## Engage NY Eureka Math 6th Grade Module 2 Lesson 15 Answer Key

### Eureka Math Grade 6 Module 2 Lesson 15 Example Answer Key

Use Mental Math to Find Quotients

Example 1.

Use mental math to evaluate 105 ÷ 35.

Answer:

\(\frac{105 \times 2}{35 \times 2}=\frac{210}{70}=\frac{21}{7}=3\)

Example 2.

Mental Math and Division of Decimals

Evaluate the expression 175 ÷ 3. 5 using mental math techniques.

Answer:

\(\frac{175 \times 2}{3.5 \times 2}\) = 50

Example 3:

Mental Math and the Division Algorithm

Evaluate the expression 4,564 ÷ 3. 5 using mental math techniques and the division algorithm.

Answer:

\(\frac{4,564 \times 2}{3.5 \times 2}=\frac{9,128}{7}\)

Example 4:

Mental Math and Reasonable Work

Shelly was given this number sentence and was asked to place the decimal point correctly in the quotient.

55. 6875 ÷ 6.75 = 0.825

Do you agree with Shelly?

Answer:

No, I do not agree with Shelly. When I round the dividend to 54 and the divisor to 6, the quotient is 9. I know that 91 is in the ones place, so the decimal should be placed after the 8 in the quotient.

Divide to prove your answer is correct.

Answer:

### Eureka Math Grade 6 Module 2 Lesson 15 Exercise Answer Key

Use mental math techniques to evaluate the expressions.

Exercise 1.

770 ÷ 14

Answer:

\(\frac{770 \div 7}{14 \div 7}=\frac{110}{2}=55\)

Exercise 2.

1005 ÷ 5

Answer:

\(\frac{1,005 \times 2}{5 \times 2}=\frac{2010}{10}=201\)

Exercise 3.

1,500 ÷ 8

Answer:

\(\frac{1,500 \div 2}{8 \div 2}=\frac{750 \div 2}{4 \div 2}=\frac{375}{2}=187.5\)

Exercise 4.

1,260 ÷ 5

Answer:

\(\frac{1,250}{10}\) = 126 × 2 = 252

Use mental math techniques to evaluate the expressions.

Exercise 5.

25 ÷ 6.25

Answer:

\(\frac{25 \times 4}{6.25 \times 4}=\frac{100}{25}=4\)

Exercise 6.

6.3 ÷ 1.5

Answer:

\(\frac{6.3 \times 2}{1.5 \times 2}=\frac{12.6}{3}=4.2\)

Exercise 7.

425 ÷ 2.5

Answer:

\(\frac{425 \times 2}{2.5 \times 2}=\frac{850}{5}=170\)

### Eureka Math Grade 6 Module 2 Lesson 15 Problem Set Answer Key

Use mental math, estimation, and the division algorithm to evaluate the expressions.

Question 1.

118.4 ÷ 6.4

Answer:

18.5

Question 2.

314.944 ÷ 3.7

Answer:

85. 12

Question 3.

1,840.5072 ÷ 23.56

Answer:

78. 12

Question 4.

325 ÷ 2.5

Answer:

130

Question 5.

196 ÷ 3.5

Answer:

56

Question 6.

405 ÷ 4.5

Answer:

90

Question 7.

3,437.5 ÷ 5.5

Answer:

625

Question 8.

393.75 ÷ 5.25

Answer:

75

Question 9.

2,625 ÷ 6.25

Answer:

420

Question 10.

231 ÷ 8.25

Answer:

28

Question 11.

92 ÷ 5.75

Answer:

16

Question 12.

196 ÷ 12.25

Answer:

16

Question 13.

117÷6.5

Answer:

18

Question 14.

936 ÷ 9.75

Answer:

96

Question 15.

305 ÷ 12.2

Answer:

25

Place the decimal point in the correct place to make the number sentence true.

Question 16.

83.375 ÷ 2.3 = 3,625

Answer:

83.375 ÷ 2.3 = 36.25

Question 17.

183.575 ÷ 5,245 = 3.5

Answer:

183.575 ÷ 52.45 = 3.5

Question 18.

326,025 ÷ 9.45 = 3.45

Answer:

32.6025 ÷ 9.45 = 3.45

Question 19.

449.5 ÷ 725 = 6.2

Answer:

449.5 ÷ 72.5 = 6.2

Question 20.

446,642 ÷ 85.4 = 52.3

Answer:

4,466.42 ÷ 85.4 = 52.3

### Eureka Math Grade 6 Module 2 Lesson 15 Exit Ticket Answer Key

Question 1.

Evaluate the expression using mental math techniques and the division algorithm. Explain your reasoning.

18.75 ÷ 2.5

Answer:

\(\frac{18.75 \times 2}{2.5 \times 2}=\frac{37.5}{5}\)

I find it easier to divide by 5, so I doubled both the divisor and the dividend. I knew that the dividend would be divisible by 5 since it has a 5 in the hundredths place.

18.75 ÷ 2.5 = 7.5

### Eureka Math Grade 6 Module 2 Lesson 15 Opening Exercise Answer Key

Use mental math to evaluate the numeric expressions.

a. 99 + 44

Answer:

44 gives 1 to 99.

100 + 43 = 143

b. 86 – 39

Answer:

Increase both by 1.

87 – 40 = 47

c. 50 × 14

Answer:

Double 50; halve 14.

100 × 7 = 700

d. 180 ÷ 5

Answer:

Double both.

360 ÷ 10 = 36