Engage NY Eureka Math 4th Grade Module 2 Lesson 1 Answer Key
Eureka Math Grade 4 Module 2 Lesson 1 Problem Set Answer Key
Question 1.
Convert the measurements.
a. 1 km = _______1000________ m
b. 4 km = _______4000________ m
c. 7 km = ________7000_______ m
d. ___18_______ km = 18,000 m
e. 1 m = _______100________ cm
f. 3 m = _______300________ cm
g. 80 m = ______8000_________ cm
h. ____120____ m = 12,000 cm
a. 1 km = 1000 m,
Explanation:
1 km is equal to 103 meter,
1 km = 1 X 10 X 10 X 10 = 1000 meter,
So 1 km = 1000 m.
b. 4 km = 4000 km,
Explanation:
4 km is equal to 4 X 103 meter,
4 km = 4 X 10 X 10 X 10 = 4000 meter,
So 1 km = 4000 m.
c. 7 km = 7000 km,
Explanation:
7 km is equal to 7 X 103 meter,
7 km = 7 X 10 X 10 X 10 = 7000 meter,
So 7 km = 7000 m.
d. 18 km = 18000 km,
Explanation:
18 km is equal to 18 X 103 meter,
18 km = 18 X 10 X 10 X 10 = 18000 meter,
So 18 km = 18000 m.
e. 1 m = 100cm,
Explanation:
1 m is equal to 102 centimeter,
1 m = 1 X 10 X 10 = 100 centimeter,
So 1 m = 100 cm.
f. 3 m = 300cm,
Explanation:
3 m is equal to 3 X 102 centimeter,
3 m = 3 X 10 X 10 = 100 centimeter,
So 3 m = 300 cm.
g. 80 m = 8000 cm,
Explanation:
80 m is equal to 80 X 102 centimeter,
80 m = 80 X 10 X 10 = 8000 centimeter,
So 80 m = 8000 cm.
h. 120 m = 12,000 cm,
Explanation:
120 m is equal to 120 X 102 centimeter,
120 m = 120 X 10 X 10 = 12,000 centimeter,
So 120 m = 12,000 cm.
Question 2.
Convert the measurements.
a. 3 km 312 m = _____3,312__________ m
b. 13 km 27 m = ______13,027_________ m
c. 915 km 8 m = _______9,15,008________ m
d. 3 m 56 cm = ________3,56_______ cm
e. 14 m 8 cm = _________1,408______ cm
f. 120 m 46 cm = _______12,046________ cm
a. 3 km 312 m = 3,312 m,
Explanation:
As we know 1 km is equal to 103 meter,
So 3 km 312 m = 3 X 103 + 312 = 3,312 meter,
Therefore 3 km 312 m = 3,312 m.
b. 13 km 27 m = 13,027 m,
Explanation:
As we know 1 km is equal to 103 meter,
So 13 km 27 m = 13 X 103 + 27 = 13,027 meter,
Therefore 13 km 27 m = 13,027 m.
c. 915 km 8 m = 9,15,008 m,
Explanation:
As we know 1 km is equal to 103 meter,
So 915 km 8 m = 915 X 103 + 8 = 9,15,008 meter,
Therefore 915 km 8 m = 9,15,007 m.
d. 3 m 56 cm = 3,56 cm
Explanation:
As we know 1 m is equal to 102 centimeter,
3 m 56 cm = 3 X 102 + 56 = 300 + 56 = 3,56 centimeter,
So 3 m 56 cm = 3,56 cm.
e. 14 m 8 cm = 1,408 cm,
Explanation:
As we know 1 m is equal to 102 centimeter,
14 m 8 cm = 14 X 102 + 8 = 1400 + 8 = 1,408 centimeter,
So 14 m 8 cm = 1,408 cm.
f. 120 m 46 cm = 12,046 cm,
Explanation:
As we know 1 m is equal to 102 centimeter,
120 m 46 cm = 120 X 102 + 46 = 12000 + 46 = 12,046 centimeter,
So 120 m 46 cm = 12,046 cm.
Question 3.
Solve.
a. 4 km − 280 m
b. 1 m 15 cm – 34 cm
c. Express your answer in the smaller unit:
1 km 431 m + 13 km 169 m
d. Express your answer in the smaller unit:
231 m 31 cm − 14 m 48 cm
e. 67 km 230 m + 11 km 879 m
f. 67 km 230 m − 11 km 879 m
Use a tape diagram to model each problem.
Solve using a simplifying strategy or an algorithm, and
write your answer as a statement.
a. 4 km − 280 m
4 km – 280 m = 3,720 m
4 kilometers minus 280 meters is equal to 3,720 meters,
Explanation:
Given 4 km − 280 m as
4 km = 4 X 103 m = 4,000 m,
Used a tape diagram to model 4 km – 280 m = 3,720 m
as shown above in the picture,
so 4000 m
-280 m
3,720 m
Statement is 4 kilometers minus 280 meters is
equal to 3,720 meters.
b. 1 m 15 cm – 34 cm
1 m 15 cm – 34 cm =81 cm
1 meter 15 centimeters minus 34 centimeter
is equal to 81centimeters,
Explanation:
Given 1 m 15 cm − 34 cm as
1 m 15 cm = 1 X 102 + 15 = 100 + 15 = 115 cm,
Used a tape diagram to model 115 cm – 34 cm = 81 cm
as shown above in the picture,
so 115 cm
– 34 cm
81 cm
Statement is 1 meter 15 centimeters minus
34 centimeters is equal to 81 centimeters.
c.1 km 431 m + 13 km 169 m
1 km 431 m + 13 km 169 m = 14,600 m
or 14,600,000,000 mm,
1 kilometer and 431 meters plus 13 kilometers and
169 meters is 14,600 meters or 14,600,000 millimeters,
Explanation:
Given 1 km 431 m + 13 km 169 m as
1 km 431 m = 1 X 103 + 431 = 1000 + 431 = 1,431 m
and 13 km 169 m = 13 X 103 + 169 =13,169 m
Used a tape diagram to model 1431 m + 13169 m =
14,600 m as shown above in the picture,
001431 m
+13169 m
14,600 m
Now 14,600 m in the smaller unit in millimeter is as
1 meter is equal to 1000 millimeter,
So 14,600 X 1000 = 14,600,000 millimeters.
Statement : 1 kilometer and 431 meters plus 13 kilometers
169 meters gives 14,600,000 millimeters.
d. 231 m 31 cm − 14 m 48 cm
231 m 31 cm – 14m 48 cm = 21,683 cm
or 2,16,830 millimeter
231 meter and 31 centimeters minus 14 meters
48 centimeters gives 216,830 millimeters,
Explanation:
Given 231 m 31 cm – 14 m 48 cm as
231 m 31 cm = 231 X 102 + 31 = 23100 + 31 = 23,131 cm
and 14 m 48 cm = 14 X 102 + 48 =1,448 cm
Used a tape diagram to model 23,131 cm – 1,448 cm =
21,683 cm as shown above in the picture,
23134 cm
– 1448 cm
21,683 cm
Now 21,683 cm in the smaller unit millimeters is as
1 centimeter is equal to 10 millimeter,
So 21,683 X 10 = 216,830 millimeters.
Statement : 231 meter and 31 centimeters minus 14 meters
48 centimeters gives 216,830 millimeters.
e. 67 km 230 m + 11 km 879 m
67 km 230 m + 11 km 879 m = 79,109 m
67 kilometer and 230 meters plus 11 kilometers and
879 meters is 79,109 meters,
Explanation:
Given 67 km 230 m + 11 km 879 m as
67 km 230 m = 67 X 103 + 230 = 67000 + 230 = 67,230 m
and 11 km 879 m = 11 X 103 + 879 =11,879 m
Used a tape diagram to model 67230 m + 11879 m =
79,109 m as shown above in the picture,
67230 m
+11879 m
79,109 m
So 67 km 230 m + 11 km 879 m = 79,109 m,
Statement : 67 kilometer and 230 meters plus 11 kilometers and
879 meters is 79,109 meters.
f. 67 km 230 m − 11 km 879 m
67 km 230 m – 11 km 879 m = 55,351 m
67 kilometer and 230 meters minus 11 kilometers and
879 meters is 55,351 meters,
Explanation:
Given 67 km 230 m – 11 km 879 m as
67 km 230 m = 67 X 103 + 230 = 67000 + 230 = 67,230 m
and 11 km 879 m = 11 X 103 + 879 =11,879 m
Used a tape diagram to model 67230 m – 11879 m =
55,351 m as shown above in the picture,
67230 m
-11879 m
55,351 m
So 67 km 230 m – 11 km 879 m = 55,351 m,
Statement : 67 kilometer and 230 meters minus 11 kilometers and
879 meters is 55,351 meters.
Question 4.
The length of Carter’s driveway is 12 m 38 cm.
His neighbor’s driveway is 4 m 99 cm longer.
How long is his neighbor’s driveway?
Neighbor’s drive is 17 m 37 cm or 1737 cm,
Explanation:
Given The length of Carter’s driveway is 12 m 38 cm and
his neighbor’s driveway is 4 m 99 cm longer.
So neighbor’s drive is 12 m 38 cm plus 4 m 99 cm
we know 1 m is equal to 102 centimeter,
12 m 38 cm = 12 X 102 + 38 = 1238 cm
and 4 m 99 cm = 4 X 102 + 99 = 499 cm,
now 1238 cm + 499 cm =
1238 cm
+499 cm
1737 cm
Therefore, Neighbor’s drive is 17 m 37 cm or 1737 cm.
Question 5.
Enya walked 2 km 309 m from school to the store.
Then, she walked from the store to her home.
If she walked a total of 5 km, how far was it from
the store to her home?
It is 2691 m from the store to her home,
Explanation:
Given Enya walked 2 km 309 m from school to the store.
Then, she walked from the store to her home.
If she walked a total of 5 km, it is 5 km – 2 km 309m from
the store to her home, So 5 km means 5 X 103 – (2 X 103 + 309) =
5000 m – 2309 m =
5000 m
-2309 m
2691 m
Therefore, It is 2691 m from the store to her home.
Question 6.
Rachael has a rope 5 m 32 cm long that she cut
into two pieces. One piece is 249 cm long.
How many centimeters long is the other piece of rope?
The other piece of rope 283 cm long,
Explanation:
Given Rachael has a rope 5 m 32 cm long that she cut
into two pieces and one piece is 249 cm long.
The other piece of rope is 5 m 32 cm minus 249 cm long,
So, 5 m 32 cm – 249 cm = 5 X 102 + 32 – 249 = 532 – 249 = 283 cm,
therefore, the other piece of rope 283 cm long.
Question 7.
Jason rode his bike 529 fewer meters than Allison.
Jason rode 1 km 850 m. How many meters did Allison ride?
Allison rode 2 km 379 meters or 2379 meters,
Explanation:
Given Jason rode his bike 529 fewer meters than Allison.
Jason rode 1 km 850 m. Number of meters Allison rode is
1 km 850 m + 529 m = 1 X 103 + 850 + 529 = 1850 + 529 =
2379 meters. Therefore Allison rode 2 km 379 meters or 2379 meters.
Eureka Math Grade 4 Module 2 Lesson 1 Exit Ticket Answer Key
Question 1.
Complete the conversion table.
|
Distance |
|
| 71 km | ___71,000___ m |
| ______30____ km | 30,000 m |
| 81 m | ____8,100______ cm |
| ____4______ m | 400 cm |
Explanation:
71 km is equal to 71 X 103 = 71 X 1000 = 71,000 m,
so 71 km = 71,000 m.
30 km is equal to 30 X 103 = 30 X 1000 = 30,000 m,
so 30 km = 30,000 m.
81 m is equal to 81 X 102 = 81 X 100 = 8,100 cm,
so 81 m = 8,100 cm.
4 m is equal to 4 X 102 = 4 X 100 = 400 cm,
so 4 m = 400 cm.
Question 2.
13 km 20 m = ____13020___ m
13 km 20 m = 13,020 m
Explanation:
Given 13 km 20 m as 1 km is equal to 103 m so
13 km 20 m = 13 X 103+ 20 m = 13 X 1000 + 20 =
13000 + 20 = 13020, therefore 13 km 20 m = 13,020 m.
Question 3.
401 km 101 m – 34 km 153 m = _366,948 m or 366 km 948 m__
401 km 101 m – 34 km 153 m = 366,948 m or 366 km 948 m,
Explanation:
Given 401 km 101 m – 34 km 153 m as
401 km 101 m = 401 X 103 + 101 = 401000 + 101 = 401,101 m
and 34 km 153 m = 34 X 103 + 153 = 34153 m
Now 401,101 – 34,153 =
401101 m
-34153 m
366,948 m
So, 401 km 101 m – 34 km 153 m = 366,948 m or 366 km 948 m.
Question 4.
Gabe built a toy tower that measured 1 m 78 cm.
After building some more, he measured it, and
it was 82 cm taller. How tall is his tower now?
Draw a tape diagram to model this problem.
Use a simplifying strategy or an algorithm to solve
and write your answer as a statement.
Gabe toy tower is 260 cm or 2 m 60 cm tall,
Statement: Gabe tower is 2 meter 60 centimeter tall or 260 centimeter tall,
Explanation:
Given Gabe built a toy tower that measured 1 m 78 cm.
After building some more, he measured it, and
it was 82 cm taller. So Gabe tower is 1 m 78 cm + 82 cm =
1 X 102 + 78 cm + 82 cm = 178 cm + 82 cm =
178 cm
+ 82 cm
260 cm tall.
Drawn a tape diagram to model this problem.
Used a simplifying strategy to solve
and wrote my statement as Gabe tower is 2 meter 60 centimeter tall or
260 centimeter tall.
Eureka Math Grade 4 Module 2 Lesson 1 Homework Answer Key
Question 1.
Find the equivalent measures.
a. 5 km = ______5,000_________ m
b. 13 km = _____13,000__________ m
c. _____17__________ km = 17,000 m
d. 60 km = ______60,000_________ m
e. 7 m = ________700_______ cm
f. 19 m = _______1,900________ cm
g. ______24_________ m = 2,400 cm
h. 90 m = _____9,000______ cm
a. 5 km = 5000 m,
Explanation:
1 km is equal to 103 meter,
5 km = 5 X 10 X 10 X 10 = 5000 meter,
So 5 km = 5000 m.
b. 13 km = 13,000 km,
Explanation:
1 km is equal to 103 meter,
13 km = 13 X 10 X 10 X 10 = 13000 meter,
So 13 km = 13,000 m.
c. _______________ km = 17,000 m,
17 km = 17,000 m,
Explanation:
1 m is equal to 1 ÷ 103 km,
17,000 m = 17,000 ÷ 10 X 10 X 10 = 17000 ÷ 1000 = 17 km,
So 17 km = 17,000 m.
d. 60 km = 60,000 m,
Explanation:
1 km is equal to 103 meter,
60 km = 60 X 10 X 10 X 10 = 60,000 meter,
So 60 km = 60,000 m.
e. 7 m = 700 cm,
Explanation:
1 m is equal to 102 centimeter,
7 m = 7 X 10 X 10 = 700 centimeter,
So 7 m = 700 centimeter.
f. 19 m = 1,900 cm,
Explanation:
1 m is equal to 102 centimeter,
19 m = 19 X 10 X 10 = 1,900 centimeter,
So 19 m = 1,900 centimeter.
g. ____________ m = 2,400 cm,
Explanation:
1 cm is equal to 1 ÷ 102 m,
2,400 cm = 2,400 ÷ 10 X 10 = 2400 ÷ 100 = 24 m,
So 24 m = 2,400 cm.
h. 90 m = 9,000 cm,
Explanation:
90 m is equal to 102 centimeter,
90 m = 90 X 10 X 10 = 9,000 centimeter,
So 90 m = 9,000 centimeter.
Question 2.
Find the equivalent measures.
a. 7 km 123 m = _______7,123________ m
b. 22 km 22 m = ______22,022_________ m
c. 875 km 4 m = _______875,004________ m
d. 7 m 45 cm = _______745________ cm
e. 67 m 7 cm = ________6707_______ cm
f. 204 m 89 cm = ____204,89__________ cm
a. 7 km 123 m = 7,123 m,
Explanation:
1 km is equal to 103 meter,
7 km 123 m = 7 X 10 X 10 X 10 + 123 = 7,000 + 123 = 7,123 meter,
So, 7 km 123 m = 7,123 m.
b. 22 km 22 m = 22,022 m,
Explanation:
1 km is equal to 103 meter,
22 km 22 m = 22 X 10 X 10 X 10 + 22 = 22,000 + 22 = 22,022 meter,
So, 22 km 22 m = 22,022 m.
c. 875 km 4 m = 875,004 m,
Explanation:
1 km is equal to 103 meter,
875 km 4 m = 875 X 10 X 10 X 10 + 4 =
875,000 + 4 = 875004 meter,
So, 875 km 4 m = 875,004 m.
d. 7 m 45 cm =745 cm,
Explanation:
1 m is equal to 102 meter,
7 m 45 cm = 7 X 10 X 10 + 45 = 745 cm,
So, 7 m 45 cm =745 cm.
e. 67 m 7 cm = 6,707 cm,
Explanation:
1 m is equal to 102 meter,
67 m 7 cm = 67 X 10 X 10 + 7 = 6700 + 7 = 6,707 cm,
So, 67 m 7 cm = 6,707 cm.
f. 204 m 89 cm = 204,89 cm,
Explanation:
1 m is equal to 102 meter,
204 m 89 cm = 204 X 10 X 10 + 89 = 20400 + 89 = 204,89 cm,
So, 204 m 89 cm = 204,89 cm.
Question 3.
Solve.
a. 2 km 303 m – 556 m
b. 2 m – 54 cm
c. Express your answer in the smaller unit:
338 km 853 m + 62 km 71 m
d. Express your answer in the smaller unit:
800 m 35 cm – 154 m 49 cm
e. 701 km – 523 km 445 m
f. 231 km 811 m + 485 km 829 m
Use a tape diagram to model each problem. Solve using a simplifying strategy or an algorithm, and write your answer as a statement.
a. 2 km 303 m – 556 m
2 km 303 m – 556 m = 1,747 m,
2 kilometers 303 m minus 556 meters is equal to 1,747 meters,
Explanation:
Given 2 km 303 m − 556 m as
2 km 303 m = 2 X 103 m + 303 m = 2,303 m,
Used a tape diagram to model 2,303 m – 556 m = 1,747 m
as shown above in the picture,
2303 m
– 556 m
1,747 m
Statement is 2 kilometers 303 m minus 556 meters is
equal to 1,747 meters.
b. 2 m – 54 cm
2 m – 54 cm = 146 cm,
2 meters minus 54 cm is equal to 146 centimeters,
Explanation:
Given 2 m − 54 cm as
2 m = 2 X 102 cm so 200 cm – 54 cm = 146 cm,
Used a tape diagram to model 200 cm – 54 cm = 146 cm
as shown above in the picture,
200 cm
– 54 cm
146 cm
Statement is 2 meters minus 54 centimeters is
equal to 146 centimeters.
c. Express your answer in the smaller unit:
338 km 853 m + 62 km 71 m,
338 km 853 m + 62 km 71m = 400,924 m
or 400,924,000 mm,
338 kilometer and 853 meters plus 62 kilometers and
71 meters is 400,924 meters or 400,924,000 millimeters,
Explanation:
Given 338 km 853 m + 62 km 71 m as
338 km 853 m = 338 X 103 + 853 = 338000 + 853 = 338853 m
and 62 km 71 m = 62 X 103 + 71 =62000 + 71 m = 62071 m
Used a tape diagram to model 338853 m + 62071 m = 400,924 m
as shown above in the picture,
338853 m
+62071 m
400,924 m
Now 400,924 m in the smaller unit in millimeter is as
1 meter is equal to 1000 millimeter,
So 400,924 X 1000 = 400,924,000 millimeters.
Statement : 338 kilometer and 853 meters plus 62 kilometers and
71 meters is 400,924 meters or 400,924,000 millimeters,
d. Express your answer in the smaller unit:
800 m 35 cm – 154 m 49 cm
800 m 35 cm – 154 m 49 cm = 64,586 cm
or 645,860 millimeter,
800 meter and 35 centimeters minus 154 meters
49 centimeters gives 645,860 millimeters,
Explanation:
Given 800 m 35 cm – 154 m 49 cm as
800 m 35 cm = 800 X 102 + 35 = 80000 + 35 = 80,035 cm
and 154 m 49 cm = 154 X 102 + 49 =15,449 cm
Used a tape diagram to model 80,035 cm – 15,449 cm =
64,586 cm as shown above in the picture,
80,035 cm
– 15449 cm
64,586 cm
Now 64,586 cm in the smaller unit millimeters is as
1 centimeter is equal to 10 millimeter,
So 64,586 X 10 = 645,860 millimeters.
Statement : 800 meter and 35 centimeters minus 154 meters
49 centimeters gives 64,586 cm or 645,860 millimeters.
e. 701 km – 523 km 445 m
701 km – 523 km 445 m =
701 kilometers minus 523 kilometers 445 meters
is equal to 177,555 meters,
Explanation:
Given 701 km − 523 km 445 m,
701 km = 701 X 103 m = 701000 m,
and 523 km 445 m = 523 X 103 m + 445 m = 523445 m
Used a tape diagram to model 701000 m – 523445 m = 177,555 m
as shown above in the picture,
701000 m
-523445 m
177,555 m
Statement is 701 kilometers minus 523 kilometers 445 meters
is equal to 177,555 meters.
f. 231 km 811 m + 485 km 829 m
231 km 811 m + 485 km 829 m = 717,640 m,
231 kilometers 811 meters plus 485 kilometers 829 meters
is equal to 717,640 meters,
Explanation:
Given 231 km 811 m + 485 km 829 m,
231 km 811 m = 231 X 103 m =231000 m + 811 m = 231811m
and 485 km 829 m = 485 X 103 m + 829 m = 485829 m
Used a tape diagram to model 231811 m + 485829 m = 717640 m
as shown above in the picture,
231811 m
+485829 m
717640 m
Statement is 231 kilometers 811 meters plus
485 kilometers 829 meters is equal to 717,640 meters,
Question 4.
The length of Celia’s garden is 15 m 24 cm.
The length of her friend’s garden is 2 m 98 cm more than Celia’s.
What is the length of her friend’s garden?
The length of Celia’s friend garden is 1822 cm or 18 m 22 cm,
Explanation:
Given the length of Celia’s garden is 15 m 24 cm,
the length of her friend’s garden is 2 m 98 cm
more than Celia’s. So the length of her friend’s garden
is 15 m 24 cm + 2 m 98 cm =
1 m = 102 cm, 15 m 24 cm = 15 X 102 + 24 cm =
1500 + 24 = 1524 cm and 2 m 98 cm = 2 X 102 + 98 cm =
200 + 98 = 298 cm, Now 1524 cm + 298 cm =
1524 cm
+298 cm
1822 cm
Therefore, the length of Celia’s friend garden is
1822 cm or 18 m 22 cm.
Question 5.
Sylvia ran 3 km 290 m in the morning. Then, she ran
some more in the evening. If she ran a total of 10 km,
how far did Sylvia run in the evening?
Sylvia ran 6 km 710 m or 6710 m in the evening,
Explanation:
Sylvia ran 3 km 290 m in the morning. Then, she ran
some more in the evening. If she ran a total of 10 km,
So Sylvia ran in the evening is 10 km – 3 km 290 m =
as 1 km = 103 m so 10 km = 10000 m and 3 km 290 m =
3 X 103 m + 290 m =3290 m
10000 m
-3290 m
6710 m
Therefore, Sylvia ran 6 km 710 m or 6710 m in the evening.
Question 6.
Jenny’s sprinting distance was 356 meters shorter than Tyler’s.
Tyler sprinted a distance of 1 km 3 m.
How many meters did Jenny sprint?
Jenny sprint distance is 647 m,
Explanation:
Given Jenny’s sprinting distance was 356 meters
shorter than Tyler’s. Tyler sprinted a distance of 1 km 3 m.
So number of meters did Jenny sprint is 1 km 3 m – 356 m =
1 km = 103 m so 1 km 3 m = 1 X 103 m +3 m = 1000 + 3 = 1003 m,
Now 1003 m – 356 m
1003 m
-356 m
647 m
Therefore, Jenny sprint distance is 647 m.
Question 7.
The electrician had 7 m 23 cm of electrical wire.
He used 551 cm for one wiring project.
How many centimeters of wire does he have left?
The electrician is left with 172 cm electrical wire,
Explanation:
Given the electrician had 7 m 23 cm of electrical wire.
He used 551 cm for one wiring project.
So number of centimeters of wire left is
7 m 23 cm – 551 cm =
as 1 m = 102 cm So 7 m 23 cm = 7 X 102 + 23 =
700 + 23 = 723 cm – 551 cm =
723 cm
-551 cm
172 cm
therefore, the electrician is left with 172 cm electrical wire.