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

A
Subtract Decimals

Question 1.
5 – 1 =
5 – 1 = 4

Question 2.
5.9 – 1 =
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 =
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 =
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 =
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 =
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 =
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 =
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 =
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 =
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 =

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 =
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 =
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 =
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 =
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 =
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 =
1.857 – 0.02 = 1.837

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

Question 19.
0.005 – 0.001 =
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 =
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 =
7.905 – 0.001 = 7.904

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

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

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

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

Question 26.
2.785 – 0.1 =
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 =
2.785 – 0.5 = 2.285

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

Question 29.
3.58 – 0.01 =
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 =
3.586 – 0.01 = 3.576

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

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

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

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

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

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

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

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

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

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

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

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

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

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

B
Subtract Decimals

Question 1.
6 – 1 =
6 – 1 = 5

Question 2.
6.9 – 1 =
6.9 – 1 = 5.9

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Question 44.
1.627 – 0.004 =
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$$\frac{1}{4}$$).

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, $$\frac{1}{4}$$).
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$$\frac{3}{4}$$

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, $$\frac{1}{4}$$).

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 $$\overleftrightarrow{G H}$$.
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)

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.

 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

 Point x y (x , y) R S

 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.

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).

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$$\frac{1}{2}$$).
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.

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).

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, $$\frac{1}{2}$$).
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$$\frac{1}{2}$$)

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 .

Question 1.
Write a rule for the line that contains the points (0, $$\frac{1}{4}$$) and (2$$\frac{1}{2}$$, 2$$\frac{3}{4}$$).

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$$\frac{1}{4}$$.
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$$\frac{1}{4}$$)

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 $$\overleftrightarrow{G H}$$.
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$$\frac{1}{2}$$)

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.

 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

 Point x y (x , y) R S

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)