Eureka Math Grade 5 Module 6 Lesson 12 Answer Key

Engage NY Eureka Math 5th Grade Module 6 Lesson 12 Answer Key

Eureka Math Grade 5 Module 6 Lesson 12 Sprint Answer Key

A
Subtract Decimals
Engage NY Math 5th Grade Module 6 Lesson 12 Sprint Answer Key 1

Question 1.
5 – 1 =
Answer:
5 – 1 = 4

Question 2.
5.9 – 1 =
Answer:
5.9 – 1 = 4.9
Explanation :

Line the decimals up: 5.9
1
“Pad” with zeros: 5.9
1.0
Subtract: 5.9
1.0
4.9

Question 3.
5.93 – 1 =
Answer:
5.93 – 1 = 4.93
Explanation :

Line the decimals up: 5.93
1
“Pad” with zeros: 5.93
1.00
Subtract: 5.93
1.00
4.93

Question 4.
5.932 – 1 =
Answer:
5.932 -1 = 4.932

Explanation :

Line the decimals up: 5.932
1
“Pad” with zeros: 5.932
1.000
Subtract: 5.932
1.000
4.932

Question 5.
5.932 – 2 =
Answer:
5.932 – 2 = 3.932

Explanation :

Line the decimals up: 5.932
2
“Pad” with zeros: 5.932
2.000
Subtract: 5.932
2.000
3.932

 

Question 6.
5.932 – 4 =
Answer:
5.932 – 4 = 1.932

Explanation :

Line the decimals up: 5.932
4
“Pad” with zeros: 5.932
4.000
Subtract: 5.932
4.000
1.932

Question 7.
0.5 – 0.1 =
Answer:
0.5 – 0.1 = 0.4

Explanation :

Line the decimals up: 0.5
0.1
“Pad” with zeros: 0.5
0.1
Subtract: 0.5
0.1
0.4

 

Question 8.
0.53 – 0.1 =
Answer:
0.53 – 0.1 = 0.43
Explanation :

Line the decimals up: 0.53
0.1
“Pad” with zeros: 0.53
0.10
Subtract: 0.53
0.10
0.43

Question 9.
0.539 – 0.1 =
Answer:
0.539 – 0.1 = 0.439
Explanation :

Line the decimals up: 0.539
0.1
“Pad” with zeros: 0.539
0.100
Subtract: 0.539
0.100
0.439

 

Question 10.
8.539 – 0.1 =
Answer:
8.539 – 0.1 = 8.439

Explanation :

Line the decimals up: 8.539
0.1
“Pad” with zeros: 8.539
0.100
Subtract: 8.539
0.100
8.439

Question 11.
8.539 – 0.2 =
Answer:

Explanation :

Line the decimals up: 8.539
0.2
“Pad” with zeros: 8.539
0.200
Subtract: 8.539
0.200
8.339

Question 12.
8.539 – 0.4 =
Answer:
8.539 – 0.4 = 8.139

Explanation :

Line the decimals up: 8.539
0.4
“Pad” with zeros: 8.539
0.400
Subtract: 8.539
0.400
8.139

Question 13.
0.05 – 0.01 =
Answer:
0.05 – 0.01 = 0.04

Explanation :

Line the decimals up: 0.05
0.01
“Pad” with zeros: 0.05
0.01
Subtract: 0.05
0.01
0.04

 

Question 14.
0.057 – 0.01 =
Answer:
0.057 – 0.01 =0.047

Explanation :

Line the decimals up: 0.057
0.01
“Pad” with zeros: 0.057
0.010
Subtract: 0.057
0.010
0.047

Question 15.
1.057 – 0.01 =
Answer:
1.057 – 0.01 = 1.047
Explanation :

Line the decimals up: 1.057
0.01
“Pad” with zeros: 1.057
0.010
Subtract: 1.057
0.010
1.047

Question 16.
1.857 – 0.01 =
Answer:
1.857 – 0.01 = 1.847
Explanation :

Line the decimals up: 1.857
0.01
“Pad” with zeros: 1.857
0.010
Subtract: 1.857
0.010
1.847

Question 17.
1.857 – 0.02 =
Answer:
1.857 – 0.02 = 1.837

Question 18.
1.857 – 0.04 =
Answer:
1.857 – 0.04 = 1.817

Question 19.
0.005 – 0.001 =
Answer:
0.005 – 0.001 = 0.004
Explanation :

Line the decimals up: 0.005
0.001
“Pad” with zeros: 0.005
0.001
Subtract: 0.005
0.001
0.004

Question 20.
7.005 – 0.001 =
Answer:
7.005 – 0.001 = 7.004
Explanation :

Line the decimals up: 7.005
0.001
“Pad” with zeros: 7.005
0.001
Subtract: 7.005
0.001
7.004

Question 21.
7.905 – 0.001 =
Answer:
7.905 – 0.001 = 7.904

Question 22.
7.985 – 0.001 =
Answer:
7.985 – 0.001 = 7.984

Question 23.
7.985 – 0.002 =
Answer:
7.985 – 0.002 = 7.983

Question 24.
7.985 – 0.004 =
Answer:
7.985 – 0.004 =7.981

Question 25.
2.7 – 0.1 =
Answer:
2.7 – 0.1 = 2.6

Question 26.
2.785 – 0.1 =
Answer:
2.785 – 0.1 = 2.775
Explanation :

Line the decimals up: 2.785
0.1
“Pad” with zeros: 2.785
0.100
Subtract: 2.785
0.100
2.685

Question 27.
2.785 – 0.5 =
Answer:
2.785 – 0.5 = 2.285

Question 28.
4.913 – 0.4 =
Answer:
4.913 – 0.4 = 4.513

Question 29.
3.58 – 0.01 =
Answer:
3.58 – 0.01 = 3.47

Explanation :

Line the decimals up: 3.58
0.01
“Pad” with zeros: 3.58
0.01
Subtract: 3.58
0.01
3.57

Question 30.
3.586 – 0.01 =
Answer:
3.586 – 0.01 = 3.576

Question 31.
3.586 – 0.05 =
Answer:
3.586 – 0.05 = 3.536

Question 32.
7.982 – 0.04 =
Answer:
7.982 – 0.04 = 7.942

Question 33.
6.126 – 0.001 =
Answer:
6.126 – 0.001 = 6.125

Question 34.
6.126 – 0.004 =
Answer:
6.126 – 0.004 = 6.122

Question 35.
9.348 – 0.006 =
Answer:
9.348 – 0.006 = 9.342

Question 36.
8.347 – 0.3 =
Answer:
8.347 – 0.3 = 8.047

Question 37.
9.157 – 0.05 =
Answer:
9.157 – 0.05 = 9.107

Question 38.
6.879 – 0.009 =
Answer:
6.879 – 0.009 = 6.870

Question 39.
6.548 – 2 =
Answer:
6.548 – 2 = 6.348

Question 40.
6.548 – 0.2 =
Answer:
6.548 – 0.2 = 6.348

Question 41.
6.548 – 0.02 =
Answer:
6.548 – 0.02 = 6.528

Question 42.
6.548 – 0.002 =
Answer:
6.548 – 0.002 = 6.546

Question 43.
6.196 – 0.06 =
Answer:
6.196 – 0.06 = 6.136

Question 44.
9.517 – 0.004 =
Answer:
9.517 – 0.004 = 9.513

B
Subtract Decimals
Engage NY Math 5th Grade Module 6 Lesson 12 Sprint Answer Key 2

Question 1.
6 – 1 =
Answer:
6 – 1 = 5

Question 2.
6.9 – 1 =
Answer:
6.9 – 1 = 5.9

Question 3.
6.93 – 1 =
Answer:
6.93 – 1 = 5.93

Question 4.
6.932 – 1 =
Answer:
6.932 – 1 = 5.932

Question 5.
6.932 – 2 =
Answer:
6.932 – 2 = 4.932

Question 6.
6.932 – 4 =
Answer:
6.932 – 4 = 2.932

Question 7.
0.6 – 0.1 =
Answer:
0.6 – 0.1 = 0.5

Question 8.
0.63 – 0.1 =
Answer:
0.63 – 0.1 = 0.53

Question 9.
0.639 – 0.1 =
Answer:
0.639 – 0.1 = 0.539

Question 10.
8.639 – 0.1 =
Answer:
8.639 – 0.1 = 8.539

Question 11.
8.639 – 0.2 =
Answer:
8.639 – 0.2 = 8.439

Question 12.
8.639 – 0.4 =
Answer:
8.639 – 0.4 = 8.239

Question 13.
0.06 – 0.01 =
Answer:
0.06 – 0.01 = 0.05

Question 14.
0.067 – 0.01 =
Answer:
0.067 – 0.01 = 0.057

Question 15.
1.067 – 0.01 =
Answer:
1.067 – 0.01 = 1.057

Question 16.
1.867 – 0.01 =
Answer:
1.867 – 0.01 = 1.857

Question 17.
1.867 – 0.02 =
Answer:
1.867 – 0.02 = 1.847

Question 18.
1.867 – 0.04 =
Answer:
1.867 – 0.04 = 1.827

Question 19.
0.006 – 0.001 =
Answer:
0.006 – 0.001 = 0.005

Question 20.
7.006 – 0.001 =
Answer:
7.006 – 0.001 = 7.005

Question 21.
7.906 – 0.001 =
Answer:
7.906 – 0.001 = 7.905

Question 22.
7.986 – 0.001 =
Answer:
7.986 – 0.001 = 7.985

Question 23.
7.986 – 0.002 =
Answer:
7.986 – 0.002 = 7.984

Question 24.
7.986 – 0.004 =
Answer:
7.986 – 0.004 = 7.982

Question 25.
3.7 – 0.1 =
Answer:
3.7 – 0.1 = 3.6

Question 26.
3.785 – 0.1 =
Answer:
3.785 – 0.1 = 3.685

Question 27.
3.785 – 0.5 =
Answer:
3.785 – 0.5 = 3.285

Question 28.
5.924 – 0.4 =
Answer:
5.924 – 0.4 = 5.524

Question 29.
4.58 – 0.01 =
Answer:
4.58 – 0.01 = 4.57

Question 30.
4.586 – 0.01 =
Answer:
4.586 – 0.01 = 4.576

Question 31.
4.586 – 0.05 =
Answer:
4.586 – 0.05 = 4.536

Question 32.
6.183 – 0.04 =
Answer:
6.183 – 0.04 =6.143

Question 33.
7.127 – 0.001 =
Answer:
7.127 – 0.001 = 7.126

Question 34.
7.127 – 0.004 =
Answer:
7.127 – 0.004 = 7.123

Question 35.
1.459 – 0.006 =
Answer:
1.459 – 0.006 = 1.453

Question 36.
8.457 – 0.4 =
Answer:
8.457 – 0.4 = 8.057

Question 37.
1.267 – 0.06 =
Answer:
1.267 – 0.06 = 1.207

Question 38.
7.981 – 0.001 =
Answer:
7.981 – 0.001 = 7.980

Question 39.
7.548 – 2 =
Answer:
7.548 – 2 = 5.548

Question 40.
7.548 – 0.2 =
Answer:
7.548 – 0.2 = 7.348

Question 41.
7.548 – 0.02 =
Answer:
7.548 – 0.02 = 7.528

Question 42.
7.548 – 0.002 =
Answer:
7.548 – 0.002 = 7.546

Question 43.
7.197 – 0.06 =
Answer:
7.197 – 0.06 = 7.191

Question 44.
1.627 – 0.004 =
Answer:
1.627 – 0.004 =1.623

Eureka Math Grade 5 Module 6 Lesson 12 Problem Set Answer Key

Question 1.
Write a rule for the line that contains the points (0, \(\frac{3}{4}\)) and (2\(\frac{1}{2}\), 3\(\frac{1}{4}\)).
Engage NY Math Grade 5 Module 6 Lesson 12 Problem Set Answer Key 1
a. Identify 2 more points on this line. Draw the line on the grid below.

Point

x y

(x , y)

B
C

b. Write a rule for a line that is parallel to \(\overleftrightarrow{B C}\) and goes through point (1, \(\frac{1}{4}\)).
Answer:
a.
(0, \(\frac{3}{4}\)) and (2\(\frac{1}{2}\), 3\(\frac{1}{4}\)).
Rule : add \(\frac{3}{4}\) to x .
y = x + add \(\frac{3}{4}\)

Point

x y

(x , y)

B 1 1\(\frac{3}{4}\) 1\(\frac{3}{4}\)
C 2 2\(\frac{3}{4}\) 2\(\frac{3}{4}\)

Engage-NY-Eureka-Math-5th-Grade-Module-6-Lesson-12-Answer-Key-Eureka-Math-Grade-5-Module-6-Lesson-12-Problem-Set-Answer-Key-Question-1
b. A rule for a line that is parallel to \(\overleftrightarrow{B C}\) and goes through point (1, \(\frac{1}{4}\)).
Rule : subtract \(\frac{3}{4}\) from x .
D = (1, \(\frac{1}{4}\)).
Engage-NY-Eureka-Math-5th-Grade-Module-6-Lesson-12-Answer-Key-Eureka-Math-Grade-5-Module-6-Lesson-12-Problem-Set-Answer-Key-Question-1-b

Question 2.
Create a rule for the line that contains the points (1, \(\frac{1}{4}\) and (3, \(\frac{3}{4}\)).
a. Identify 2 more points on this line. Draw the line on the grid on the right.

Point

x y

(x , y)

G
H

b. Write a rule for a line that passes through the origin and lies between \(\overleftrightarrow{B C}\) and \(\overleftrightarrow{G H}\).
Answer:
a. Rule :Multiply x by \(\frac{1}{4}\)
(1, \(\frac{1}{4}\) and (3, \(\frac{3}{4}\))

Point

x y

(x , y)

G 2 \(\frac{1}{2}\) (2, \(\frac{1}{2}\))
H 4 1 (4, 1)

Engage-NY-Eureka-Math-5th-Grade-Module-6-Lesson-12-Answer-Key-Eureka-Math-Grade-5-Module-6-Lesson-12-Problem-Set-Answer-Key-Question-2-b
b. Rule :Multiply x by \(\frac{3}{4}\) .

Question 3.
Create a rule for a line that contains the point (\(\frac{1}{4}\), 1\(\frac{1}{4}\)) using the operation or description below. Then, name 2 other points that would fall on each line.
a. Addition: _________

Point

x y

(x , y)

T
U

b. A line parallel to the x-axis: _________

Point

x y

(x , y)

G
H

c. Multiplication: _________

Point

x y

(x , y)

A
B

d. A line parallel to the y-axis: _________

Point

x y

(x , y)

V
W

e. Multiplication with addition: _________

Point

x y

(x , y)

R
S

Answer:

a. Addition:  add 1 to x

Point

x y

(x , y)

T 2 3 (2, 3)
U 3 4 (3, 4)

b. A line parallel to the x-axis: y is always 1\(\frac{1}{4}\).

Point

x y

(x , y)

G 1 1\(\frac{1}{4}\) ( 1, 1\(\frac{1}{4}\))
H 2 1\(\frac{1}{4}\) (2, 1\(\frac{1}{4}\))

c. Multiplication: multiply x by 5 .

Point

x y

(x , y)

A 2 10 (2, 10)
B 3 15 (3, 15)

d. A line parallel to the y-axis: x coordinate is always 4

Point

x y

(x , y)

V 4 3  (4, 3)
W 4 4  (4, 4)

e. Multiplication with addition: multiply x and add \(\frac{1}{4}\)

Point

x y

(x , y)

R \(\frac{1}{2}\) 2\(\frac{1}{4}\) (\(\frac{1}{2}\), 2\(\frac{1}{4}\))
S 2 8\(\frac{1}{4}\) (2, 8\(\frac{1}{4}\))

 

Question 4.
Mrs. Boyd asked her students to give a rule that could describe a line that contains the point (0.6, 1.8). Avi said the rule could be multiply x by 3. Ezra claims this could be a vertical line, and the rule could be x is always 0.6. Erik thinks the rule could be add 1.2 to x. Mrs. Boyd says that all the lines they are describing could describe a line that contains the point she gave. Explain how that is possible, and draw the lines on the coordinate plane to support your response.
Engage NY Math Grade 5 Module 6 Lesson 12 Problem Set Answer Key 2
Answer:
Engage-NY-Eureka-Math-5th-Grade-Module-6-Lesson-12-Answer-Key-Eureka-Math-Grade-5-Module-6-Lesson-12-Problem-Set-Answer-Key-Question-4

Explanation :
Mrs. Boyd’s gave only one point (0.6, 1.8) on the line .Many lines can be drawn from one point . With 2 points we can say the rule but without 2 points we cannot say the rule.

Question 5.
Create a mixed operation rule for the line that contains the points (0, 1) and (1, 3).
Engage NY Math Grade 5 Module 6 Lesson 12 Problem Set Answer Key 3
a. Identify 2 more points, O and P, on this line. Draw the line on the grid.

Point

x y

(x , y)

O
P

b. Write a rule for a line that is parallel to \(\overleftrightarrow{O P}\) and goes through point (1, 2\(\frac{1}{2}\)).
Answer:
Rule : Multiply x by 2 and add 1 .
a.

Point

x y

(x , y)

O \(\frac{1}{2}\) 2 (\(\frac{1}{2}\), 2)
P 1\(\frac{1}{2}\) 4 (1\(\frac{1}{2}\), 4)

b. Rule : Multiply by x and add 2.
Engage-NY-Eureka-Math-5th-Grade-Module-6-Lesson-12-Answer-Key-Eureka-Math-Grade-5-Module-6-Lesson-12-Problem-Set-Answer-Key-Question-5

Eureka Math Grade 5 Module 6 Lesson 12 Exit Ticket Answer Key

Write the rule for the line that contains the points (0, 1\(\frac{1}{2}\)) and (1\(\frac{1}{2}\), 3).
Eureka Math 5th Grade Module 6 Lesson 12 Exit Ticket Answer Key 1
a. Identify 2 more points on this line. Draw the line on the grid.

Point

x y

(x , y)

B
C

b. Write a rule for a line that is parallel to \(\overleftrightarrow{B C}\) and goes through point (1, \(\frac{1}{2}\)).
Answer:
Rule : add \(\frac{1}{2}\) to x .

Point

x y

(x , y)

B 1 2\(\frac{1}{2}\) (1,2\(\frac{1}{2}\))
C 2 3\(\frac{1}{2}\) (2, 3\(\frac{1}{2}\))

Engage-NY-Eureka-Math-5th-Grade-Module-6-Lesson-12-Answer-Key-Eureka-Math-Grade-5-Module-6-Lesson-12-Exit-Ticket-Answer-Key-Question-1

b.
The Rule that is parallel to \(\overleftrightarrow{B C}\) and goes through point (1, \(\frac{1}{2}\)) is  Subtract \(\frac{1}{2}\) from x .

Eureka Math Grade 5 Module 6 Lesson 12 Homework Answer Key

Question 1.
Write a rule for the line that contains the points (0, \(\frac{1}{4}\)) and (2\(\frac{1}{2}\), 2\(\frac{3}{4}\)).
Eureka Math Grade 5 Module 6 Lesson 12 Homework Answer Key 1
a. Identify 2 more points on this line. Draw the line on the grid below.

Point

x y

(x , y)

B
C

b. Write a rule for a line that is parallel to \(\overleftrightarrow{B C}\) and goes through point (1, 2\(\frac{1}{4}\).
Answer:
Rule : Add \(\frac{1}{4}\) to x .

Point

x y

(x , y)

B \(\frac{3}{4}\) 1 (\(\frac{3}{4}\), 1)
C 2 2\(\frac{1}{4}\) (2, 2\(\frac{1}{4}\))

 

Engage-NY-Eureka-Math-5th-Grade-Module-6-Lesson-12-Answer-Key-Eureka-Math-Grade-5-Module-6-Lesson-12-Homework-Answer-Key-Question-1
b.
Rule for a line that is parallel to \(\overleftrightarrow{B C}\) and goes through point (1, 2\(\frac{1}{4}\) is add 1\(\frac{1}{4}\) to x .

Question 2.
Give the rule for the line that contains the points (1, 2\(\frac{1}{2}\)) and (2\(\frac{1}{2}\), 2\(\frac{1}{2}\)).
a. Identify 2 more points on this line. Draw the line on the grid above.

Point

x y

(x , y)

G
H

b. Write a rule for a line that is parallel to \(\overleftrightarrow{G H}\).
Answer:
a.
Rule : For all x-coordinates the y- coordinate is 2\(\frac{1}{2}\)

Point

x y

(x , y)

G 3 2\(\frac{1}{2}\) (3, 2\(\frac{1}{2}\))
H 4 2\(\frac{1}{2}\) (4, 2\(\frac{1}{2}\))

Engage-NY-Eureka-Math-5th-Grade-Module-6-Lesson-12-Answer-Key-Eureka-Math-Grade-5-Module-6-Lesson-12-Homework-Answer-Key-Question-2
b. A rule for a line that is parallel to \(\overleftrightarrow{G H}\) is
For all x-coordinates the y- coordinate is 1\(\frac{3}{4}\) .

Question 3.
Give the rule for a line that contains the point (\(\frac{3}{4}\), 1\(\frac{1}{2}\)) using the operation or description below. Then, name 2 other points that would fall on each line.
a. Addition: ________________

Point

x y

(x , y)

T
U

b. A line parallel to the x-axis: ________________

Point

x y

(x , y)

G
H

c. Multiplication: ________________

Point

x y

(x , y)

A
B

d. A line parallel to the y-axis: ________________

Point

x y

(x , y)

V
W

e. Multiplication with addition: _____________

Point

x y

(x , y)

R
S

Answer:

a. Addition: add \(\frac{3}{4}\) to x

Point

x y

(x , y)

T \(\frac{3}{4}\) 1\(\frac{1}{2}\) (\(\frac{3}{4}\), 1\(\frac{1}{2}\))
U 2 2\(\frac{3}{4}\) (2, 2\(\frac{3}{4}\))

b. A line parallel to the x-axis: all x coordinate have y coordinate as 2

Point

x y

(x , y)

G 1 2 (1, 2)
H 2 2 (2, 2)

c. Multiplication: multiply by 2

Point

x y

(x , y)

A 1 2 (1, 2)
B 2 4 (2, 4)

d. A line parallel to the y-axis: All y coordinates have the same x coordinate 2

Point

x y

(x , y)

V 3 1 (3, 1)
W 3 2 (3, 2)

e. Multiplication with addition: multiply by 2 and add 1

Point

x y

(x , y)

R 1 3 (1, 3)
S 2 5 (2, 5)

 

Question 4.
On the grid, two lines intersect at (1.2, 1.2). If line a passes through the origin and line b contains the point (1.2, 0), write a rule for line a and line b.
Eureka Math Grade 5 Module 6 Lesson 12 Homework Answer Key 2
Answer:
Engage-NY-Eureka-Math-5th-Grade-Module-6-Lesson-12-Answer-Key-Eureka-Math-Grade-5-Module-6-Lesson-12-Homework-Answer-Key-Question-4
For line a the Rule is x coordinate . The y coordinate is same the x coordinate .
For line b the Rule is All y coordinates have the same x coordinate 1.2 .

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