ________________________ Answer: Given that, Serena can paint = 60 square feet. The time taken to paint = half-hour = 0.5 hours. 0.5 hours = 60 square feet’s. For 1 hour = 60/0.5 = 120 sq. feet’s. For I hours = 120i sq. feet’s. Let us consider that the total area is y. The relation between the I hours to the independent variable is y = 120I Can Serena paint 400 square feet of wall space in 3.5 hours? Put y = 400 and I = 3.5 then 400 = 120(3.5) 400 is not equal to 420. Therefore Serena cannot paint 400 square feet in 3.5 hours.

Find the unit rate.

Question 6. \(\frac{1}{4}\) kilometer in \(\frac{1}{3}\) hour Answer: Given that, \(\frac {1}{4} \) kilometre = 1/4 kilometre. \(\frac {1}{3} \) hour = 1/3 hour Divide the kilometre by hours The unit rate is 1/4 ÷ 1/3 = 3/4 = 0.75 kilometre/hour.

Question 7. \(\frac{7}{8}\) square foot in \(\frac{1}{4}\) hour Answer: Given that, \(\frac {7}{8} \) square foot = 7/8 square foot. \(\frac {1}{4} \) hour = 1/4 hour Divide the square foot by the hour. The unit rate is 7/8 ÷ 1/4 = 3.5 square feet/hour.

Question 8. $6.50 for 3\(\frac{1}{4}\) pounds of grapes Answer: Given that, Cost of the graphs = $6.50 The weight of the graphs = 3\(\frac {1}{4} \) pounds = 3 x 1/4 pounds. Divide dollar by pounds. The unit rate is $6.50 ÷ 3 x 1/4 = $6.50 ÷ 0.75 = 8.6 dollar/pounds

Question 9. $49.50 for 5\(\frac{1}{2}\) hours Answer: Given that, $49.50 for 5\(\frac {1}{2} \) hours. $49.50 for 5 x 1/2 hours. Divide dollar by hours $49.50 ÷ 5 x 1/2 $49.50 ÷ 2.5 = 19.8 The unit rate is 19.8 dollars/hour.

Question 10. 247 heart beats in 6\(\frac{1}{2}\) minutes Answer: Given that, 247 heartbeats in 6\(\frac {1}{2} \) minutes. 247 heartbeats in 6 x 1/2. Divide heartbeats by minutes. 247 ÷ 6 x 1/2 = 247 ÷ 3 = 82.33 heartbeats/minutes. The unit rate is 82.33 heartbeats/minutes.

Question 11. 8\(\frac{1}{2}\) miles in \(\frac{1}{2}\) hour Answer: Given that, 8\(\frac {1}{2} \) miles = 8 x 1/2. \(\frac {1}{2} \) hour = 1/2 hour. Know divide miles by hours. 8 x 1/2 ÷ 1/2 = 4 ÷ 0.5 = 8 The unit rate is 8 miles/hour.

Question 12. Select all the rates equivalent to the rate \(\frac{3}{4}\) cup per pound. A. \(\frac{3}{8}\) cup per \(\frac{1}{2}\) pound B. \(\frac{1}{4}\) cup per \(\frac{1}{2}\) pound C. 3 cups for every 2 pounds D. 1\(\frac{1}{2}\) cups for every 2 pounds E. 0.1875 cup for every 0.25 pound Answer:

Question 13. Jordan cooked a 16-\(\frac{1}{5}\)-pound turkey in 5\(\frac{2}{5}\) hours. How many minutes per pound did it take to cook the turkey? Express your answer as a unit rate. ____________________ Answer: Given that, Jordan cooked 16-\(\frac {1}{5} \)-pound turkey in 5\(\frac {2}{5} \) hours. Jordan cooked 16 x 1/5-pound turkey in 5 x 2/5 hours. 16 x 1/5 = 81/5 lb. 5 x 2/5 = 27/5 hours 1 hour = 60 minutes 27/5 x 60 = 324 minutes Know Divide the total time by the total weight. 324/81/5 = 1.620/81 = 20 min/lb The unit rate is 20 min/lb

Question 14. Mr. March sells popcorn at his theater. He uses 3\(\frac{3}{4}\) cups of unpopped corn to make 15 bags of popped corn. Write an equation for the number of bags of popcorn b that can be made with c cups of unpopped corn. Answer: Given that, Mr. March uses 3\(\frac{3}{4}\) cups of unpopped corn to make 15 bags of popped corn. 3\(\frac{3}{4}\) cups = 3 x 3/4. The equation for the number of bags of popcorn b that can be made with c cups of unpopped corn is b/c = Divide bags of popped corn into cups of unpopped corn. b/c = 15 ÷ 3 x 3/4 b/c = 15 ÷ 2.25 b/c = 6.66 bags of popped corn/cups of unpopped corn.

Question 15. Lucia uses 3 ounces of pasta to make \(\frac{3}{4}\) serving of pasta. How many ounces of pasta are there per serving? How many ounces of pasta should Lucia use to make 5 servings? A. 3 ounces; 15 ounces B. 4 ounces: 20 ounces C. 6 ounces; 30 ounces D. 9 ounces; 40 ounces Answer: Given that, Lucia uses 3 ounces of pasta to make \(\frac {3}{4} \) serving of pasta. 3 ounces of pasta to make 3/4 serving of pasta. Divide ounces by servings. 3 ÷ 3/4 = 3 ÷ 0.75 = 4 ounces/servings The ounces of pasta should Lucia use to make 5 servings is 4 ounces x 5. = 20 ounces. 4 ounces: 20 ounces. Option B is the correct answer.

Spiral Review

Question 16. John left school with $8.43. He found a quarter on his way home and then stopped to buy an apple for $0.89. How much money did he have when he got home? Answer: Given that John left the school with $8.43. On the way home, John buys an apple for $0.89. Therefore $8.43 – $0.89 = $7.54 John has $7.54 when he got home.

Question 17. Arian is making bracelets. For each bracelet, it takes \(\frac{1}{10}\) hour to pick out materials and \(\frac{1}{4}\) hour to braid it together. How many bracelets can Arian make in 5 hours? Answer: Given that, For each bracelet to pick out the materials = \(\frac {1}{10} \) = 1/10 hours. For each bracelet to band it together = \(\frac {1}{4} \) = 1/4 hours. Therefore 1/10 + 1/4 = 7/20 hours. For 1 bracelets = 7/10 hours. Divide available time by given time. 5 ÷ 7/20 = 14.285 Arian can make 14 bracelets in 5 hours.

Question 18. For a game, 3 people are chosen in the first round. Each of those people chooses 3 people in the second round, and so on. How many people are chosen in the sixth round? ____________________ Answer: In the first round, 3 people are chosen. In the second round, these 3 people choose 3 people. It means 3 x 3 = 9 In the third round again 3 people are chosen = 9 x 3 = 27 In the fourth round again 3 people are chosen = 27 x 3 = 81 In the fifth round again 3 people are chosen = 81 x 3 = 243 In the sixth round again 3 people are chosen = 243 x 3 = 729. The 729 people are chosen in the sixth round.

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