Name: Y/anavi Calmo Date: 2-27-202 Lesson 16: Using Unit Rates To Find Equivalent Ratios Solve Each Problem. Show Your Work.1. Rachel Mows 5 Lawns In 8 Hours. At This Rate, How Many Lawns Can She Mow In 40 Hours? - Calculate The Unit Rate:

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Introduction

In this lesson, we will learn how to use unit rates to find equivalent ratios. A unit rate is a ratio in which the second term is 1. We will use this concept to solve a problem involving Rachel, who mows lawns at a certain rate.

Problem 1: Rachel Mows Lawns

Rachel mows 5 lawns in 8 hours. At this rate, how many lawns can she mow in 40 hours?

Step 1: Calculate the Unit Rate

To find the unit rate, we need to divide the number of lawns by the number of hours.

Unit Rate = Number of Lawns / Number of Hours

Unit Rate = 5 Lawns / 8 Hours

Unit Rate = 0.625 Lawns per Hour

Step 2: Find the Equivalent Ratio

Now that we have the unit rate, we can find the equivalent ratio for 40 hours.

Equivalent Ratio = Unit Rate x Number of Hours

Equivalent Ratio = 0.625 Lawns per Hour x 40 Hours

Equivalent Ratio = 25 Lawns

Therefore, Rachel can mow 25 lawns in 40 hours.

Discussion

This problem requires us to use the concept of unit rates to find equivalent ratios. We first calculate the unit rate by dividing the number of lawns by the number of hours. Then, we use the unit rate to find the equivalent ratio for 40 hours. This concept is useful in real-life situations where we need to compare rates or quantities.

Example 2: Tom's Baking

Tom bakes 12 cakes in 6 hours. At this rate, how many cakes can he bake in 24 hours?

Step 1: Calculate the Unit Rate

Unit Rate = Number of Cakes / Number of Hours

Unit Rate = 12 Cakes / 6 Hours

Unit Rate = 2 Cakes per Hour

Step 2: Find the Equivalent Ratio

Equivalent Ratio = Unit Rate x Number of Hours

Equivalent Ratio = 2 Cakes per Hour x 24 Hours

Equivalent Ratio = 48 Cakes

Therefore, Tom can bake 48 cakes in 24 hours.

Conclusion

In this lesson, we learned how to use unit rates to find equivalent ratios. We used this concept to solve two problems involving Rachel and Tom. We first calculated the unit rate by dividing the number of lawns or cakes by the number of hours. Then, we used the unit rate to find the equivalent ratio for a given number of hours. This concept is useful in real-life situations where we need to compare rates or quantities.

Key Takeaways

  • A unit rate is a ratio in which the second term is 1.
  • To find the unit rate, divide the number of lawns or cakes by the number of hours.
  • To find the equivalent ratio, multiply the unit rate by the number of hours.
  • This concept is useful in real-life situations where we need to compare rates or quantities.

Practice Problems

  1. A car travels 250 miles in 5 hours. At this rate, how many miles can it travel in 10 hours?
  2. A machine produces 15 widgets in 3 hours. At this rate, how many widgets can it produce in 6 hours?
  3. A person can type 120 words in 2 minutes. At this rate, how many words can they type in 4 minutes?

Answer Key

  1. 500 miles
  2. 30 widgets
  3. 240 words
    Q&A: Using Unit Rates to Find Equivalent Ratios =====================================================

Introduction

In the previous lesson, we learned how to use unit rates to find equivalent ratios. In this article, we will answer some frequently asked questions about this concept.

Q: What is a unit rate?

A: A unit rate is a ratio in which the second term is 1. For example, if a person can mow 5 lawns in 8 hours, the unit rate is 5 lawns / 8 hours, which simplifies to 0.625 lawns per hour.

Q: How do I calculate the unit rate?

A: To calculate the unit rate, divide the number of lawns or cakes by the number of hours. For example, if a person can mow 5 lawns in 8 hours, the unit rate is 5 lawns / 8 hours.

Q: How do I find the equivalent ratio?

A: To find the equivalent ratio, multiply the unit rate by the number of hours. For example, if a person can mow 5 lawns in 8 hours, and we want to find the number of lawns they can mow in 40 hours, we multiply the unit rate (0.625 lawns per hour) by 40 hours.

Q: What is the difference between a unit rate and a ratio?

A: A unit rate is a ratio in which the second term is 1, while a ratio is a comparison of two quantities. For example, if a person can mow 5 lawns in 8 hours, the ratio is 5 lawns / 8 hours, while the unit rate is 0.625 lawns per hour.

Q: When would I use unit rates in real life?

A: You would use unit rates in real life when you need to compare rates or quantities. For example, if you are planning a road trip and you want to know how many miles you can travel per hour, you would use unit rates to calculate the equivalent ratio.

Q: Can I use unit rates to compare different types of quantities?

A: Yes, you can use unit rates to compare different types of quantities. For example, if you are comparing the cost of different types of food, you can use unit rates to compare the cost per pound or per serving.

Q: How do I convert a ratio to a unit rate?

A: To convert a ratio to a unit rate, divide the first term by the second term. For example, if a person can mow 5 lawns in 8 hours, the ratio is 5 lawns / 8 hours, while the unit rate is 0.625 lawns per hour.

Q: Can I use unit rates to solve problems involving time and distance?

A: Yes, you can use unit rates to solve problems involving time and distance. For example, if a car travels 250 miles in 5 hours, you can use unit rates to calculate the equivalent ratio and find the number of miles it can travel in 10 hours.

Conclusion

In this article, we answered some frequently asked questions about using unit rates to find equivalent ratios. We hope this article has helped you understand this concept better and has provided you with the tools you need to solve problems involving unit rates.

Key Takeaways

  • A unit rate is a ratio in which the second term is 1.
  • To calculate the unit rate, divide the number of lawns or cakes by the number of hours.
  • To find the equivalent ratio, multiply the unit rate by the number of hours.
  • Unit rates can be used to compare rates or quantities.
  • Unit rates can be used to solve problems involving time and distance.

Practice Problems

  1. A person can type 120 words in 2 minutes. At this rate, how many words can they type in 4 minutes?
  2. A machine produces 15 widgets in 3 hours. At this rate, how many widgets can it produce in 6 hours?
  3. A car travels 250 miles in 5 hours. At this rate, how many miles can it travel in 10 hours?

Answer Key

  1. 240 words
  2. 30 widgets
  3. 500 miles