## Engage NY Eureka Math 6th Grade Module 2 Lesson 9 Answer Key

### Eureka Math Grade 6 Module 2 Lesson 9 Example Answer Key

Example 1.
25$$\frac{3}{10}$$ + 376$$\frac{77}{100}$$
Convert the mixed numbers into decimals.
→ 25.3 + 376.77

→ Round the addends to the nearest whole number. Then, find the estimated sum.
25 + 377 = 402

Example 2.
426$$\frac{1}{5}$$ – 275$$\frac{1}{2}$$
Each group should get the same value as their answer; however, the fraction group has 150$$\frac{7}{10}$$ and the decimal group has 150.7.

It is important for students to see that these numbers have the same value. Students solving the problem using fractions most likely take longer to solve the problem and make more mistakes. Point out to students that the answers represent the same value, but using decimals made the problem easier to solve.

When discussing the problem, use the correct vocabulary. 426$$\frac{1}{5}$$ is the minuend, 275$$\frac{1}{2}$$ is the subtrahend, and 150$$\frac{7}{10}$$ is the difference.

### Eureka Math Grade 6 Module 2 Lesson 9 Exercise Answer Key

Calculate each sum or difference.

Exercise 1.
Samantha and her friends are going on a road trip that is 245$$\frac{7}{50}$$ miles long. They have already driven How much farther do they have to drive?
Expression: 245$$\frac{7}{50}$$ – 128$$\frac{53}{100}$$                Estimated answer: 245 – 129 = 116
Actual answer: 245. 14 – 128.53 = 116.61

Exercise 2.
Ben needs to replace two sides of his fence. One side is 367$$\frac{9}{100}$$ meters long, and the other is 329 meters long. How much fence does Ben need to buy?
Expression: 367$$\frac{9}{100}$$ + 329$$\frac{3}{10}$$               Estimated answer: 367 + 329 = 696
Actual answer: 367.09 + 329.3 = 696.39

Exercise 3.
Mike wants to paint his new office with two different colors. If he needs 4$$\frac{4}{5}$$ gallons of red paint and 3$$\frac{1}{10}$$ gallons of brown paint, how much paint does he need in total?
This problem is an example of where it may not be easiest to convert mixed numbers into decimals. Either method would result in a correct answer, but discuss with students why it may just be easier to find the sum by keeping the addends as mixed numbers.
Expression: 4$$\frac{4}{5}$$ + 3$$\frac{1}{10}$$               Estimated answer: 5 + 3 = 8
Actual answer: $$4 \frac{8}{10}+3 \frac{1}{10}=7 \frac{9}{10}$$

Exercise 4.
After Arianna completed some work, she figured she still had 78$$\frac{21}{100}$$ pictures to paint. If she completed another 34$$\frac{23}{25}$$ pictures, how many pictures does Arianna still have to paint?
Expression: 78$$\frac{21}{100}$$ – 34$$\frac{23}{25}$$               Estimated answer: 78 – 35 = 43
Actual answer: 78.21 – 34.92 = 43.29

Use a calculator to convert the fractions into decimals before calculating the sum or difference.

Exercise 5.
Rahzel wants to determine how much gasoline he and his wife use In a month. He calculated that he used
78$$\frac{1}{3}$$ gallons of gas last month. Rahzel’s wife used 41$$\frac{3}{8}$$ gallons of gas last month. How much total gas did Rahzel and his wife use last month? Round your answer to the nearest hundredth.
Expression: 78$$\frac{1}{3}$$ + 41$$\frac{3}{8}$$               Estimated answer: 78 + 41 = 119
Actual answer: 78.333 + 41. 375 ≈ 119.71

### Eureka Math Grade 6 Module 2 Lesson 9 Problem Set Answer Key

Question 1.
Find each sum or difference.
a. 381$$\frac{1}{10}$$ – 214$$\frac{43}{100}$$
381.1 – 214.43 = 166.67

b. 32$$\frac{3}{4}$$ – 12$$\frac{1}{2}$$
32$$\frac{3}{4}$$ – 12$$\frac{2}{4}$$ = 20$$\frac{1}{4}$$ or 20.25

c. 517$$\frac{37}{50}$$ + 312$$\frac{3}{100}$$
517.74 + 312.03 = 829.77

d. 632$$\frac{16}{25}$$ + 32$$\frac{3}{10}$$
632. 64 + 32.3 = 664.94

e. 421$$\frac{3}{50}$$ – 212$$\frac{9}{10}$$
421.06 – 212.9 = 208.16

Question 2.
Use a calculator to find each sum or difference. Round your answer to the nearest hundredth.
a. 422$$\frac{3}{7}$$ – 367$$\frac{5}{9}$$
422. 428571 – 367.555556 ≈ 54.87

b. 23$$\frac{1}{5}$$ + 45$$\frac{7}{8}$$
23.2 + 45.875 ≈ 69.08

### Eureka Math Grade 6 Module 2 Lesson 9 Exit Ticket Answer Key

Solve each problem. Show that the placement of the decimal is correct through either estimation or fraction calculation.

Question 1.
382$$\frac{3}{10}$$ – 191$$\frac{87}{100}$$
594$$\frac{7}{25}$$ + 89$$\frac{37}{100}$$