We included **HMH Into Math Grade 8 Answer Key**** PDF** **Module 5 Proportional Relationships **to make students experts in learning maths.

## HMH Into Math Grade 8 Module 5 Answer Key Proportional Relationships

**Auto Engineer**

Auto engineers design new vehicles and improve existing vehicles. Some auto engineers work on improving a carâ€™s performance, fuel efficiency, or safety. Others specialize in certain components, such as brakes or electrical systems. Auto engineers must understand how some quantities, such as a carâ€™s braking distance, depend on other quantities, such as the carâ€™s speed.

**Stem Task:**

Three quantities related to a car engineâ€™s performance are torque, horsepower, and revolutions per minute (RPM). These quantities are related by the equation

where torque is measured in pound-feet. How much torque is required to produce 300 horsepower at

2500 RPM? At 5000 RPM? How are the two torques related?

**Learning Mindset!**

**Challenge-Seeking Defines Own Challenges**

As you grow, you discover the pleasure of setting your own goals and challenges, and designing ways to meet them. Maybe you want to learn a new language, write a book, or become more successful academically. Here are some things to keep in mind as you seek and define new challenges.

- Believe in your ability to improve skills which are challenges for you now. Use positive self-talk to address any fixed-mindset voices telling you that you can’t reach your goal. Believe in the power of “yet.”
- Think about how you will handle unexpected difficulties. Don’t become discouraged. Every failure can help you get closer the next time.
- Be flexible. You may find it necessary to adjust your plan or even redefine the end goal.
- Don’t be afraid to ask for advice and assistance from content resources or people with more experience than you have currently.

**Reflect**

Question.

How do you know whether a task is the right level of challenge for you?

Answer:

Question.

Was the STEM Task an appropriate challenge for you? If not, what reasonable challenge would you set for yourself?

**Proportional Smoothies**

The owners of a smoothie shop want the price of each size of smoothie to be proportional to the amount of liquid it contains. A small smoothie will be 16 fluid ounces and sell for $3.52.

Complete the shop’s price chart by deciding how many fluid ounces the other smoothie sizes will have and then determine the price of each smoothie.

**Turn and Talk**

- Explain how you know that the prices of the smoothies are proportional to their volumes.
- The shop owners decide to charge $0.99 for each smoothie add-in. For smoothies with a single add-in, is the total price proportional to the fluid ounces? Explain.

**Are You Ready?**

**Complete these problems to review prior concepts and skills you will need for this module.**

**Tables and Graphs of Equivalent Ratios**

**Complete each table to represent the relationship.**

Question 1.

Collette runs 6.5 kilometers each week. Let d represent the total distance, in kilometers, she runs in w weeks.

Answer:

Given,

Collette runs 6.5 kilometers each week. Let d represent the total distance, in kilometers, she runs in w weeks.

1 week = 6.5 km

2 week = 2 Ã— 6.5 = **13 km
**19.5 km = x week

6.5 km = 1 week

19.5 = 6.5

19.5/6.5 =

**3 weeks**

5 weeks = 5 Ã— 6.5 = 32.5 km

Question 2.

A theater charges a service fee of $0.95 per ticket bought online. Let t represent the total fee paid for ordering n tickets.

Answer:

A theater charges a service fee of $0.95 per ticket bought online. Let t represent the total fee paid for ordering n tickets.

t = 0.95n

t = 0.95 Ã— 3 = 2.85

5.70/0.95 = 6

**Identify Proportional Relationships**

**Tell whether each relationship is proportional. Explain your reasoning.**

Question 3.

Answer:

6:48 = 1:8

8:64 = 1:8

12:96 = 1:8

15:120 = 180

The given table is proportional.

Question 4.

Answer:

9:18 = 1:2

15:24 = 5:3

18:27 = 2:3

36:45 = 4:5

The given table is not proportional.

**Similar Triangles**

**Tell whether each pair of triangles is similar. Explain your reasoning.**

Question 5.

Answer:

No, both the triangles are not similar.

Sum of angles = 180Â°

90Â° + 48Â° + xÂ° = 180Â°

138Â° + x = 180Â°

x = 180Â° – 138Â°

x = 42Â°

Question 6.

Answer:

Yes, both the triangles are similar.

Sum of angles = 180Â°

90Â° + 36Â° + xÂ° = 180Â°

126Â° + x = 180Â°

x = 180Â° – 126Â°

x = 54Â°