## 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 Ã· 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 Ã· 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 Ã· 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 Ã· 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 Ã· 14
$$\frac{770 \div 7}{14 \div 7}=\frac{110}{2}=55$$

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

Exercise 3.
1,500 Ã· 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 Ã· 5
$$\frac{1,250}{10}$$ = 126 Ã— 2 = 252

Use mental math techniques to evaluate the expressions.

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

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

Exercise 7.
425 Ã· 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 Ã· 6.4
18.5

Question 2.
314.944 Ã· 3.7
85. 12

Question 3.
1,840.5072 Ã· 23.56
78. 12

Question 4.
325 Ã· 2.5
130

Question 5.
196 Ã· 3.5
56

Question 6.
405 Ã· 4.5
90

Question 7.
3,437.5 Ã· 5.5
625

Question 8.
393.75 Ã· 5.25
75

Question 9.
2,625 Ã· 6.25
420

Question 10.
231 Ã· 8.25
28

Question 11.
92 Ã· 5.75
16

Question 12.
196 Ã· 12.25
16

Question 13.
117Ã·6.5
18

Question 14.
936 Ã· 9.75
96

Question 15.
305 Ã· 12.2
25

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

Question 16.
83.375 Ã· 2.3 = 3,625
83.375 Ã· 2.3 = 36.25

Question 17.
183.575 Ã· 5,245 = 3.5
183.575 Ã· 52.45 = 3.5

Question 18.
326,025 Ã· 9.45 = 3.45
32.6025 Ã· 9.45 = 3.45

Question 19.
449.5 Ã· 725 = 6.2
449.5 Ã· 72.5 = 6.2

Question 20.
446,642 Ã· 85.4 = 52.3
4,466.42 Ã· 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 Ã· 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 Ã· 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 Ã— 14