## 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.
$$\frac{105 \times 2}{35 \times 2}=\frac{210}{70}=\frac{21}{7}=3$$

Example 2.
Mental Math and Division of Decimals
Evaluate the expression 175 ÷ 3. 5 using mental math techniques.
$$\frac{175 \times 2}{3.5 \times 2}$$ = 50

Example 3:
Mental Math and the Division Algorithm
Evaluate the expression 4,564 ÷ 3. 5 using mental math techniques and the division algorithm.
$$\frac{4,564 \times 2}{3.5 \times 2}=\frac{9,128}{7}$$

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?
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.

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

Use mental math techniques to evaluate the expressions.

Exercise 1.
770 ÷ 14
$$\frac{770 \div 7}{14 \div 7}=\frac{110}{2}=55$$

Exercise 2.
1005 ÷ 5
$$\frac{1,005 \times 2}{5 \times 2}=\frac{2010}{10}=201$$

Exercise 3.
1,500 ÷ 8
$$\frac{1,500 \div 2}{8 \div 2}=\frac{750 \div 2}{4 \div 2}=\frac{375}{2}=187.5$$

Exercise 4.
1,260 ÷ 5
$$\frac{1,250}{10}$$ = 126 × 2 = 252

Use mental math techniques to evaluate the expressions.

Exercise 5.
25 ÷ 6.25
$$\frac{25 \times 4}{6.25 \times 4}=\frac{100}{25}=4$$

Exercise 6.
6.3 ÷ 1.5
$$\frac{6.3 \times 2}{1.5 \times 2}=\frac{12.6}{3}=4.2$$

Exercise 7.
425 ÷ 2.5
$$\frac{425 \times 2}{2.5 \times 2}=\frac{850}{5}=170$$

### 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
18.5

Question 2.
314.944 ÷ 3.7
85. 12

Question 3.
1,840.5072 ÷ 23.56
78. 12

Question 4.
325 ÷ 2.5
130

Question 5.
196 ÷ 3.5
56

Question 6.
405 ÷ 4.5
90

Question 7.
3,437.5 ÷ 5.5
625

Question 8.
393.75 ÷ 5.25
75

Question 9.
2,625 ÷ 6.25
420

Question 10.
231 ÷ 8.25
28

Question 11.
92 ÷ 5.75
16

Question 12.
196 ÷ 12.25
16

Question 13.
117÷6.5
18

Question 14.
936 ÷ 9.75
96

Question 15.
305 ÷ 12.2
25

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

Question 16.
83.375 ÷ 2.3 = 3,625
83.375 ÷ 2.3 = 36.25

Question 17.
183.575 ÷ 5,245 = 3.5
183.575 ÷ 52.45 = 3.5

Question 18.
326,025 ÷ 9.45 = 3.45
32.6025 ÷ 9.45 = 3.45

Question 19.
449.5 ÷ 725 = 6.2
449.5 ÷ 72.5 = 6.2

Question 20.
446,642 ÷ 85.4 = 52.3
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
$$\frac{18.75 \times 2}{2.5 \times 2}=\frac{37.5}{5}$$
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
44 gives 1 to 99.
100 + 43 = 143

b. 86 – 39
Increase both by 1.
87 – 40 = 47

c. 50 × 14
Double 50; halve 14.
100 × 7 = 700

d. 180 ÷ 5