## Engage NY Eureka Math 4th Grade Module 5 Lesson 18 Answer Key

### Eureka Math Grade 4 Module 5 Lesson 18 Practice Sheet Answer Key 1/8 + 3/8 + 4/8= 1.

Explanation:
In the above-given question,
given that,
1/8 + 3/8.
4/8.
4/8 + 4/8.
8/8 = 1.

1/6 + 4/6 + 2/6= 7/6.

Explanation:
In the above-given question,
given that,
1/6 + 4/6.
5/6.
5/6 + 2/6.
7/6.

11/10 – 4/10 – 1/10 = 6/10.

Explanation:
In the above-given question,
given that,
11/10 – 4/10.
7/10 – 1/10.
6/10._____________ 1 – 3/12 – 5/12 = 4/12.

Explanation:
In the above-given question,
given that,
1 – 3/12.
9/12.
9/12 – 5/12.
4/12.

5/8 + 4/8 + 1/8= 10/8.

Explanation:
In the above-given question,
given that,
5/8 + 4/8.
9/8.
9/8 + 1/8.
10/8.

1(1/5) – 2/5 – 3/5= 1/5.

Explanation:
In the above-given question,
given that,
1(1/5) – 2/5.
6/5 – 2/5.
4/5 – 1/5.
3/5.

### Eureka Math Grade 4 Module 5 Lesson 18 Problem Set Answer Key

Question 1.
Show one way to solve each problem. Express sums and differences as a mixed number when possible. Use number bonds when it helps you. Part (a) is partially completed.

a. $$\frac{2}{5}$$ + $$\frac{3}{5}$$ + $$\frac{1}{5}$$
= $$\frac{5}{5}$$ + $$\frac{1}{5}$$ = 1 + $$\frac{1}{5}$$
=1 $$\frac{1}{5}$$.

1$$\frac{1}{5}$$.

Explanation:
In the above-given question,
given that,
Express sums and differences as a mixed number when possible.
$$\frac{2}{5}$$ + $$\frac{3}{5}$$ + $$\frac{1}{5}$$
2/5 + 3/5 = 5/5.
$$\frac{5}{5}$$ + $$\frac{1}{5}$$.
5/5 = 1.
5/5 + 1/5 = 6/5.
1$$\frac{1}{5}$$.

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

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

Explanation:
In the above-given question,
given that,
Express sums and differences as a mixed number when possible.
$$\frac{3}{6}$$ + $$\frac{1}{6}$$ + $$\frac{3}{6}$$
3/6 + 1/6 = 4/6.
$$\frac{4}{6}$$ + $$\frac{3}{6}$$.
4/6 + 3/6.
7/6.
1$$\frac{1}{6}$$.

c. $$\frac{5}{7}$$ + $$\frac{7}{7}$$ + $$\frac{2}{7}$$

$$\frac{14}{7}$$.

Explanation:
In the above-given question,
given that,
Express sums and differences as a mixed number when possible.
$$\frac{5}{7}$$ + $$\frac{7}{7}$$ + $$\frac{2}{7}$$
5/7 + 7/7 = 12/7.
$$\frac{12}{7}$$ + $$\frac{2}{7}$$.
12/7 + 2/7 = 14/7.
1$$\frac{7}{7}$$.

d. $$\frac{7}{8}$$ – $$\frac{3}{8}$$ – $$\frac{1}{8}$$

$$\frac{3}{8}$$.

Explanation:
In the above-given question,
given that,
Express sums and differences as a mixed number when possible.
$$\frac{7}{8}$$ – $$\frac{3}{8}$$ – $$\frac{1}{8}$$
7/8 – 3/8 = 4/8.
$$\frac{4}{8}$$ – $$\frac{1}{8}$$.
4/8 – 1/8 = 3/8.
1$$\frac{5}{8}$$.

e. $$\frac{7}{9}$$ + $$\frac{1}{9}$$ + $$\frac{4}{9}$$

$$\frac{12}{9}$$.

Explanation:
In the above-given question,
given that,
Express sums and differences as a mixed number when possible.
$$\frac{7}{9}$$ + $$\frac{1}{9}$$ + $$\frac{4}{9}$$
7/9 + 1/9 = 8/9.
$$\frac{8}{9}$$ + $$\frac{4}{9}$$.
8/9 + 4/9 = 12/9.
1$$\frac{3}{9}$$.

f. $$\frac{4}{10}$$ + $$\frac{11}{10}$$ + $$\frac{5}{10}$$

$$\frac{20}{10}$$.

Explanation:
In the above-given question,
given that,
Express sums and differences as a mixed number when possible.
$$\frac{4}{10}$$ + $$\frac{11}{10}$$ + $$\frac{5}{10}$$
4/10 + 11/10 = 15/10.
$$\frac{15}{10}$$ + $$\frac{5}{10}$$.
15/10 + 5/10 = 20/10.
1$$\frac{10}{10}$$.

g. 1 – $$\frac{3}{12}$$ – $$\frac{4}{12}$$

$$\frac{5}{12}$$.

Explanation:
In the above-given question,
given that,
Express sums and differences as a mixed number when possible.
$$\frac{12}{12}$$ – $$\frac{3}{12}$$ – $$\frac{4}{12}$$
12 – 3/12 = 9/12.
$$\frac{9}{12}$$ – $$\frac{4}{12}$$.
9/12 – 4/12 = 5/12.
1 – $$\frac{7}{12}$$.

h. 1$$\frac{2}{3}$$ – $$\frac{1}{3}$$ – $$\frac{1}{3}$$

$$\frac{0}{3}$$.

Explanation:
In the above-given question,
given that,
Express sums and differences as a mixed number when possible.
$$\frac{2}{3}$$ – $$\frac{1}{3}$$ – $$\frac{1}{3}$$
2/3 – 1/3 = 1/3.
$$\frac{1}{3}$$ – $$\frac{1}{3}$$.
1/3 – 1/3 = 0.
$$\frac{0}{3}$$.

i. $$\frac{10}{12}$$ + $$\frac{5}{12}$$ + $$\frac{2}{12}$$ + $$\frac{7}{12}$$

$$\frac{24}{12}$$.

Explanation:
In the above-given question,
given that,
Express sums and differences as a mixed number when possible.
$$\frac{10}{12}$$ + $$\frac{5}{12}$$ + $$\frac{2}{12}$$ + $$\frac{7}{12}$$
10/12 + 5/12 = 15/12.
$$\frac{15}{12}$$ + $$\frac{2}{12}$$.
15/12 + 2 /12 = 17/12.
$$\frac{17}{12}$$ + $$\frac{7}{12}$$.
17/12 + 7/12.
24/12.
1$$\frac{12}{12}$$.

Question 2.
Monica and Stuart used different strategies to solve $$\frac{5}{8}$$ + $$\frac{2}{8}$$ + $$\frac{5}{8}$$. Whose strategy do you like best? Why?

Stuart’s way is the best.

Explanation:
In the above-given question,
given that,
Monica and Stuart used  different strategies to solve $$\frac{5}{8}$$ + $$\frac{2}{8}$$ + $$\frac{5}{8}$$.
Monica explained in detail.
Stuart’s also explained in detail.
he explained in a simple way.
so Stuart’s way is the best.

Question 3.
You gave one solution for each part of Problem 1. Now, for each problem indicated below, give a different solution method. e. 5/7 + 7/7 + 2/7 = 14/7.

Explanation:
In the above-given question,
given that,
5/7 + 7/7.
12/7.
12/7 + 2/7.
14/7.
5/7 + 7/7 + 2/7 = 14/7.

f. 4/10 + 11/10 + 5/10 = 20/10.

Explanation:
In the above-given question,
given that,
4/10 + 11/10.
15/10.
15/10 + 5/10.
20/10.
4/10 + 11/10 + 5/10 = 20/10. ### Eureka Math Grade 4 Module 5 Lesson 18 Exit Ticket Answer Key

Question 1.
$$\frac{5}{9}$$ + $$\frac{2}{9}$$ + $$\frac{4}{9}$$

$$\frac{11}{9}$$.

Explanation:
In the above-given question,
given that,
Express sums and differences as a mixed number when possible.
$$\frac{5}{9}$$ + $$\frac{2}{9}$$ + $$\frac{4}{9}$$
5/9 + 2/9 = 7/9.
$$\frac{7}{9}$$ + $$\frac{4}{9}$$.
7/9 + 4/9 = 11/9.
$$\frac{11}{9}$$.

Question 2.
1 – $$\frac{5}{8}$$ – $$\frac{1}{8}$$

$$\frac{2}{8}$$.

Explanation:
In the above-given question,
given that,
Express sums and differences as a mixed number when possible.
$$\frac{8}{1}$$ – $$\frac{5}{8}$$ – $$\frac{1}{8}$$
8 – 5/8 = 3/8.
$$\frac{3}{8}$$ – $$\frac{1}{8}$$.
3/8 – 1/8 = 2/8.
$$\frac{2}{8}$$.

### Eureka Math Grade 4 Module 5 Lesson 18 Homework Answer Key

Question 1.
Show one way to solve each problem. Express sums and differences as a mixed number when possible. Use number bonds when it helps you. Part (a) is partially completed.

a. $$\frac{1}{3}$$ + $$\frac{2}{3}$$ + $$\frac{1}{3}$$
= $$\frac{3}{3}$$ + $$\frac{1}{3}$$ = 1 + $$\frac{1}{3}$$
= __4/3______

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

Explanation:
In the above-given question,
given that,
Express sums and differences as a mixed number when possible.
$$\frac{3}{3}$$ + $$\frac{1}{3}$$ + $$\frac{1}{3}$$
1 + 1/3 =2 /3.
$$\frac{3}{3}$$ + $$\frac{1}{3}$$.
2/3 + 2/3 = 4/3.
1$$\frac{1}{3}$$.

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

1$$\frac{5}{8}$$.

Explanation:
In the above-given question,
given that,
Express sums and differences as a mixed number when possible.
$$\frac{5}{8}$$ + $$\frac{5}{8}$$ + $$\frac{3}{8}$$
5/8 + 5/8 = 10/8.
$$\frac{10}{8}$$ + $$\frac{3}{8}$$.
10/8 + 3/8 = 13/8.
1$$\frac{5}{8}$$.

c. $$\frac{4}{6}$$ + $$\frac{6}{6}$$ + $$\frac{1}{6}$$

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

Explanation:
In the above-given question,
given that,
Express sums and differences as a mixed number when possible.
$$\frac{4}{6}$$ + $$\frac{6}{6}$$ + $$\frac{1}{6}$$
4/6 + 6/6 = 10/6.
$$\frac{10}{6}$$ + $$\frac{1}{6}$$.
10/6 + 1/6 = 11/6.
1$$\frac{5}{6}$$.

d. 1$$\frac{2}{12}$$ – $$\frac{2}{12}$$ – $$\frac{1}{12}$$

1 – $$\frac{1}{12}$$.

Explanation:
In the above-given question,
given that,
Express sums and differences as a mixed number when possible.
1$$\frac{2}{12}$$ – $$\frac{2}{12}$$ – $$\frac{1}{12}$$
14/12 – 2/12 = 12/12.
$$\frac{12}{12}$$ – $$\frac{1}{12}$$.
1 – 1/12 = 11/12.
1 – $$\frac{11}{12}$$.

e. $$\frac{5}{7}$$ + $$\frac{1}{7}$$ + $$\frac{4}{7}$$

1$$\frac{3}{7}$$.

Explanation:
In the above-given question,
given that,
Express sums and differences as a mixed number when possible.
$$\frac{5}{7}$$ + $$\frac{1}{7}$$ + $$\frac{4}{7}$$
5/7 + 1/7 = 6/7.
$$\frac{6}{7}$$ + $$\frac{4}{7}$$.
6/7 + 4/7 = 10/7.
1$$\frac{3}{7}$$.

f. $$\frac{4}{10}$$ + $$\frac{7}{10}$$ + $$\frac{9}{10}$$

1$$\frac{10}{20}$$.

Explanation:
In the above-given question,
given that,
Express sums and differences as a mixed number when possible.
$$\frac{4}{10}$$ + $$\frac{7}{10}$$ + $$\frac{9}{10}$$
4/10 + 7/10 = 11/10.
$$\frac{11}{10}$$ + $$\frac{9}{10}$$.
11/10 + 9/10 = 20/10.
1$$\frac{10}{20}$$.

g. 1 – $$\frac{3}{10}$$ – $$\frac{1}{10}$$

1 – $$\frac{4}{10}$$.

Explanation:
In the above-given question,
given that,
Express sums and differences as a mixed number when possible.
1 – $$\frac{3}{10}$$ – $$\frac{1}{10}$$.
10 – 3/10 = 7/10.
$$\frac{7}{10}$$ – $$\frac{1}{10}$$.
7/10 – 1/10 = 6/10.
1 – $$\frac{4}{10}$$.

h. 1$$\frac{3}{5}$$ – $$\frac{4}{5}$$ – $$\frac{1}{5}$$

1 – $$\frac{2}{5}$$.

Explanation:
In the above-given question,
given that,
Express sums and differences as a mixed number when possible.
1$$\frac{3}{5}$$ – $$\frac{4}{5}$$ – $$\frac{1}{5}$$
8/5 – 4/5 = 4/5.
$$\frac{4}{5}$$ – $$\frac{1}{5}$$.
4/5 –  1/5 = 3/5.
1$$\frac{2}{5}$$.

i. $$\frac{10}{15}$$ + $$\frac{7}{15}$$ + $$\frac{12}{15}$$ + $$\frac{1}{15}$$

1$$\frac{15}{15}$$.

Explanation:
In the above-given question,
given that,
Express sums and differences as a mixed number when possible.
$$\frac{10}{15}$$ + $$\frac{7}{15}$$ + $$\frac{12}{15}$$ + $$\frac{1}{15}$$.
10/15 + 7/15 = 17/15.
$$\frac{12}{15}$$ + $$\frac{1}{15}$$.
12/15 + 1/15 = 13/15.
13/15 + 17/15.
1$$\frac{15}{15}$$.

Question 2.
Bonnie used two different strategies to solve $$\frac{5}{10}$$ + $$\frac{4}{10}$$ + $$\frac{3}{10}$$. Which strategy do you like best? Why?

Bonnie’s Second Strategy is the best.

Explanation:
In the above-given question,
given that,
Bonnie’s first and second used  different strategies to solve $$\frac{5}{10}$$ + $$\frac{4}{10}$$ + $$\frac{3}{10}$$.
Bonnie’s second strategy explained in detail.
Bonnie’s first strategy also explained in detail.
he explained in a simple way.
so the second way is the best.

Question 3.
You gave one solution for each part of Problem 1. Now, for each problem indicated below, give a different solution method. b. 5/8 + 5/8 + 3/8 = 13/8.

Explanation:
In the above-given question,
given that,
5/8 + 5/8.
10/8.
10/8 + 3/8.
13/8.
5/8 + 5/8 + 3/8 = 13/8.

e. 5/7 + 1/7 + 4/7 = 10/7.

Explanation:
In the above-given question,
given that,
5/7 + 1/7.
6/7.
6/7 + 4/7.
10/7.
5/7 + 1/7 + 4/7 = 10/7. 