## 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. $$\frac{1}{4}$$ + $$\frac{1}{8}$$

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. $$\frac{1}{4}$$ + $$\frac{1}{12}$$

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. $$\frac{2}{6}$$ + $$\frac{1}{3}$$

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. $$\frac{1}{2}$$ + $$\frac{3}{8}$$

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. $$\frac{3}{10}$$ + $$\frac{3}{5}$$

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. $$\frac{2}{3}$$ + $$\frac{2}{9}$$

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.

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. $$\frac{1}{2}$$ + $$\frac{4}{10}$$

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. $$\frac{6}{10}$$ + $$\frac{1}{2}$$

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. $$\frac{2}{3}$$ + $$\frac{3}{6}$$

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. $$\frac{3}{4}$$ + $$\frac{6}{8}$$

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. $$\frac{4}{10}$$ + $$\frac{6}{5}$$

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.
$$\frac{2}{3}$$ + $$\frac{4}{6}$$

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.
$$\frac{5}{8}$$ + $$\frac{2}{4}$$

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.
$$\frac{3}{4}$$ + $$\frac{1}{2}$$

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. $$\frac{1}{3}$$ + $$\frac{1}{6}$$

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. $$\frac{1}{2}$$ + $$\frac{1}{4}$$

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. $$\frac{3}{4}$$ + $$\frac{1}{8}$$

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. $$\frac{1}{4}$$ + $$\frac{5}{12}$$

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. $$\frac{3}{8}$$ + $$\frac{1}{2}$$

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. $$\frac{3}{5}$$ + $$\frac{3}{10}$$

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.

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. $$\frac{3}{5}$$ + $$\frac{7}{10}$$

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. $$\frac{5}{12}$$ + $$\frac{1}{4}$$

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. $$\frac{3}{4}$$ + $$\frac{5}{8}$$

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. $$\frac{7}{8}$$ + $$\frac{3}{4}$$

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. $$\frac{1}{6}$$ + $$\frac{5}{3}$$

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.
$$\frac{5}{6}$$ + $$\frac{1}{3}$$

$$\frac{5}{6}$$ + $$\frac{1}{3}$$.