## Engage NY Eureka Math 4th Grade Module 2 End of Module Assessment Answer Key

Question 1.
Complete the conversion charts.

 Length 3 km 3,000              m 9 km 9,000             m 6 km 435 m 6,435               m 12 km 12 m 12,012               m

Explanation:
Given 3 km as 1 kilometer = 1,000 meter
so 3 km = 3 X 1,000 m = 3,000 m,

9 km = 9 X 1,000 m = 9,000 m,

6 km 435 m = 6 X 1,000 m + 435 m =
6,000 m + 435 m = 6,435m,

12 km 12 m = 12 X 1,000 m + 12 m =
12,000 m + 12 m = 12,012 m.

 Mass 3 kg 3000           g 20 kg 300 g 20,300              g 1 kg 74 g 1,074                 g 403 kg 4 g 403,004              g

Explanation:
Given 3 kg as 1 kilogram = 1,000 gram,
so 3 kg = 3 X 1,000 g = 3,000 g,

20 kg 300 g  = 20 X 1,000 g + 300 g =
20,000 g + 300 g = 20,300 g,

1 kg 74 g = 1 X 1,000 g + 74 g =
1,000 g + 74 g = 1,074 g,

403 kg 4 g = 403 X 1,000 g + 4 g =
403,000 g + 4 g = 403,004 g.

 Capacity 4 L 4,000                mL 48 L 808 mL 48,808             mL 2 L 20 mL 2,020              mL 639 L 6 mL 639,006               mL

Explanation:
Given 4 L as 1 liter = 1,000 milliliters,
So 4 L = 4 X 1,000 mL = 4,000 mL,

48 L 808 mL = 48 X 1,000 mL =
48,000 mL, + 808 mL = 48,808 mL,

2 L 20 mL = 2 X 1,000 mL + 20 mL =
2,000 mL + 20 mL = 2,020 mL,

639 L 6 mL = 639 X 1,000 mL + 6 mL =
639,000 mL + 6 mL = 639,006 mL.

Question 2.
A student completed the problem below. Check his work. Explain how you know if each solution is correct or incorrect. a. 24 km = 24,000 m, solution is correct,
b. 16 L = 16,000 mL, solution is correct,
c. 38 kg = 38,000 kg not 3,800 g so solution is incorrect,

Explanation:
Given a student completed the problem as shown above.
Checking his work as below
a. 24 km = 24,000 m, solution is correct because
24 km = 24 X 1000 m = 24,000 m,

b. 16 L = 16,000 mL, solution is correct because
16 L = 16 X 1000 mL = 16,000 mL,

c. 38 kg = 38,000 kg not 3,800 g so solution is incorrect
because 38 kg = 38 X 1000 g = 38,000 g not 3,800 g.

Question 3.
Find the sum or difference.
a. 493 km 43 m + 17 km 57 m

b. 25 kg 32 g – 23 kg 83 g

c. 100 L 99 mL + 2,999 mL

a. 493 km 43 m + 17 km 57 m = 510 km 100 m

Explanation:
Given 493 km 43 m + 17 km 57 m as
493 km 43 m = 493 X 1000 m + 43 m =
493000 m + 43 m = 493,043 m and
17 km 57 m = 17 X 1000 m + 57 m =
17,000 m + 57 m = 17,057 m
So 493,043 m + 17,057 m = 510,100 m or
510,100 m ÷ 1000 = 510 km 100 m,
therefore, 493 km 43 m + 17 km 57 m =510,100 m or 510 km 100 m.

b. 25 kg 32 g – 23 kg 83 g = 1,949 g or 1 kg 949 g,

Explanation:
Given 25 kg 32 g – 23 kg 83 g as
25 kg 32 g = 25 X 1000 g + 32 g = 25,032 g and
23 kg 83 g = 23 X 1000 g + 83 g = 23,083 g,
Now 25,032 g – 23,083 g = 1,949 g or 1,949 g ÷ 1000 =
1 kg 949 g, therefore 25 kg 32 g – 23 kg 83 g = 1,949 g or 1 kg 949 g.

c. 100 L 99 mL + 2,999 mL = 103,098 mL or 103 L 098 mL,

Explanation:
Given 100 L 99 mL + 2,999 mL as
100 L  99 mL = 100 X 1000 mL + 99 mL =
100,000 mL + 99 mL = 100,099 mL ,
So 100,099 mL + 2,999 mL = 103,098 mL or
103,098 mL ÷ 1000 = 103 L 098 mL,
therefore 100 L 99 mL + 2,999 mL = 103,098 mL or 103 L 098 mL.

Question 4.
Billy is training for a half marathon. For the problems below, use tape diagrams, numbers, and words to explain each answer.
a. Each day, Billy runs on the treadmill for 5 kilometers and runs on the outdoor track for 6,000 meters. In all, how many meters does Billy run each day?
b. Since Billy has started training, he has also been drinking more water. On Saturday, he drank 2 liters 755 milliliters of water. On Sunday, he drank some more. If Billy drank a total of 4 liters 255 milliliters of water on Saturday and Sunday, how many milliliters of water did Billy drink on Sunday?
c. Since he began exercising so much for his half marathon, Billy has been losing weight. In his first week of training, he lost 2 kilograms 530 grams. In the following two weeks of training, he lost 1 kilogram 855 grams each week. Billy now weighs 61 kilograms 760 grams. What was Billy’s weight, in grams, before he started training?
a. Billy run each day 11,000 meters or 11 kilometrs, Statement : Billy run each day eleven thousand meters or eleven kilometers,

b. Number of milliliters of water did Billy drink on Sunday is 1,500 milliliters or 1 L 500 mL, Statement : Number of milliliters of water did Billy drink on Sunday is fifteen hundred milliliters or one Liter five hunderd milliliters,

c. Billy’s weight, in grams, before he started training 68,000 grams, Statement: Billy’s weight, in grams, before he started training is sixty eight thousand grams,

Explanation:
Given Billy is training for a half marathon.
a. Each day, Billy runs on the treadmill for 5 kilometers and runs on the outdoor track for 6,000 meters.
In all, Billy run each day is 5 km + 6,000 meters as
5 km = 5 X 1000 m = 5,000 m So 5,000 m + 6,000 m =
11,000 m or 11,000 m ÷ 1,000 = 11 km,
used a tape diagrams to show problem as shown above, therefore Billy run each day 11,000 meters or 11 kilometrs.

b. Since Billy has started training, he has also been drinking more water. On Saturday, he drank 2 liters 755 milliliters of water. On Sunday, he drank some more.
If Billy drank a total of 4 liters 255 milliliters of water on Saturday and Sunday, number of milliliters of water did Billy drink on Sunday is
4 L 255 mL – 2 L 755 mL as 4 L 255 mL = 4 X 1000 mL + 255 mL =
4,255 mL and 2 L 755 mL = 2 X 1000 mL + 755 mL = 2,755 mL,
therefore 4,255 mL – 2,755 mL = 1,500 mL or 1,500 mL ÷ 1,000 =
1 L 500 mL, used a tape diagrams to show problem as shown above,
therefore Number of milliliters of water did Billy drink on Sunday is 1,500 milliliters or 1 L 500 mL.

c. Since he began exercising so much for his half marathon,
Billy has been losing weight. In his first week of training, he lost 2 kilograms 530 grams. In the following two weeks of training, he lost 1 kilogram 855 grams each week.
Billy lost in three weeks is 2 kg 530 g + 1 kg 855 g + 1 kg 855 kg
as 2 kg 530 g = 2 X 1000 g + 530 g = 2,530 g
1 kg 855 g = 1 X 1000 g + 855 g = 1,855 g
So lost weight is 2,530  g + 1,855 g + 1,855 g = 6,240 g,
Billy now weighs 61 kilograms 760 grams.
Billy’s weight, in grams, before he started training is
61 kg 760 g + 6,240 g as 61 kg 760 g = 61 X 1000 g + 760 g =
61,760 g so 61,760 g + 6,240 g = 68,000 grams,
used a tape diagrams to show problem as shown above,
therefore, Billy’s weight, in grams, before he started training 68,000 grams.