## Engage NY Eureka Math 4th Grade Module 5 Lesson 20 Answer Key

Question 1.

Use a tape diagram to represent each addend. Decompose one of the tape diagrams to make like units. Then, write the complete number sentence. Part (a) is partially completed.

a. \(\frac{1}{4}\) + \(\frac{1}{8}\)

Answer:

2/8 + 1/8 = 3/8.

Explanation:

In the above-given question,

given that,

\(\frac{1}{4}\) + \(\frac{1}{8}\).

1/4 + 1/8.

1/4 = 2/8.

2/8 + 1/8 = 3/8.

b. \(\frac{1}{4}\) + \(\frac{1}{12}\)

Answer:

4/12 + 1/12 = 5/12.

Explanation:

In the above-given question,

given that,

\(\frac{1}{4}\) + \(\frac{1}{12}\).

1/4 + 1/12.

1/4 = 4/12.

4/12 + 1/12 = 5/12.

c. \(\frac{2}{6}\) + \(\frac{1}{3}\)

Answer:

2/6 + 1/3 = 4/6.

Explanation:

In the above-given question,

given that,

\(\frac{1}{4}\) + \(\frac{1}{8}\).

1/3 + 2/6.

1/3 = 2/6.

2/6 + 2/6 = 4/6.

d. \(\frac{1}{2}\) + \(\frac{3}{8}\)

Answer:

1/2 + 3/8 = 6/8.

Explanation:

In the above-given question,

given that,

\(\frac{1}{4}\) + \(\frac{1}{8}\).

1/2 + 3/8.

1/2 = 3/8.

3/8 + 3/8 = 6/8.

e. \(\frac{3}{10}\) + \(\frac{3}{5}\)

Answer:

3/10 + 3/5 = 9/10.

Explanation:

In the above-given question,

given that,

\(\frac{1}{4}\) + \(\frac{1}{8}\).

3/10 + 3/5.

3/5 = 3/10.

3/10 + 3/5 = 9/10.

f. \(\frac{2}{3}\) + \(\frac{2}{9}\)

Answer:

2/3 + 2/9 = 4/9.

Explanation:

In the above-given question,

given that,

\(\frac{2}{3}\) + \(\frac{2}{9}\).

2/9 + 2/3.

2/3 = 2/9.

2/3 + 2/9 = 4/9.

Question 2.

Estimate to determine if the sum is between 0 and 1 or 1 and 2. Draw a number line to model the addition. Then, write a complete number sentence. Part (a) has been completed for you.

a.

Answer:

1/2 + 1/4 = 3/4.

Explanation:

In the above-given question,

given that,

1/2 + 1/4.

2/4 = 1/2.

2/4 + 1/4 = 3/4.

1/2 + 1/4 = 3/4.

b. \(\frac{1}{2}\) + \(\frac{4}{10}\)

Answer:

1/2 + 4/10 = 9/10.

Explanation:

In the above-given question,

given that,

1/2 + 4/10.

5/10 = 1/2.

5/10 + 4/10 = 9/10.

1/2 + 4/10 = 9/10.

c. \(\frac{6}{10}\) + \(\frac{1}{2}\)

Answer:

6/10 + 1/2 = 11/10.

Explanation:

In the above-given question,

given that,

1/2 + 6/10.

5/10 = 1/2.

5/10 + 6/10 = 11/10.

1/2 + 6/10 = 11/10.

d. \(\frac{2}{3}\) + \(\frac{3}{6}\)

Answer:

2/3 + 3/6 = 5/6.

Explanation:

In the above-given question,

given that,

2/3 + 3/6.

2/3 + 3/6 = 5/6.

e. \(\frac{3}{4}\) + \(\frac{6}{8}\)

Answer:

3/4 + 6/8 = 6/4.

Explanation:

In the above-given question,

given that,

3/4 + 6/8.

6/8 = 3/4.

3/4 + 3/4 = 6/4.

3/4 + 6/8 = 6/4.

f. \(\frac{4}{10}\) + \(\frac{6}{5}\)

Answer:

4/10 + 6/5 = 8/5.

Explanation:

In the above-given question,

given that,

4/10 + 6/5.

4/10 = 2/5.

6/5 + 2/5 = 8/5.

6/5 + 4/10 = 8/5.

Question 3.

Solve the following addition problem without drawing a model. Show your work.

\(\frac{2}{3}\) + \(\frac{4}{6}\)

Answer:

2/3 + 4/6 = 4/3.

Explanation:

In the above-given question,

given that,

2/3 + 4/6.

4/6 = 2/3.

2/3 + 2/3 = 4/3.

2/3 + 4/6 = 4/3.

### Eureka Math Grade 4 Module 5 Lesson 20 Exit Ticket Answer Key

Question 1.

Draw a number line to model the addition. Solve, and then write a complete number sentence.

\(\frac{5}{8}\) + \(\frac{2}{4}\)

Answer:

5/8 + 2/4 = 7/8.

Explanation:

In the above-given question,

given that,

5/8 + 2/4.

4, 8 = 8.

5/8 + 2/4 = 7/8.

Question 2.

Solve without drawing a model.

\(\frac{3}{4}\) + \(\frac{1}{2}\)

Answer:

3/4 + 1/2 = 4/4.

Explanation:

In the above-given question,

given that,

3/4 + 1/2.

l.c.m of 4, 2 = 4.

3/4 + 1/2 = 4/4.

3/4 + 1/2 = 1.

### Eureka Math Grade 4 Module 5 Lesson 20 Homework Answer Key

Question 1.

Use a tape diagram to represent each addend. Decompose one of the tape diagrams to make like units. Then, write the complete number sentence.

a. \(\frac{1}{3}\) + \(\frac{1}{6}\)

Answer:

1/3 + 1/6 = 2/6.

Explanation:

In the above-given question,

given that,

1/3 + 1/6.

l.c.m of 3,6 = 6.

1/3 + 1/6 = 2/6.

b. \(\frac{1}{2}\) + \(\frac{1}{4}\)

Answer:

1/2 + 1/4 = 2/4.

Explanation:

In the above-given question,

given that,

1/2 + 1/4.

l.c.m of 2, 4 = 4.

1/2 + 1/4 = 2/4.

c. \(\frac{3}{4}\) + \(\frac{1}{8}\)

Answer:

3/4 + 1/8 = 4/8.

Explanation:

In the above-given question,

given that,

3/4 + 1/8.

L.C.M of 4,8 = 4.

3/4 + 1/8 = 4/8.

d. \(\frac{1}{4}\) + \(\frac{5}{12}\)

Answer:

1/4 + 5/12 = 6/12.

Explanation:

In the above-given question,

given that,

1/4 + 5/12.

l.c.m of 4,12 = 12.

1/4 + 5/12 = 6/12.

e. \(\frac{3}{8}\) + \(\frac{1}{2}\)

Answer:

3/8 + 1/2 = 7/8.

Explanation:

In the above-given question,

given that,

3/8 + 1/2.

4/8 = 1/2.

3/8 + 4/8 = 7/8.

3/8 + 1/2 = 7/8.

f. \(\frac{3}{5}\) + \(\frac{3}{10}\)

Answer:

3/5 + 3/10 = 6/10.

Explanation:

In the above-given question,

given that,

3/5 + 3/10.

3/5 + 3/10 = 6/10.

Question 2.

Estimate to determine if the sum is between 0 and 1 or 1 and 2. Draw a number line to model the addition. Then, write a complete number sentence. The first one has been completed for you.

a.

Answer:

1/3 + 1/6 = 2/6.

Explanation:

In the above-given question,

given that,

\(\frac{1}{3}\) + \(\frac{1}{6}\).

1/3 + 1/6.

l.c.m of 3,6 = 6.

1/3 + 1/6 = 2/6.

b. \(\frac{3}{5}\) + \(\frac{7}{10}\)

Answer:

3/5 + 7/10 = 10/10.

Explanation:

In the above-given question,

given that,

\(\frac{3}{5}\) + \(\frac{7}{10}\).

3/5 + 7/10.

L.c.m of 5,10 = 10.

3/5 + 7/10 = 10/10.

c. \(\frac{5}{12}\) + \(\frac{1}{4}\)

Answer:

5/12 + 1/4 = 2/4.

Explanation:

In the above-given question,

given that,

\(\frac{5}{12}\) + \(\frac{1}{4}\).

5/12 + 1/4.

5/12 = 1/4.

5/12 + 1/4 = 2/4.

d. \(\frac{3}{4}\) + \(\frac{5}{8}\)

Answer:

3/4 + 5/8 = 8/8.

Explanation:

In the above-given question,

given that,

\(\frac{3}{4}\) + \(\frac{5}{8}\).

3/4 + 5/8.

l.c.m of 4,8 = 8.

3/4 + 5/8 = 8/8.

e. \(\frac{7}{8}\) + \(\frac{3}{4}\)

Answer:

7/8 + 3/4 = 10/8.

Explanation:

In the above-given question,

given that,

\(\frac{7}{8}\) + \(\frac{3}{4}\).

7/8 + 3/4.

l.c.m of 8,4 = 8.

7/8 + 3/4 = 10/8.

f. \(\frac{1}{6}\) + \(\frac{5}{3}\)

Answer:

1/6 + 5/3 = 6/6.

Explanation:

In the above-given question,

given that,

\(\frac{1}{4}\) + \(\frac{1}{8}\).

1/6 + 5/3.

l.c.m of 6,3 = 6.

1/6 + 5/3 = 6/6.

Question 3.

Solve the following addition problem without drawing a model. Show your work.

\(\frac{5}{6}\) + \(\frac{1}{3}\)

Answer:

5/6 + 1/3 = 6/6.

Explanation:

In the above-given question,

given that,

\(\frac{5}{6}\) + \(\frac{1}{3}\).

5/6 + 1/3.

l.c.m of 6,3 = 6.

5/6 + 1/3 = 6/6.