Engage NY Eureka Math 4th Grade Module 5 Lesson 27 Answer Key
Eureka Math Grade 4 Module 5 Lesson 27 Problem Set Answer Key
Question 1.
Draw a tape diagram to model each comparison. Use >, <, or = to compare.
a. 3\(\frac{2}{3}\) ________ 3\(\frac{5}{6}\)
Answer:
3(2/3) < 3(5/6).
Explanation:
In the above-given question,
given that,
3(2/3) = 3 x 3.
3 x 3 = 9 + 2/3.
11/3 = 3.6.
3(5/6) = 3 x 6.
3 x 6 = 18 + 5/6.
23/6 = 3.8.
3.6 < 3.8.
b. 3\(\frac{2}{5}\) ________ 3\(\frac{6}{10}\)
Answer:
3(2/5) < 3(6/10).
Explanation:
In the above-given question,
given that,
3(2/5) = 3 x 5.
3 x 5 = 15 + 2/5.
17/5 = 3.4.
3(6/10) = 3 x 10.
3 x 10 = 30 + 6/10.
36/10 = 3.6.
3.4 < 3.6.
c. 4\(\frac{3}{6}\) ________ 4\(\frac{1}{3}\)
Answer:
4(3/6) > 4(1/3).
Explanation:
In the above-given question,
given that,
4(3/6) = 4 x 6.
4 x 6 = 24 + 3/6.
27/6 = 4.5.
4(1/3) = 3 x 4.
3 x 4 = 12 + 1/3.
13/3 = 4.3.
4.5 > 4.3.
d. 4\(\frac{5}{8}\) _________ \(\frac{19}{4}\)
Answer:
4(5/8) < (19/4).
Explanation:
In the above-given question,
given that,
4(5/8) = 4 x 8.
4 x 8 = 32 + 5/8.
37/8 = 4.625.
19/4 = 4.75.
4.6 < 4.7.
Question 2.
Use an area model to make like units. Then, use >, <, or = to compare.
a. 2\(\frac{3}{5}\) _________ \(\frac{18}{7}\)
Answer:
2(3/5) < (18/7).
Explanation:
In the above-given question,
given that,
2(3/5) = 2 x 5.
2 x 5 = 10 + 3/5.
18/7 = 2.5.
23/6 = 3.8.
2.5 < 3.8.
b. 2\(\frac{3}{8}\) _________ 2\(\frac{1}{3}\)
Answer:
2(3/8) = 2(1/3).
Explanation:
In the above-given question,
given that,
2(3/8) = 2 x 8.
2 x 8 = 16 + 3/8.
19/8 = 2.375.
2(1/3) = 3 x 2.
3 x 2 = 6 + 1/3.
7/3 = 2.3.
2.3 = 2.3.
Question 3.
Compare each pair of fractions using >, <, or = using any strategy.
a. 5\(\frac{3}{4}\) _________ 5\(\frac{3}{8}\)
Answer:
5(3/4) > 5(3/8).
Explanation:
In the above-given question,
given that,
5(3/4) = 5 x 4.
5 x 4 = 20 + 3/4.
23/4 = 5.7.
5(3/8) = 5 x 8.
5 x 8 = 40 + 3/8.
43/8 = 5.3.
5.7 > 5.3.
b. 5\(\frac{2}{5}\) ________ 5\(\frac{8}{10}\)
Answer:
5(2/5) < 5(8/10).
Explanation:
In the above-given question,
given that,
5(2/5) = 5 x 5.
5 x 5 = 25 + 2/5.
27/5 = 3.6.
5(8/10) = 5 x 10.
5 x 10 = 50 + 8/10.
58/10 = 5.8.
3.6 < 5.8.
c. 5\(\frac{6}{10}\) _________ \(\frac{27}{5}\)
Answer:
5(6/10) > (27/5).
Explanation:
In the above-given question,
given that,
5(6/10) = 5 x 10.
5 x 10 = 50 + 6/10.
56/10 = 5.6.
27/5 = 5.4.
5.6 > 5.4.
d. 5\(\frac{2}{3}\) ________ 5\(\frac{9}{15}\)
Answer:
5(2/3) < 5(9/15).
Explanation:
In the above-given question,
given that,
5(2/3) = 5 x 3.
5 x 3 = 15 + 2/3.
17/3 = 5.6.
5(9/15) = 5 x 15.
5 x 15 = 75 + 9/15.
84/9 = 9.3.
5.6 < 9.3.
e. \(\frac{7}{2}\) ________ \(\frac{7}{2}\)
Answer:
(7/2) = (7/2).
Explanation:
In the above-given question,
given that,
7/2 = 3.5.
7/2 = 3.5.
3.5 = 3.5.
f. \(\frac{12}{3}\) ________ \(\frac{15}{4}\)
Answer:
(12/3) = (15/4).
Explanation:
In the above-given question,
given that,
12/3 = 4.
15/4 = 3.75.
4 > 3.75.
g. \(\frac{22}{5}\) _________ 4\(\frac{2}{7}\)
Answer:
(22/5) > 4(2/7).
Explanation:
In the above-given question,
given that,
22/5 = 4.4.
4(2/7) = 7 x 4 = 28.
28 + 2/7 = 30/7.
30/7 = 4.2.
4.4 > 4.2.
h. \(\frac{21}{4}\) ________ 5\(\frac{2}{5}\)
Answer:
(21/4) < 5(2/5).
Explanation:
In the above-given question,
given that,
21/4 = 5.25.
5(2/5) = 5 x 5 = 25.
25 + 2/5 = 27/5.
27/5 = 5.4.
5.25 < 5.4.
i. \(\frac{29}{8}\) _________ \(\frac{11}{3}\)
Answer:
(29/8) = (11/3).
Explanation:
In the above-given question,
given that,
29/8 = 3.6.
11/3 = 3.6.
3.6 = 3.6.
j. 3\(\frac{3}{4}\) _________ 3\(\frac{4}{7}\)
Answer:
3(3/4) > 3(4/7).
Explanation:
In the above-given question,
given that,
3(3/4) = 4 x 3.
4 x 3 = 12 + 3/4.
15/4 = 3.75.
3(4/7) = 7 x 3.
7 x 3 = 21 + 4/7.
25/7 = 3.57.
3.75 > 3.57.
Eureka Math Grade 4 Module 5 Lesson 27 Exit Ticket Answer Key
Compare each pair of fractions using >, <, or = using any strategy.
Question 1.
4\(\frac{3}{8}\) ________ 4\(\frac{1}{4}\)
Answer:
4(3/8) > 4(1/4).
Explanation:
In the above-given question,
given that,
4(3/8) = 4 x 8.
8 x 4 = 32 + 3/8.
35/8 = 4.375.
4(1/4) = 4 x 4.
4 x 4 = 16 + 1/4.
17/4 = 4.25.
4.3 > 4.2.
Question 2.
3\(\frac{4}{5}\) _________ 2\(\frac{2}{5}\)
Answer:
3(4/5) > 2(2/5).
Explanation:
In the above-given question,
given that,
3(4/5) = 5 x 3.
5 x 3 = 15 + 4/5.
19/5 = 3.8.
2(2/5) = 5 x 2.
2 x 5 = 10 + 2/5.
12/5 = 2.4.
3.8 > 2.4.
Question 3.
2\(\frac{1}{3}\) ________ 2\(\frac{2}{5}\)
Answer:
2(1/3) < 2(2/5).
Explanation:
In the above-given question,
given that,
2(1/3) = 2 x 3.
2 x 3 = 6 + 1/3.
7/3 = 2.3.
2(2/5) = 5 x 2.
5 x 2 = 10 + 2/5.
12/5 = 2.4.
2.3 < 2.4.
Question 4.
10\(\frac{2}{5}\) _______ 10\(\frac{3}{4}\)
Answer:
10(2/5) < 10(3/4).
Explanation:
In the above-given question,
given that,
10(2/5) = 5 x 10.
5 x 10 = 50 + 2/5.
52/5 = 10.4.
10(3/4) = 4 x 10.
4 x 10 = 40 + 3/4.
43/4 = 10.75.
10.4 < 10.7.
Eureka Math Grade 4 Module 5 Lesson 27 Homework Answer Key
Question 1.
Draw a tape diagram to model each comparison. Use >, <, or = to compare.
a. 2\(\frac{3}{4}\) ________ 2\(\frac{7}{8}\)
Answer:
2(3/4) < 2(7/8).
Explanation:
In the above-given question,
given that,
2(3/4) = 2 x 4.
2 x 4 = 8 + 3/4.
11/4 = 2.75.
2(7/8) = 2 x 8.
2 x 8 = 16 + 7/8.
23/8 = 2.8.
2.75 < 2.8.
b. 10\(\frac{2}{6}\) __________ 10\(\frac{1}{3}\)
Answer:
10(2/6) = 10(1/3).
Explanation:
In the above-given question,
given that,
10(2/6) = 10 x 6.
10 x 6 = 60 + 2/6.
62/6 = 10.3.
10(1/3) = 3 x 10.
3 x 10 = 30 + 1/3.
31/3 = 10.3.
10.3 = 10.3.
c. 5\(\frac{3}{8}\) ________ 5\(\frac{1}{4}\)
Answer:
5(3/8) > 5(1/4).
Explanation:
In the above-given question,
given that,
5(3/8) = 5 x 8.
5 x 8 = 40 + 3/8.
43/8 = 5.3.
5(1/4) = 5 x 4.
5 x 4 = 20 + 1/4.
21/4 = 5.25.
5.3 > 5.2.
d. 2\(\frac{5}{9}\) _________ \(\frac{21}{3}\)
Answer:
2(5/9) < (21/3).
Explanation:
In the above-given question,
given that,
2(5/9) = 2 x 9.
2 x 9 = 18 + 5/9.
23/9 = 2.5.
21/3 = 7.
2.5 < 7.
Question 2.
Use an area model to make like units. Then, use >, <, or = to compare.
a. 2\(\frac{4}{5}\) ________ \(\frac{11}{4}\)
Answer:
2(4/5) > (11/4).
Explanation:
In the above-given question,
given that,
2(4/5) = 2 x 5.
2 x 5 = 10 + 4/5.
14/5 = 3.5.
11/4 = 2.75.
3.5 > 2.75.
b. 2\(\frac{3}{5}\) _________ 2\(\frac{2}{3}\)
Answer:
2(3/5) = 2(2/3).
Explanation:
In the above-given question,
given that,
2(3/5) = 5 x 2.
5 x 2 = 10 + 3/5.
13/5 = 2.6.
2(2/3) = 3 x 2.
3 x 2 = 6 + 2/3.
8/3 = 2.6.
2.6 = 2.6.
Question 3.
Compare each pair of fractions using >, <, or = using any strategy.
a. 6\(\frac{1}{2}\) _________ 6\(\frac{3}{8}\)
Answer:
6(1/2) > 6(3/8).
Explanation:
In the above-given question,
given that,
6(1/2) = 6 x 2.
6 x 2 = 12 + 1/2.
13/2 = 6.5.
6(3/8) = 6 x 8.
6 x 8 = 48 + 3/8.
51/8 = 6.3.
6.5 > 6.3.
b. 7\(\frac{5}{6}\) ________ 7\(\frac{11}{12}\)
Answer:
7(5/6) < 7(11/12).
Explanation:
In the above-given question,
given that,
7(5/6) = 7 x 6.
7 x 6 = 42 + 5/6.
47/6 = 7.8.
7(11/12) = 7 x 12.
7 x 12 = 84 + 11/12.
95/12 = 7.9.
7.8 < 7.9.
c. 3\(\frac{6}{10}\) __________ 3\(\frac{2}{5}\)
Answer:
3(6/10) > 3(2/5).
Explanation:
In the above-given question,
given that,
3(6/10) = 3 x 10.
3 x 10 = 30 + 6/10.
36/10 = 3.6.
3(2/5) = 3 x 5.
3 x 5 = 15 + 2/5.
17/5 = 3.4.
3.6 > 3.4.
d. 2\(\frac{2}{5}\) _________ 2\(\frac{8}{15}\)
Answer:
2(2/5) < 2(8/15).
Explanation:
In the above-given question,
given that,
2(2/5) = 5 x 2.
5 x 2 = 10 + 2/5.
12/5 = 2.4.
2(8/15) = 15 x 2.
15 x 2 = 30 + 8/15.
38/15 = 2.5.
2.4 < 2.5.
e. \(\frac{10}{3}\) __________ \(\frac{10}{4}\)
Answer:
(10/3) > (10/4).
Explanation:
In the above-given question,
given that,
10/3 = 3.3.
10/4 = 2.5.
3.3 > 2.5.
f. \(\frac{12}{4}\) ___________ \(\frac{10}{3}\)
Answer:
(12/4) = (10/3).
Explanation:
In the above-given question,
given that,
12/4 = 3.
10/3 = 3.3.
3 < 3.3.
g. \(\frac{38}{9}\) __________ 4\(\frac{2}{12}\)
Answer:
4(2/12) < (38/9).
Explanation:
In the above-given question,
given that,
4(2/12) = 12 x 4.
12 x 4 = 46 + 2/12.
48/12 = 4.
38/9 = 4.2.
4 < 4.2.
h. \(\frac{23}{4}\) __________ 5\(\frac{2}{3}\)
Answer:
5(2/3) < (23/4).
Explanation:
In the above-given question,
given that,
5(2/3) = 5 x 3.
5 x 3 = 15 + 2/3.
17/3 = 5.6.
23/4 = 5.75.
5.6 < 5.7.
i. \(\frac{30}{8}\) ____________ 3\(\frac{7}{12}\)
Answer:
(30/8) > 3(7/12).
Explanation:
In the above-given question,
given that,
30/8 = 3.75.
3(7/12) = 12 x 3.
12 x 3 = 36.
36 + 7/12 = 43/12.
43/12 = 3.58.
3.75 > 3.58.
j. 10\(\frac{3}{4}\) ___________ 10\(\frac{4}{6}\)
Answer:
10(3/4) > 10(4/6).
Explanation:
In the above-given question,
given that,
10(3/4) = 10 x 4.
10 x 4 = 40 + 3/4.
43/4 = 10.75.
10(4/6) = 10 x 6.
10 x 6 = 60 + 4/6.
64/6 = 10.6.
10.7 > 10.6.
