## Engage NY Eureka Math 6th Grade Module 2 Lesson 11 Answer Key

### Eureka Math Grade 6 Module 2 Lesson 11 Exercise Answer Key

Exercise 1.

Calculate the product. 324.56 × 54.82

Answer:

324.56 × 54.82 = 17, 792. 3792

Exercise 2.

Kevin spends $11.25 on lunch every week during the school year. If there are 35.5 weeks during the school year, how much does Kevin spend on lunch over the entire school year? Remember to round to the nearest penny.

Answer:

11.25 × 35.5 = 399. 375 ≈ 399.38

Kevin would spend $399.38 on lunch over the entire school year.

Exercise 3.

Gunnar’s car gets 22.4 miles per gallon, and his gas tank can hold 17.82 gallons of gas. How many miles can Gunnar travel If he uses all of the gas in the gas tank?

Answer:

22.4 × 17.82 = 399. 168

Gunnar can drive 399. 168 miles on an entire tank of gas.

Exercise 4.

The principal of East High School wants to buy a new cover for the sand pit used in the long-jump competition. He measured the sand pit and found that the length is 29.2 feet and the width is 9. 8 feet. What will the area of the new cover be?

Answer:

29.2 × 9.8 = 286.16

The cover should have an area of 286. 16 square feet.

### Eureka Math Grade 6 Module 2 Lesson 11 Problem Set Answer Key

Solve each problem. Remember to round to the nearest penny when necessary.

Question 1.

Calculate the product. 45.67 × 32.58

Answer:

45.67 × 32.58 = 1,487.9286

Question 2.

Deprina buys a large cup of coffee for $4. 70 on her way to work every day. If there are 24 workdays in the month, how much does Deprina spend on coffee throughout the entire month?

Answer:

4.70 × 24 = 112.80

Deprina would spend $112.80 a month on coffee.

Question 3.

Krego earns $2, 456.75 every month. He also earns an extra $4. 75 every time he sells a new gym membership. Last month, Krego sold 32 new gym memberships. How much money did Krego earn last month?

Answer:

2,456.75 + (4.75 × 32) = 2,608.75

Krego earned $2, 608.75 last month.

Question 4.

Kendra just bought a new house and needs to buy new sod for her backyard. If the dimensions of her yard are 24.6 feet by 14. 8 feet, what is the area of her yard?

Answer:

24.6 × 14.8 = 364.08

The area of Kendra’s yard is 364.08 square feet.

### Eureka Math Grade 6 Module 2 Lesson 11 Exit Ticket Answer Key

Use estimation or fraction multiplication to determine if your answer is reasonable.

Question 1.

Calculate the product. 78.93 × 32.45

Answer:

78.93 × 32.45 = 2,561.2785

Question 2.

Paint costs $29.95 per gallon. Nikki needs 12. 25 gallons to complete a painting project. How much will Nikki spend on paint? Remember to round to the nearest penny.

Answer:

29.95 × 12.25 = 366.89

Nikki would spend $366.89 on paint to complete her project.

### Eureka Math Grade 6 Module 2 Lesson 11 Exploratory Challenge Answer Key

You not only need to solve each problem, but your groups also need to prove to the class that the decimal in the product is located in the correct place. As a group, you are expected to present your Informal proof to the class.

a. Calculate the product. 34.62 × 12.8

Answer:

34.62 × 12.8 = 443. 136

Some possible proofs:

Using estimation: 35 × 13 = 455 If the decimal was located in a different place, the product would not be close to 455.

Using fractions: \(34 \frac{62}{100} \times 12 \frac{8}{10}=\frac{3,462}{100} \times \frac{128}{10}=\frac{443,136}{1,000}\) Because the denominator is 1,000, the last digit should be in the thousandths place when writing the fraction as a decimal. Therefore, the answer would be 443. 136.

b. Xavier earns $11. 50 per hour working at the nearby grocery store. Last week, Xavier worked 13. 5 hours. How much money did Xavier earn last week? Remember to round to the nearest penny.

Answer:

11.5 × 13.5 = 155.25

Some possible proofs:

Using estimation: 12 × 14 = 168 If the decimal was located In a different place, the product would not be close to 168.

Using fractions: \(11 \frac{5}{10} \times 13 \frac{5}{10}=\frac{115}{10} \times \frac{135}{10}=\frac{15,525}{100}\) Because the denominator is 100, the last digit should be In the hundredths place when writing the fraction as a decimal. Therefore, the answer would be $155. 25.

Discussion

Record notes from the Discussion in the box below.

Answer:

→ Do you see a connection between the number of decimal digits in the factors and the product?

→ In the first problem, there are two decimal digits in the first factor and one decimal digit in the second factor, which is a total of three decimal digits. The product has three decimal digits.

→ In the second problem, both factors have one decimal digit for a total of two decimal digits in the factors. The product also has two decimal digits.

Show students that this is another way to determine if their decimal points are in the correct place. If this point was brought up by students in their presentations, the discussion can reiterate this method to find the correct placement of the decimal. Remind students to place the decimal before eliminating any unnecessary zeros from the answer.

At the end of the discussion, have students record notes on decimal placement in the student materials.