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Eureka Math ® is a holistic Prekindergarten through Grade 12 curriculum that carefully sequences mathematical progressions in expertly crafted modules, making math a joy to teach and learn. We provide in-depth professional development, learning materials, and a community of support.

What are the four core components of a Eureka Math TEKS lesson?

Lesson Components Within every lesson, students experience the same four core components: - Fluency Practice, - Application Problem, - Concept Development (which includes a Problem Set), and - Student Debrief (which includes an Exit Ticket) .

Is Eureka Math good or bad?

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Is Eureka Math developmentally appropriate?

Eureka Math is a math curriculum developed by a team of math master teachers and mathematicians to ensure that the quality of the curriculum builds upon students' prior-knowledge and teaches mathematical concepts and skills in a coherent and developmentally-appropriate way .

What is the most used math curriculum?

According to the RAND Corporation, over 50% of U.S. school teachers DFFHVV Eureka Math or the version of the curriculum found on the EngageNY website. Additionally, Eureka Math is the only curriculum found by EdReports.org to align fully with the Common Core State Standards for Mathematics for all grades, K–8.

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In addition to our Learn, Practice, Succeed configuration you can get student workbooks, teacher editions, and assessment and fluency materials for Grades PK–12 . These materials are also available in Spanish for Grades K–8.

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Eureka Math Grade 4 Module 5 Lesson 16 Answer Key (2024)

Engage NY Eureka Math 4th Grade Module 5 Lesson 16 Answer Key

Eureka Math Grade 4 Module 5 Lesson 16 Problem Set Answer Key

Question 1.
Solve.
a. 3 fifths – 1 fifth = _____2 __fifths_____

Answer:
3 fifths – 1 fifth = 2 fifths.

Explanation:
In the above-given question,
given that,
3 fifths = 3/5.
3/5 = 0.6.
1 fifth = 1/5.
1/5 = 0.2.
0.6 – 0.2 = 0.4.
2/5 = 0.4.
3 fifths – 1 fifth = 2 fifths.

b. 5 fifths – 3 fifths = _____2_fifths._________

Answer:
5 fifths – 3 fifth = 2 fifths.

Explanation:
In the above-given question,
given that,
5 fifths = 5/5.
5/5 = 1.
3 fifth = 3/5.
3/5 = 0.6.
1 – 0.6 = 0.4.
2/5 = 0.4.
3 fifths – 1 fifth = 2 fifths.

c. 3 halves – 2 halves = _____1_ halves._____

Answer:
3 halves – 2 halves = 1 halves

Explanation:
In the above-given question,
given that,
3 halves = 3/2.
3/2 = 1.5.
2 halves = 2/2.
2/2 = 1.
1.5 – 1 = 0.5.
1/2 = 0.5.
3 halves – 2 halves = 1 half.

d. 6 fourths – 3 fourths = ____3__fourths._______

Answer:
6 fourths – 3 fourths = 3 fourths.

Explanation:
In the above-given question,
given that,
6 fourths = 6/4.
6/4 = 1.5.
3 fourths = 3/4.
3/4 = 0.75.
1.5 – 0.75 = 0.75.
3/4 = 0.75.
6 fourths – 3 fourths = 3 fourths.

Question 2.
Solve.

a. \(\frac{5}{6}\) – \(\frac{3}{6}\)

Answer:
\(\frac{5}{6}\) – \(\frac{3}{6}\) = \(\frac{2}{6}\)

Explanation:
In the above-given question,
given that,
5 sixths = 5/6.
5/6 = 0.83.
3 sixths = 3/6.
3/6 = 0.5.
0.83 – 0.5 = 0.33.
2/6 = 0.33.
\(\frac{5}{6}\) – \(\frac{3}{6}\) = \(\frac{2}{6}\)

b. \(\frac{6}{8}\) – \(\frac{4}{8}\)

Answer:
\(\frac{6}{8}\) – \(\frac{4}{8}\) = \(\frac{2}{8}\)

Explanation:
In the above-given question,
given that,
6 eights = 6/8.
6/8 = 0.75.
4 eights = 4/8.
4/8 = 0.5.
0.75 – 0.5 = 0.25.
2/8 = 0.25.
\(\frac{6}{8}\) – \(\frac{4}{8}\) = \(\frac{2}{8}\)

c. \(\frac{3}{10}\) – \(\frac{3}{10}\)

Answer:
\(\frac{3}{10}\) – \(\frac{3}{10}\) = \(\frac{0}{0}\)

Explanation:
In the above-given question,
given that,
3 tens = 3/10.
3/10 = 0.3.
3 tens = 3/10.
3/10 = 0.3.
0.3 – 0.3 = 0.
0/6 = 0.
\(\frac{3}{10}\) – \(\frac{3}{10}\) = \(\frac{0}{0}\)

d. \(\frac{5}{5}\) – \(\frac{4}{5}\)

Answer:
\(\frac{5}{5}\) – \(\frac{4}{5}\) = \(\frac{1}{5}\)

Explanation:
In the above-given question,
given that,
5 fifths = 5/5.
5/5 = 1.
4 fifths = 4/5.
4/5 = 0.8.
1 – 0.8 = 0.2.
1/5 = 0.2.
\(\frac{5}{5}\) – \(\frac{4}{5}\) = \(\frac{1}{5}\)

e. \(\frac{5}{4}\) – \(\frac{4}{4}\)

Answer:
\(\frac{5}{4}\) – \(\frac{4}{4}\) = \(\frac{1}{4}\)

Explanation:
In the above-given question,
given that,
5 fours = 5/4.
5/4 = 1.25.
4 fours = 4/4.
4/4 = 1.
1.25 – 1 = 0.25.
1/4 = 0.25.
\(\frac{5}{4}\) – \(\frac{4}{4}\) = \(\frac{1}{4}\)

f. \(\frac{5}{4}\) – \(\frac{3}{4}\)

Answer:
\(\frac{5}{4}\) – \(\frac{3}{4}\) = \(\frac{2}{4}\)

Explanation:
In the above-given question,
given that,
5 fours = 5/4.
5/4 = 1.25.
3 fours = 3/4.
3/4 = 0.75.
1.25 – 0.75 = 0.5.
2/4 = 0.5.
\(\frac{5}{4}\) – \(\frac{3}{4}\) = \(\frac{2}{4}\)

Question 3.
Solve. Use a number bond to show how to convert the difference to a mixed number. Problem (a) has been completed for you.
a.

Answer:
12/8 – 3/8 = 9/8.

Explanation:
In the above-given question,
given that,
Use a number bond to show how to convert the difference to a mixed number.
12/8 – 3/8.
9/8.
9/8 = 8/8 + 1/8.

b. \(\frac{12}{6}\) – \(\frac{5}{6}\)

Answer:
12/6 – 5/6 = 7/6.

Explanation:
In the above-given question,
given that,
Use a number bond to show how to convert the difference to a mixed number.
12/6 – 5/6.
7/6.
7/6 = 6/6 + 1/6.

c. \(\frac{9}{5}\) – \(\frac{3}{5}\)

Answer:
9/5 – 3/5 = 6/5.

Explanation:
In the above-given question,
given that,
Use a number bond to show how to convert the difference to a mixed number.
9/5 – 3/5.
6/5.
6/5 = 5/5 + 1/5.

d. \(\frac{14}{8}\) – \(\frac{3}{8}\)

Answer:
14/8 – 3/8 = 11/8.

Eureka Math Grade 4 Module 5 Lesson 16 Exit Ticket Answer Key

Question 1.
Solve. Use a number bond to decompose the difference. Record your final answer as a mixed number.
\(\frac{16}{9}\) – \(\frac{5}{9}\)

Answer:
16/9 – 5/9 = 11/9.

Explanation:
In the above-given question,
given that,
Use a number bond to show how to convert the difference to a mixed number.
16/9 – 5/9.
11/9.
11/9 = 9/9 + 2/9.

Question 2.
Solve. Use a number bond to decompose the sum. Record your final answer as a mixed number.
\(\frac{5}{12}\) + \(\frac{10}{12}\)

Answer:
5/12 + 10/12 = 15/12.

Explanation:
In the above-given question,
given that,
Use a number bond to decompose the sum.
5/12 + 10/12.
15/12.
15/12 = 12/12 + 3/12.

Eureka Math Grade 4 Module 5 Lesson 16 Homework Answer Key

Question 1.
Solve.
a. 3 sixths – 2 sixths = __1__sixths___________

Answer:
3 sixths – 2 sixths = 1 sixths.

Explanation:
In the above-given question,
given that,
3 sixths = 3/6.
3/6 = 0.5.
2 sixths = 2/6.
2/6 = 0.33.
0.5 – 0.3 = 0.1.
1/6 = 0.1.

b. 5 tenths – 3 tenths = ___2 tenths._____

Answer:
5 tenths – 3 tenths = 2 tenths.

Explanation:
In the above-given question,
given that,
5 tenths = 5/10.
5/10 = 0.5.
3 tenths = 3/10.
3/10 = 0.3.
0.5 – 0.3 = 0.2.
2/10 = 0.2.

c. 3 fourths – 2 fourths = ____1__fourth._________

Answer:
3 fourths – 2 fourths = 1 fourth.

Explanation:
In the above-given question,
given that,
3 fourths = 3/4.
3/4 = 0.75.
2 fourths = 2/4.
2/4 = 0.5.
0.75 – 0.5 = 0.25.
1/4 = 0.25.

d. 5 thirds – 2 thirds = ___3__thirds._____

Answer:
5 thirds – 2 thirds = 3 thirds.

Explanation:
In the above-given question,
given that,
5 thirds = 5/3.
3/5 = 1.6.
2 thirds = 2/3.
2/3 = 0.6.
1.6 – 0.6 = 1.
3/3 = 1.

Question 2.
Solve.

a. \(\frac{3}{5}\) – \(\frac{2}{5}\)

Answer:
\(\frac{3}{5}\) – \(\frac{2}{5}\) = \(\frac{1}{5}\)

Explanation:
In the above-given question,
given that,
3 fives = 3/5.
3/5 = 0.6.
2 fives = 2/5.
2/5 = 0.4.
0.6 – 0.4 = 0.2.
1/5 = 0.2.
\(\frac{3}{5}\) – \(\frac{2}{5}\) = \(\frac{1}{5}\)

b. \(\frac{7}{9}\) – \(\frac{3}{9}\)

Answer:
\(\frac{7}{9}\) – \(\frac{3}{9}\) = \(\frac{4}{9}\)

Explanation:
In the above-given question,
given that,
7 nines = 7/9.
7/9 = 0.7.
3 nines = 3/9.
3/9 = 0.3.
0.7 – 0.3 = 0.4.
4/9 = 0.4.
\(\frac{7}{9}\) – \(\frac{3}{9}\) = \(\frac{4}{9}\)

c. \(\frac{7}{12}\) – \(\frac{3}{12}\)

Answer:
\(\frac{7}{12}\) – \(\frac{3}{12}\) = \(\frac{4}{12}\)

Explanation:
In the above-given question,
given that,
7 twelfths = 7/12.
7/12 = 0.58.
3 twelfths = 3/12.
3/12 = 0.25.
0.58 – 0.25 = 0.33.
4/12 = 0.33.
\(\frac{7}{12}\) – \(\frac{3}{12}\) = \(\frac{4}{12}\)

d. \(\frac{6}{6}\) – \(\frac{4}{6}\)

Answer:
\(\frac{6}{6}\) – \(\frac{4}{6}\) = \(\frac{2}{6}\)

Explanation:
In the above-given question,
given that,
6 sixs = 6/6.
6/6 = 1.
4 sixs = 4/6.
4/6 = 0.6.
1 – 0.6 = 0.4.
2/6 = 0.4.
\(\frac{6}{6}\) – \(\frac{4}{6}\) = \(\frac{2}{6}\)

e. \(\frac{5}{3}\) – \(\frac{2}{3}\)

Answer:
\(\frac{5}{3}\) – \(\frac{2}{3}\) = \(\frac{3}{3}\)

Explanation:
In the above-given question,
given that,
5 threes = 5/3.
5/3 = 1.6.
2 threes = 2/3.
2/3 = 0.6.
1.25 – 1 = 0.25.
3/3 = 1.
\(\frac{5}{3}\) – \(\frac{2}{3}\) = \(\frac{3}{3}\)

f. \(\frac{7}{4}\) – \(\frac{5}{4}\)

Answer:
\(\frac{7}{4}\) – \(\frac{5}{4}\) = \(\frac{3}{4}\)

Explanation:
In the above-given question,
given that,
7 fours = 7/4.
7/4 = 1.75.
5 fours = 4/4.
5/4 = 1.25.
1.75 – 1.25 = 0.75.
3/4 = 0.75.
\(\frac{7}{4}\) – \(\frac{5}{4}\) = \(\frac{3}{4}\)

Question 3.
Solve. Use a number bond to decompose the difference. Record your final answer as a mixed number. Problem (a) has been completed for you.

Answer:
12/6 – 3/6 = 9/6.

Explanation:
In the above-given question,
given that,
Use a number bond to show how to convert the difference to a mixed number.
12/6 – 3/4.
9/6.
9/6 = 6/6 + 3/6.

b. \(\frac{17}{8}\) – \(\frac{6}{8}\)

Answer:
17/8 – 6/8 = 11/8.

Explanation:
In the above-given question,
given that,
Use a number bond to show how to convert the difference to a mixed number.
17/8 – 6/8.
11/8.
11/8 = 8/8 + 2/8.

c. \(\frac{9}{5}\) – \(\frac{3}{5}\)

Answer:
9/5 – 3/5 = 6/5.

Explanation:
In the above-given question,
given that,
Use a number bond to show how to convert the difference to a mixed number.
9/5 – 3/5.
6/5.
6/5 = 5/5 + 1/6.

d. \(\frac{11}{4}\) – \(\frac{6}{4}\)

Answer:
11/4 – 6/4 = 5/4.

Explanation:
In the above-given question,
given that,
Use a number bond to show how to convert the difference to a mixed number.
11/4 – 6/4.
5/4.
5/4 = 4/4 + 1/4.

e. \(\frac{10}{7}\) – \(\frac{2}{7}\)

Answer:
10/7 – 2/7 = 8/7.

Explanation:
In the above-given question,
given that,
Use a number bond to show how to convert the difference to a mixed number.
10/7 – 2/7.
8/7.
8/7 = 7/7 + 1/7.

f. \(\frac{21}{10}\) – \(\frac{9}{10}\)

Answer:
21/10 – 9/10 = 11/10.

Explanation:
In the above-given question,
given that,
Use a number bond to show how to convert the difference to a mixed number.
21/10 – 9/10.
11/10.
11/10 = 10/10 + 1/10.

Question 4.
Solve. Write the sum in unit form.
a. 4 fifths + 2 fifths = ____6__fifths.____

Answer:
4 fifths + 2 fifths = 6 fifths.

Explanation:
In the above-given question,
given that,
Use a number bond to show how to convert the difference to a mixed number.
4 fifths = 1/5 + 1/5 + 1/5 + 1/5.
2 fifths = 1/5 + 1/5.
4 fifths + 2 fifth = 6 fifths.
1/5 + 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 6/5.

b. 5 eighths + 2 eighths = __7___eights.______

Answer:
5 eights + 2 eighths = 7 eights.

Explanation:
In the above-given question,
given that,
Use a number bond to show how to convert the difference to a mixed number.
5 eights = 1/8 + 1/8 + 1/8 + 1/8 + 1/8.
2 eights = 1/8 + 1/8.
5 eights + 2 eights = 7 eights.
1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 = 7/8.

Question 5.
Solve.
a. \(\frac{3}{11}\) + \(\frac{6}{11}\)

Answer:
3/11 + 6/11 = 9/11.

Explanation:
In the above-given question,
given that,
Use a number bond to decompose the sum.
3/11 + 6/11.
9/11.
9/11 = 3/11 + 9/11.

b. \(\frac{3}{10}\) + \(\frac{6}{10}\)

Answer:
3/10 + 6/10 = 9/10.

Explanation:
In the above-given question,
given that,
Use a number bond to decompose the sum.
3/10 + 6/10.
9/10.
9/10 = 3/10 + 6/10.

Question 6.
Solve. Use a number bond to decompose the sum. Record your final answer as a mixed number.
a. \(\frac{3}{4}\) + \(\frac{3}{4}\)

Answer:
3/4 + 3/4 = 6/4.

Explanation:
In the above-given question,
given that,
Use a number bond to decompose the sum.
3/4 + 3/4.
6/4.
6/4 = 4/4 + 5/4.

b. \(\frac{8}{12}\) + \(\frac{6}{12}\)

Answer:
8/12 + 6/12 = 14/12.

Explanation:
In the above-given question,
given that,
Use a number bond to decompose the sum.
8/12 + 6/12.
14/12.
14/12 = 12/12 + 2/12.

c. \(\frac{5}{8}\) + \(\frac{7}{8}\)

Answer:
5/8 + 7/8 = 12/8.

Explanation:
In the above-given question,
given that,
Use a number bond to decompose the sum.
5/8 + 7/8.
12/8.
12/8 = 8/8 + 4/8.

d. \(\frac{8}{10}\) + \(\frac{5}{10}\)

Answer:
8/10 + 5/10 = 13/10.

Explanation:
In the above-given question,
given that,
Use a number bond to decompose the sum.
8/10 + 5/10.
13/10.
13/10 = 10/10 + 3/10.

e. \(\frac{3}{5}\) + \(\frac{6}{5}\)

Answer:
3/5 + 6/5 = 9/5.

Explanation:
In the above-given question,
given that,
Use a number bond to decompose the sum.
3/5 + 6/5.
9/5.
9/5 = 5/5 + 4/5.

Question 7.
Solve. Use a number line to model your answer.

a. \(\frac{11}{9}\) – \(\frac{5}{9}\)

Answer:
\(\frac{11}{9}\) – \(\frac{5}{9}\) = \(\frac{6}{9}\)

Explanation:
In the above-given question,
given that,
11 nines = 11/9.
11/9 = 0.58.
5 nines = 5/9.
5/9 = 0.25.
0.58 – 0.25 = 0.33.
6/9 = 0.33.
\(\frac{11}{9}\) – \(\frac{5}{9}\) = \(\frac{6}{1}\)

b. \(\frac{13}{12}\) + \(\frac{4}{12}\)

Eureka Math Grade 4 Module 5 Lesson 16 Answer Key (2024)

Engage NY Eureka Math 4th Grade Module 5 Lesson 16 Answer Key

Eureka Math Grade 4 Module 5 Lesson 16 Problem Set Answer Key

Eureka Math Grade 4 Module 5 Lesson 16 Exit Ticket Answer Key

Eureka Math Grade 4 Module 5 Lesson 16 Homework Answer Key

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