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