## Engage NY Eureka Math 5th Grade Module 6 Lesson 8 Answer Key

### Eureka Math Grade 5 Module 6 Lesson 8 Sprint Answer Key

A
Multiply Decimals by 10, 100, and 1,000

Question 1.
62.3 × 10 =
62.3 × 10 = 623

Question 2.
62.3 × 100 =
62.3 × 100 = 6230

Question 3.
62.3 × 1,000 =
62.3 × 1,000 = 62300

Question 4.
73.6 × 10 =
73.6 × 10 = 736

Question 5.
73.6 × 100 =
73.6 × 100 = 7360

Question 6.
73.6 × 1,000 =
73.6 × 1,000 = 73600

Question 7.
0.6 × 10 =
0.6 × 10 = 6

Question 8.
0.06 × 10 =
0.06 × 10 = 0.6

Question 9.
0.006 × 10 =
0.006 × 10 = 0.06

Question 10.
0.3 × 10 =
0.3 × 10 = 3

Question 11.
0.3 × 100 =
0.3 × 100 = 30

Question 12.
0.3 × 1,000 =
0.3 × 1,000 = 300

Question 13.
0.02 × 10 =
0.02 × 10 = 0.2

Question 14.
0.02 × 100 =
0.02 × 100 = 2

Question 15.
0.02 × 1,000 =
0.02 × 1,000 = 20

Question 16.
0.008 × 10 =
0.008 × 10 = 0.08

Question 17.
0.008 × 100 =
0.008 × 100 = 0.8

Question 18.
0.008 × 1,000 =
0.008 × 1,000 = 8

Question 19.
0.32 × 10 =
0.32 × 10 = 3.2

Question 20.
0.67 × 10 =
0.67 × 10 = 6.7

Question 21.
0.91 × 100 =
0.91 × 100 = 91

Question 22.
0.74 × 100 =
0.74 × 100 = 74

Question 23.
4.1 × 1,000 =
4.1 × 1,000 = 4100

Question 24.
7.6 × 1,000 =
7.6 × 1,000 = 7600

Question 25.
0.01 × 1,000 =
0.01 × 1,000 = 10

Question 26.
0.07 × 1,000 =
0.07 × 1,000 = 70

Question 27.
0.072 × 100 =
0.072 × 100 = 7.2

Question 28.
0.802 × 10 =
0.802 × 10 = 8.02

Question 29.
0.019 × 1,000 =
0.019 × 1,000 = 19

Question 30.
7.412 × 1,000 =
7.412 × 1,000 = 7412

Question 31.
6.8 × 100 =
6.8 × 100 = 680

Question 32.
4.901 × 10 =
4.901 × 10 = 49.01

Question 33.
16.07 × 100 =
16.07 × 100 = 1607

Question 34.
9.19 × 10 =
9.19 × 10 = 91.9

Question 35.
18.2 × 100 =
18.2 × 100 = 1820

Question 36.
14.7 × 1,000 =
14.7 × 1,000 = 14700

Question 37.
2.021 × 100 =
2.021 × 100 = 202.1

Question 38.
172.1 × 10 =
172.1 × 10 = 1721

Question 39.
3.2 × 20 =
3.2 × 20 = 64

Question 40.
4.1 × 20 =
4.1 × 20 = 82

Question 41.
3.2 × 30 =
3.2 × 30 = 96

Question 42.
1.3 × 30 =
1.3 × 30 = 39

Question 43.
3.12 × 40 =
3.12 × 40 = 124.8

Question 44.
14.12 × 40 =
14.12 × 40 = 564.8

B
Multiply Decimals by 10, 100, and 1,000

Question 1.
46.1 × 10 =
46.1 × 10 = 461

Question 2.
46.1 × 100 =
46.1 × 100 = 4610

Question 3.
46.1 × 1,000 =
46.1 × 1,000 = 46100

Question 4.
89.2 × 10 =
89.2 × 10 = 892

Question 5.
89.2 × 100 =
89.2 × 100 = 8920

Question 6.
89.2 × 1,000 =
89.2 × 1,000 = 89200

Question 7.
0.3 × 10 =
0.3 × 10 = 3

Question 8.
0.03 × 10 =
0.03 × 10 = 0.3

Question 9.
0.003 × 10 =
0.003 × 10 = 0.03

Question 10.
0.9 × 10 =
0.9 × 10 = 9

Question 11.
0.9 × 100 =
0.9 × 100 =90

Question 12.
0.9 × 1,000 =
0.9 × 1,000 = 900

Question 13.
0.04 × 10 =
0.04 × 10 = 0.4

Question 14.
0.04 × 100 =
0.04 × 100 = 4

Question 15.
0.04 × 1,000 =
0.04 × 1,000 = 40

Question 16.
0.007 × 10 =
0.007 × 10 = 0.07

Question 17.
0.007 × 100 =
0.007 × 100 = 0.7

Question 18.
0.007 × 1,000 =
0.007 × 1,000 = 7

Question 19.
0.45 × 10 =
0.45 × 10 = 4.5

Question 20.
0.78 × 10 =
0.78 × 10 = 7.8

Question 21.
0.28 × 100 =
0.28 × 100 = 28

Question 22.
0.19 × 100 =
0.19 × 100 = 19

Question 23.
5.2 × 1,000 =
5.2 × 1,000 = 5200

Question 24.
8.7 × 1,000 =
8.7 × 1,000 = 8700

Question 25.
0.01 × 1,000 =
0.01 × 1,000 = 10

Question 26.
0.08 × 1,000 =
0.08 × 1,000 = 80

Question 27.
0.083 × 10 =
0.083 × 10 = 0.83

Question 28.
0.903 × 10 =
0.903 × 10 =9.03

Question 29.
0.017 × 1,000 =
0.017 × 1,000 = 17

Question 30.
8.523 × 1,000 =
8.523 × 1,000 =8523

Question 31.
7.9 × 100 =
7.9 × 100 = 790

Question 32.
5.802 × 10 =
5.802 × 10 = 58.02

Question 33.
27.08 × 100 =
27.08 × 100 = 2708

Question 34.
8.18 × 10 =
8.18 × 10 = 81.8

Question 35.
29.3 × 100 =
29.3 × 100 = 2930

Question 36.
25.8 × 1,000 =
25.8 × 1,000 = 25800

Question 37.
3.032 × 100 =
3.032 × 100 = 303.2

Question 38.
283.1 × 10 =
283.1 × 10 = 2831

Question 39.
2.1 × 20 =
2.1 × 20 = 42

Question 40.
3.3 × 20 =
3.3 × 20 = 6.6

Question 41.
3.1 × 30 =
3.1 × 30 = 93

Question 42.
1.2 × 30 =
1.2 × 30 = 36

Question 43.
2.11 × 40 =
2.11 × 40 = 84.4

Question 44.
13.11 × 40 =
13.11 × 40 = 524.4

### Eureka Math Grade 5 Module 6 Lesson 8 Problem Set Answer Key

Question 1.
Create a table of 3 values for x and y such that each y-coordinate is 3 more than the corresponding x-coordinate.

 x y ( x, y)

a. Plot each point on the coordinate plane.
b. Use a straightedge to draw a line connecting these points.
c. Give the coordinates of 2 other points that fall on this line with x-coordinates greater than 12. (______ , ______) and (______ , ______)
a. 3 points are plotted on the graph where each y-coordinate is 3 more than the corresponding x-coordinate.

 x y ( x, y) 2 5 (2, 5) 3 6 (3, 6) 4 7 (4 ,7)

b. 3 points are connected with a straight line .
c. The coordinates of 2 other points that fall on this line with x-coordinates greater than 12 and each y-coordinate is 3 more than the corresponding x-coordinate are (13 , 16) and ( 15 , 18)

Question 2.
Create a table of 3 values for x and y such that each y-coordinate is 3 times as much as its corresponding x-coordinate.

 x y ( x, y)

a. Plot each point on the coordinate plane.
b. Use a straightedge to draw a line connecting these points.
c. Give the coordinates of 2 other points that fall on this line with y-coordinates greater than 25. (______ , ______) and (______ , ______)
a. 3 Points are plotted on the graph where each y-coordinate is 3 times as much as its corresponding x

 x y ( x, y) 0 0 (0, 0 ) 1 3 (1, 3) 2 6 (2, 6)

b. All the points are connected with a straight line .
c. The coordinates of 2 other points that fall on this line with y-coordinates greater than 25 and each y-coordinate is 3 times as much as its corresponding x – coordinate are (9, 27 ) and (10 , 30 )

Question 3.
Create a table of 5 values for x and y such that each y-coordinate is 1 more than 3 times as much as its corresponding x value.

 x y ( x, y)

a. Plot each point on the coordinate plane.
b. Use a straightedge to draw a line connecting these points.
c. Give the coordinates of 2 other points that would fall on this line whose x-coordinates are greater than 12. (______ , ______) and (______ , ______)
a. y = 3x + 1

 x y ( x, y) 0 1 (0, 1) 1 4 (1 , 4) 2 7 (2, 7) 3 10 ( 3, 10) 4 13 (4, 13)

b. A  straightedge line is drawn to connect these points is shown in above graph .
c. The coordinates of 2 other points that would fall on this line whose x-coordinates are greater than 12 and each      y-coordinate is 1 more than 3 times as much as its corresponding x value are (14 , 44 ) and (15 , 46 ) .

Question 4.
Use the coordinate plane below to complete the following tasks.

a. Graph the lines on the plane.
line l: x is equal to y

 x y ( x, y) A B C

line m: y is 1 more than x

 x y ( x, y) G H I

line n: y is 1 more than twice x

 x y ( x, y) S T U

b. Which two lines intersect? Give the coordinates of their intersection.
c. Which two lines are parallel?
d. Give the rule for another line that would be parallel to the lines you listed in Problem 4(c).
a.

line l: x is equal to y

 x y ( x, y) A 1 1 (1,1) B 2 2 (2,2) C 3 3 (3,3)

line m: y is 1 more than x
y=x+1

 x y ( x, y) G 2 3 (2, 3) H 3 4 (3, 4) I 5 6 (5, 6)

line n: y is 1 more than twice x
y = 2x + 1

 x y ( x, y) S 0 1 (0, 1) T 1 3 (1, 3) U 2 5 (2, 5)

b. The two lines intersect are m and n lines .The coordinates of their intersection are ( 0, 1)
c. The two parallel lines are n and m lines.
d. The rule for another line that would be parallel to the lines you listed in Problem 4(c) is y is 2 more than x

### Eureka Math Grade 5 Module 6 Lesson 8 Exit Ticket Answer Key

Complete this table with values for y such that each y-coordinate is 5 more than 2 times as much as its corresponding x-coordinate

 x y ( x, y) 0 2 3.5

a. Plot each point on the coordinate plane.
b. Use a straightedge to draw a line connecting these points.
c. Name 2 other points that fall on this line with y-coordinates greater than 25.
a.
Each y-coordinate is 5 more than 2 times as much as its corresponding x-coordinate
y = 2x + 5
All the points are plotted in the graph .

 x y ( x, y) 0 5 (0, 5) 2 9 (2, 9) 3.5 12 (3.5, 12)

b. A straightedge line is drawn to connect all these points and is shown in above graph .
c. The 2 other points that fall on this line with y-coordinates greater than 25 and each y-coordinate is 5 more than 2 times as much as its corresponding x-coordinate are (11, 27) and ( 12, 29)

### Eureka Math Grade 5 Module 6 Lesson 8 Homework Answer Key

Question 1.
Complete this table such that each y-coordinate is 4 more than the corresponding x-coordinate.

 x y ( x, y)

a. Plot each point on the coordinate plane.
b. Use a straightedge to construct a line connecting these points.
c. Give the coordinates of 2 other points that fall on this line with x-coordinates greater than 18. (______ , ______) and (______ , ______)
a.
Each y-coordinate is 4 more than the corresponding x-coordinate.
y = 4x
The points are plotted on the the coordinate plane .

 x y ( x, y) 0 0 (0, 0) 1 4 (1, 4) 2 8 (2, 8 )

b. A straightedge line is drawn to connect all these points and is shown in above graph .
c. The coordinates of 2 other points that fall on this line with x-coordinates greater than 18 and each y-coordinate is 4 more than the corresponding x-coordinate  (19 , 76 ) and (20 , 80)

Question 2.
Complete this table such that each y-coordinate is 2 times as much as its corresponding x-coordinate.

 x y ( x, y)

a. Plot each point on the coordinate plane.
b. Use a straightedge to draw a line connecting these points.
c. Give the coordinates of 2 other points that fall on this line with y-coordinates greater than 25. (______ , ______) and (______ , ______)
a.
Each y-coordinate is 2 times as much as its corresponding x-coordinate.
y = 2x
The points are plotted on the the coordinate plane .

 x y ( x, y) 1 2 (1, 2) 2 4 (2, 4) 3 6 (3, 6)

b. A straightedge line is drawn to connect all these points and is shown in above graph .
c. The coordinates of 2 other points that fall on this line with y-coordinates greater than 25 and each y-coordinate is 2 times as much as its corresponding x-coordinate. (13, 26 ) and ( 15, 30) .

Question 3.
Use the coordinate plane below to complete the following tasks.

a. Graph these lines on the plane.
line l: x is equal to y

 x y ( x, y) A B C

line m: y is 1 less than x

 x y ( x, y) G H I

line n: y is 1 less than twice x

 x y ( x, y) S T U

b. Do any of these lines intersect? If yes, identify which ones, and give the coordinates of their intersection.
c. Are any of these lines parallel? If yes, identify which ones.
d. Give the rule for another line that would be parallel to the lines you listed in Problem 3(c).
a.
line l: x is equal to y
y = x

 x y ( x, y) A 1 1 (1, 1) B 2 2 (2, 2) C 3 3 (3, 3)

line m: y is 1 less than x
y = x – 1

 x y ( x, y) G 2 1 (2, 1) H 3 2 (3, 2) I 4 3 (4, 3)

line n: y is 1 less than twice x
y = 2x – 1

 x y ( x, y) S 1 1 (1, 1) T 2 3 (2, 3) U 3 5 (3, 5)

b.
Yes, The Two lines which intersect are line l and n.
They intersect at coordinate (1, 1).
c. Yes, We have parallel lines.
The parallel lines are line l and m.
d. The rule for another line that would be parallel to the lines you listed in Problem 3(c) is y is 2 less than x .