Engage NY Eureka Math 4th Grade Module 5 Lesson 30 Answer Key

A
Change Fractions to Mixed Numbers

3 = 2 + 1, 3/2 = 2/2 + 1/2, 3/2 = 1 + 1/2, 3/2 = 1(1/2), 5 = 4 + 1, 5/4 = 4/4 + 1/4, 5/4 = 1 + 1/4, 5/4 = 1(1/4), 4 = 3 + 1, 4/3 = 3/3 + 1/3, 4/3 = 1 + 1/3, 4/3 = 1(1/3), 7 = 5 + 2, 7/5 = 5/5 + 2/5, 7/5 = 1 + 2/5, 7/5 = 1(1/5), 8/5 = 1(3/5), 9/5 = 1(4/5), 6/5 = 1(1/5), 10/5 = 2, 11/5 = 10/5 + 1/5, 11/5 = 2 + 1/5, 6/3 = 2, 8/3 = 6/3 + 2/3, 8/3 = 6/3 + 2/3, 8/3 = 2 + 2/3, 8/3 = 2(2/3), 9/4 = 8/4 + 1/4, 9/4 = 2 + 1/4, 11/4 = 2(3/4), 8/3 = 6/3 + 2/3, 8/3 = 6/3 + 2/3, 8/3 = 6/3 + 2/3, 8/3 = 2(2/3), 14/5 = 10/5 + 4/5, 14/5 = 10/5 + 4/5, 14/5 = 2(4/5), 13/5 = 2(3/5), 9/8 = 1 + 1/8, 15/8 = 1 + 7/8, 17/12 = 12/12 + 5/12, 11/8 = 1 + 3/8, 17/12 = 1 + 5/12.

Explanation:
In the above-given question,
given that,
change fractions to mixed numbers.

Question 1.
3 = 2 + ___1___

3 = 2 + 1.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
3 = 2 + 1.
2 + 1 = 3.

$$\frac{3}{2}$$ = $$\frac{2}{2}$$ + $$\frac{1}{2}$$

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

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
3/2 = 2/2 + 1/2.
2 + 1 = 3.
2/2 + 1/2 = 3/2.

Question 3.
$$\frac{3}{2}$$ = 1 + $$\frac{1}{2}$$

3/2 = 1 + 1/2.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
3/2 = 1 + 1/2.
2 + 1 = 3.
1 + 1/2 = 3/2.

Question 4.
$$\frac{3}{2}$$ = 1$$\frac{1}{2}$$

3/2 = 1 x 1/2.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
3/2 = 1 x 1/2.
2 + 1 = 3.
1 x 1/2 = 3/2.

Question 5.
5 = 4 + __1___

5 = 4 + 1.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
5 = 4 + 1.
4 + 1 = 5.

Question 6.
$$\frac{5}{4}$$ = $$\frac{4}{4}$$ + $$\frac{1}{4}$$

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

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
5/4 = 4/4 + 1/4.
4 + 1 = 5.
1/4 + 4/4 = 5/4.

Question 7.
$$\frac{5}{4}$$ = 1 + $$\frac{1}{4}$$

5/4 = 1 + 1/4.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
5/4 = 1 + 1/4.
4 + 1 = 5.
1 + 1/4 = 5/4.

Question 8.
$$\frac{5}{4}$$ = 1$$\frac{1}{4}$$

5/4 = 1 x 1/4.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
5/4 = 1 x 1/4.
4 + 1 = 5.
1 x 1/4 = 5/4.

Question 9.
4 = __3__ + 1

4 = 3 + 1.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
4 = 3 + 1.
3 + 1 = 4.

Question 10.
$$\frac{4}{3}$$ = $$\frac{3}{3}$$ + $$\frac{1}{3}$$

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

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
4/3 = 3/3 + 1/3.
3 + 1 = 4.
1/3 + 3/3 = 4/3.

Question 11.
$$\frac{4}{3}$$ = 1 + $$\frac{1}{3}$$

4/3 = 1 + 1/3.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
4/3 = 1 + 1/3.
3 + 1 = 4.
1/3 + 1 = 4/3.

Question 12.
$$\frac{4}{3}$$ = __1___ $$\frac{1}{3}$$

4/3 = 1 x 1/3.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
4/3 = 1 x 1/3.
3 + 1 = 4.
1/3 x 1 = 4/3.

Question 13.
7 = __5__ + 2

7 = 5 + 2.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
7 = 5 + 2.
2 + 5 = 7.

Question 14.
$$\frac{7}{5}$$ = $$\frac{5}{5}$$ + $$\frac{2}{5}$$

7/5 = 5/5 + 2/5.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
7/5 = 5/5 + 2/5.
5 + 2 = 7.
5/5 + 2/5 = 7/5.

Question 15.
$$\frac{7}{5}$$ = 1 + $$\frac{2}{5}$$

7/5 = 1 + 2/5.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
7/5 = 1 + 2/5.
6 + 1 = 7.
2/5 + 1 = 7/5.

Question 16.
$$\frac{7}{5}$$ = 1$$\frac{1}{5}$$

7/5 = 1 x 1/5.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
7/5 = 1 x 1/5.
6 + 1 = 7.
1/5 x 1 = 7/5.

Question 17.
$$\frac{8}{5}$$ = 1$$\frac{1}{5}$$

8/5 = 1 x 1/5.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
8/5 = 1 x 1/5.
7 + 1 = 8.
1/5 x 1 = 8/5.

Question 18.
$$\frac{9}{5}$$ = 1$$\frac{4}{5}$$

9/5 = 1 x 4/5.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
9/5 = 1 x 4/5.
8 + 1 = 9.
4/5 x 1 = 9/5.

Question 19.
$$\frac{6}{5}$$ = 1$$\frac{1}{5}$$

6/5 = 1 x 1/5.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
6/5 = 1 x 1/5.
5 + 1 = 6.
1/5 x 1 = 6/5.

Question 20.
$$\frac{10}{5}$$ = 2.

10/5 = 2.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
10/5 = 2.
5 x 2 = 10.
2 = 10/5.

Question 21.
$$\frac{11}{5}$$ = $$\frac{10}{5}$$ + $$\frac{1}{5}$$

11/5 = 10/5 + 1/5.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
11/5 = 10/5 + 1/5.
10 + 1 = 11.
10/5 + 1/5 = 11/5.

Question 22.
$$\frac{11}{5}$$ = 2 + $$\frac{1}{5}$$

11/5 = 2 + 1/5.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
11/5 = 2 + 1/5.
10 + 1 = 11.
1/5 + 2 = 11/5.

Question 23.
$$\frac{6}{3}$$ = 2.

6/3 = 2.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
6/3 = 2.
3 x 2 = 6.
2 = 6/3.

Question 24.
$$\frac{8}{3}$$ = $$\frac{6}{3}$$ + $$\frac{2}{3}$$

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

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
8/3 = 6/3 + 2/3.
6 + 2 = 8.
2/3 + 6/3 = 8/3.

Question 25.
$$\frac{8}{3}$$ = $$\frac{6}{3}$$ + $$\frac{2}{3}$$

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

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
8/3 = 6/3 + 2/3.
6 + 2 = 8.
6/3 + 2/3 = 8/3.

Question 26.
$$\frac{8}{3}$$ = 2 + $$\frac{2}{3}$$

8/3 = 2 + 2/3.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
8/3 = 2 + 2/3.
7 + 1 = 8.
2 + 2/3 = 8/3.

Question 27.
$$\frac{8}{3}$$ = 2$$\frac{2}{3}$$

8/3 = 2 + 2/3.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
8/3 = 2 + 2/3.
7 + 1 = 8.
2 + 2/3 = 8/3.

Question 28.
$$\frac{9}{4}$$ = $$\frac{8}{4}$$ + $$\frac{1}{4}$$

9/4 = 8/4 + 1/4.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
9/4 = 8/4 + 1/4.
6 + 2 = 8.
1/4 + 8/4 = 9/4.

Question 29.
$$\frac{9}{4}$$ = 2 + $$\frac{1}{4}$$

9/4 = 2 + 1/4.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
9/4 = 2 + 1/4.
8 + 1 = 9.
2 + 1/4 = 9/4.

Question 30.
$$\frac{9}{4}$$ = ___2__ $$\frac{1}{4}$$

9/4 = 2 x 1/4.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
9/4 = 2 x 1/4.
8 + 1 = 9.
2 x 1/4 = 9/4.

Question 31.
$$\frac{11}{4}$$ = ___2__ $$\frac{3}{4}$$

11/4 = 2 x 3/4.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
11/4 = 2 x 3/4.
10 + 1 = 11.
2 x 3/4 = 11/4.

Question 32.
$$\frac{8}{3}$$ = $$\frac{6}{3}$$ + $$\frac{2}{3}$$

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

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
8/3 = 6/3 + 2/3.
6 + 2 = 8.
6/3 + 2/3 = 8/3.

Question 33.
$$\frac{8}{3}$$ = $$\frac{6}{3}$$ + $$\frac{2}{3}$$

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

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
8/3 = 6/3 + 2/3.
6 + 2 = 8.
6/3 + 2/3 = 8/3.

Question 34.
$$\frac{8}{3}$$ =

8/3 = 2 + 2/3.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
8/3 = 2 + 2/3.
6 + 2 = 8.
2/3 + 2 = 8/3.

Question 35.
$$\frac{8}{3}$$ = ___2___ $$\frac{2}{3}$$

8/3 = 2 x 2/3.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
8/3 = 2 x 2/3.
6 + 2 = 8.
2/3 x 2 = 8/3.

Question 36.
$$\frac{14}{5}$$ = $$\frac{10}{5}$$ + $$\frac{4}{5}$$

14/5 = 10/5 + 4/5.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
14/5 = 10/5 + 4/5.
10 + 4 = 14.
4/5 + 10/5 = 14/5.

Question 37.
$$\frac{14}{5}$$ = ___2___ + $$\frac{4}{5}$$

14/5 = 2 + 4/5.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
14/5 = 2 + 4/5.
10 + 4 = 14.
4/5 + 2 = 14/5.

Question 38.
$$\frac{14}{5}$$ = 2$$\frac{4}{5}$$

14/5 = 2 x 4/5.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
14/5 = 2 x 4/5.
10 + 4 = 14.
4/5 x 2 = 14/5.

Question 39.
$$\frac{13}{5}$$ = 2$$\frac{3}{5}$$

13/5 = 2 x 3/5.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
13/5 = 2 x 3/5.
10 + 3 = 13.
3/5 x 2 = 13/5.

Question 40.
$$\frac{9}{8}$$ = 1 + $$\frac{1}{8}$$

9/8 = 1 + 1/8.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
9/8 = 1 + 1/8.
8 + 1 = 9.
1/8 + 1 = 9/8.

Question 41.
$$\frac{15}{8}$$ = 1 + $$\frac{7}{8}$$

15/8 = 1 + 7/8.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
15/8 = 1 + 7/8.
10 + 5 = 15.
7/8 + 1 = 15/8.

Question 42.
$$\frac{17}{12}$$ = $$\frac{12}{12}$$ + $$\frac{5}{12}$$

17/12 = 12/12 + 5/12.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
17/12 = 12/12 + 5/12.
12 + 5 = 17.
5/12 + 12/12 = 17/12.

Question 43.
$$\frac{11}{8}$$ = 1 + $$\frac{3}{8}$$

11/8 = 1 + 3/8.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
11/8 = 1 + 3/8.
10 + 1 = 11.
3/8 + 1 = 11/8.

Question 44.
$$\frac{17}{12}$$ = 1 + $$\frac{5}{12}$$

17/12 = 1 + 5/12.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
17/12 = 1 + 5/12.
10 + 1 = 11.
5/12 + 1 = 17/12.

B
Change Fractions to Mixed Numbers

6 = 5 +1, 6/5 = 5/5 + 1/5, 6/5 = 1 + 1/5, 6/5 = 1(1/5), 4 = 3 + 1, 4/3 = 3/3 + 1/3, 4/3 = 1 + 1/3, 4/3 = 1(1/3), 5 = 4 + 1, 5/4 = 4/4 + 1/4, 5/4 = 1 + 1/4, 5/4 = 1(1/4), 8 = 5 + 3, 8/5 = 5/5 + 3/8, 8/5 = 1 + 3/5, 8/5 = 1(1/5), 9/5 = 1(4/5), 6/5 = 1(1/5), 7/5 = 1(2/5), 6/3 = 2, 7/3 = 6/3 + 1/3, 7/3 = 2 + 1/3, 4/2 = 2, 5/2 = 4/2 + 1/2, 5/2 = 4/2 + 1/2, 5/2 = 4/2 + 1/2, 5/2 = 2 + 1/2, 5/2 = 2(1/2), 11/5 = 10/5 + 1/5, 11/5 = 2 + 1/5, 11/5 = 2(1/5), 13/5 = 2(3/5), 5/3 = 4/3 + 1/3, 5/2 = 4/2 + 1/2, 5/2 = 2 + 1/2, 5/2 = 2(1/2), 12/5 = 10/5 + 2/5, 12/5 = 2 + 2/5, 12/5 = 2(2/5), 14/5 = 2(4/5), 9/8 = 1 + 1/8, 11/8 = 1 + 3/8, 19/12 = 12/12 + 7/12, 15/8 = 1 + 7/8, 19/12 = 1 + 7/12.

Explanation:
In the above-given question,
given that,
change fractions to mixed numbers.

Question 1.
6 = 5 + __1____

6 = 5 + 1.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
6 = 5 + 1.
1 + 5 = 6.

Question 2.
$$\frac{6}{5}$$ = $$\frac{5}{5}$$ + $$\frac{1}{5}$$

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

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
6/5 = 5/5 + 1/5.
5 + 1 = 6.
5/5 + 1/5 = 6/5.

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

6/5 = 1 + 1/5.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
6/5 = 1 + 1/5.
5 + 1 = 6.
1/5 + 1 = 6/5.

Question 4.
$$\frac{6}{5}$$ = 1$$\frac{1}{5}$$

6/5 = 1 x 1/5.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
6/5 = 1 x 1/5.
5 + 1 = 6.
1/5 + 1 = 6/5.

Question 5.
4 = 3 + __1___

4 = 3 + 1.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
4 = 3 + 1.
1 + 3 = 4.

Question 6.
$$\frac{4}{3}$$ = $$\frac{3}{3}$$ + $$\frac{1}{3}$$

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

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
4/3 = 3/3 + 1/3.
3 + 1 = 4.
3/3 + 1/3 = 4/3.

Question 7.
$$\frac{4}{3}$$ = 1 + $$\frac{1}{3}$$

4/3 = 1 + 1/3.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
4/3 = 1 + 1/3.
3 + 1 = 4.
1/3 + 1 = 4/3.

Question 8.
$$\frac{4}{3}$$ = 1$$\frac{1}{3}$$

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

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
6/5 = 5/5 + 1/5.
5 + 1 = 6.
5/5 + 1/5 = 6/5.

Question 9.
5 = __4__ + 1

5 = 4 + 1.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
5 = 4 + 1.
1 + 4 = 5.

Question 10.
$$\frac{5}{4}$$ = $$\frac{4}{4}$$ + $$\frac{1}{4}$$

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

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
5/4 = 4/4 + 1/4.
4 + 1 = 5.
4/4 + 1/4 = 5/4.

Question 11.
$$\frac{5}{4}$$ = 1 + $$\frac{1}{4}$$

5/4 = 1 + 1/4.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
5/4 = 1 + 1/4.
4 + 1 = 5.
1/4 + 1 = 5/4.

Question 12.
$$\frac{5}{4}$$ = __1___ $$\frac{1}{4}$$

5/4 = 1 x 1/4.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
5/4 = 1 x 1/4.
4 + 1 = 5.
1/4 x 1 = 5/4.

Question 13.
8 = __5__ + 3

8 = 5 + 3.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
8 = 5 + 3.
3 + 5 = 8.

Question 14.
$$\frac{8}{5}$$ = $$\frac{5}{5}$$ + $$\frac{3}{5}$$

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

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
8/5 = 5/5 + 3/5.
7 + 1 = 8.
5/5 + 3/5 = 8/5.

Question 15.
$$\frac{8}{5}$$ = 1 + $$\frac{3}{5}$$

8/5 = 1 + 3/5.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
8/5 = 1 + 3/5.
7 + 1 = 8.
3/5 + 1 = 8/5.

Question 16.
$$\frac{8}{5}$$ = 1$$\frac{3}{5}$$

8/5 = 1 x 3/5.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
8/5 = 1 x 3/5.
7 + 1 = 8.
3/5 x 1 = 8/5.

Question 17.
$$\frac{9}{5}$$ = 1$$\frac{4}{5}$$

9/5 = 1 x 4/5.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
9/5 = 1 x 4/5.
8 + 1 = 9.
4/5 x 1 = 9/5.

Question 18.
$$\frac{6}{5}$$ = 1$$\frac{1}{5}$$

6/5 = 1 x 1/5.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
6/5 = 1 x 1/5.
5 + 1 = 6.
1/5 x 1 = 6/5.

Question 19.
$$\frac{7}{5}$$ = 1$$\frac{2}{5}$$

7/5 = 1 x 2/5.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
7/5 = 1 x 2/5.
6 + 1 = 7.
2/5 x 1 = 7/5.

Question 20.
$$\frac{6}{3}$$ = 2

2 = 6/3.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
2 = 6/3.
3 x 2 = 6.
6/3 = 2.

Question 21.
$$\frac{7}{3}$$ = $$\frac{6}{3}$$ + $$\frac{1}{3}$$

7/3 = 6/3 + 1/3.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
7/3 = 6/3 + 1/3.
6 + 1 = 7.
1/3 + 6/3 = 7/3.

Question 22.
$$\frac{7}{3}$$ = 2 + $$\frac{1}{3}$$

7/3 = 2 + 1/3.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
7/3 = 2 + 1/3.
5 + 2 = 7.
1/3 + 2 = 7/3.

Question 23.
$$\frac{4}{2}$$ = 2.

2 = 4/2.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
2 = 4/2.
2 x 2 = 4.
4/2 = 2.

Question 24.
$$\frac{5}{2}$$ = $$\frac{4}{2}$$ + $$\frac{1}{2}$$

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

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
5/2 = 4/2 + 1/2.
4 + 1 = 5.
1/2 + 4/2 = 5/2.

Question 25.
$$\frac{5}{2}$$ = $$\frac{4}{2}$$ + $$\frac{1}{2}$$

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

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
5/2 = 4/2 + 1/2.
4 + 1 = 5.
1/2 + 4/2 = 5/2.

Question 26.
$$\frac{5}{2}$$ = 2 + $$\frac{1}{2}$$

5/2 = 2 + 1/2.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
5/2 = 2 + 1/2.
4 + 1 = 5.
1/2 + 2 = 5/2.

Question 27.
$$\frac{5}{2}$$ = 2$$\frac{1}{2}$$

5/2 = 2 x 1/2.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
5/2 = 2 x 1/2.
4 + 1 = 5.
1/2 x 2 = 5/2.

Question 28.
$$\frac{11}{5}$$ = $$\frac{10}{5}$$ + $$\frac{1}{5}$$

11/5 = 10/5 + 1/5.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
11/5 = 10/5 + 1/5.
10 + 1 = 11.
10/5 + 1/5 = 11/5.

Question 29.
$$\frac{11}{5}$$ = 2 + $$\frac{1}{5}$$

11/5 = 2 + 1/5.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
11/5 = 2 + 1/5.
10 + 1 = 11.
1/5 + 2 = 11/5.

Question 30.
$$\frac{11}{5}$$ = __2___ $$\frac{1}{5}$$

11/5 = 2 x 1/5.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
11/5 = 2 x 1/5.
10 + 1 = 11.
1/5 x 2 = 11/5.

Question 31.
$$\frac{13}{5}$$ = __2___ $$\frac{3}{5}$$

13/5 = 2 x 3/5.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
13/5 = 2 x 3/5.
10 + 3 = 13.
3/5 x 2 = 13/5.

Question 32.
$$\frac{5}{3}$$ = $$\frac{4}{3}$$ + $$\frac{1}{3}$$

5/3 = 4/3 + 1/3.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
5/3 = 4/3 + 1/3.
4 + 1 = 5.
1/3 + 4/3 = 5/3.

Question 33.
$$\frac{5}{2}$$ = $$\frac{4}{2}$$ + $$\frac{1}{2}$$

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

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
5/2 = 4/2 + 1/2.
4 + 1 = 5.
1/2 + 4/2 = 5/2.

Question 34.
$$\frac{5}{2}$$ = ____2__ + $$\frac{1}{2}$$

5/2 = 2 + 1/2.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
5/2 = 2 + 1/2.
4 + 1 = 5.
1/2 + 2 = 5/2.

Question 35.
$$\frac{5}{2}$$ = __2____ $$\frac{1}{2}$$

5/2 = 2 x 1/2.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
5/2 = 2 x 1/2.
4 + 1 = 5.
1/2 x 2 = 5/2.

Question 36.
$$\frac{12}{5}$$ = $$\frac{10}{5}$$ + $$\frac{2}{5}$$

12/5 = 10/5 + 2/5.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
12/5 = 10/5 + 2/5.
10 + 2 = 12.
2/5 + 10/5 = 12/5.

Question 37.
$$\frac{12}{5}$$ = ___2___ + $$\frac{2}{5}$$

12/5 = 2 + 2/5.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
12/5 = 2 + 2/5.
11 + 1 = 12.
2/5 + 2 = 12/5.

Question 38.
$$\frac{12}{5}$$ = 2$$\frac{2}{5}$$

12/5 = 2 x 2/5.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
12/5 = 2 x 2/5.
11 + 1 = 12.
2/5 x 2 = 12/5.

Question 39.
$$\frac{14}{5}$$ = 2$$\frac{4}{5}$$

14/5 = 2 x 4/5.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
14/5 = 2 x 4/5.
13 + 1 = 14.
4/5 x 2 = 14/5.

Question 40.
$$\frac{9}{8}$$ = 1 + $$\frac{1}{8}$$

9/8 = 1 + 1/8.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
9/8 = 1 + 1/8.
8 + 1 = 9.
1/8 + 1 = 9/8.

Question 41.
$$\frac{11}{8}$$ = 1 + $$\frac{3}{8}$$

11/8 = 1 + 3/8.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
11/8 = 1 + 3/8.
8 + 1 = 9.
3/8 + 1 = 11/8.

Question 42.
$$\frac{19}{12}$$ = $$\frac{12}{12}$$ + $$\frac{7}{12}$$

19/12 = 12/12 + 7/12.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
19/12 = 12/12 + 7/12.
10 + 2 = 12.
7/12 + 12/12 = 19/12.

Question 43.
$$\frac{15}{8}$$ = 1 + $$\frac{7}{8}$$

15/8 = 1 + 7/8.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
15/8 = 1 + 7/8.
14 + 1 = 15.
7/8 + 1 = 15/8.

Question 44.
$$\frac{19}{12}$$ = 1 + $$\frac{7}{12}$$

19/12 = 1 + 7/12.

Explanation:
In the above-given question,
given that,
change mixed numbers to fractions.
19/12 = 1 + 7/12.
10 + 9 = 19.
7/12 + 1 = 19/12.

Eureka Math Grade 4 Module 5 Lesson 30 Problem Set Answer Key

Question 1.
Solve.
a. 3$$\frac{1}{4}$$ + $$\frac{1}{4}$$

3(1/4) + (1/4) = 14/4.

Explanation:
In the above-given question,
given that,
3(1/4) + (1/4).
3 x 4 = 12.
12 + 1/4 = 13/4.
13/4 + 1/4 = 14/4.
3(1/4) + (1/4) = 14/4.

b. 7$$\frac{3}{4}$$ + $$\frac{1}{4}$$

7(3/4) + (1/4) = 32/4.

Explanation:
In the above-given question,
given that,
7(3/4) + (1/4).
7 x 4 = 28.
28 + 3/4 = 31/4.
31/4 + 1/4 = 32/4.
7(3/4) + (1/4) = 32/4.

c. $$\frac{3}{8}$$ + 5$$\frac{2}{8}$$

5(2/8) + (3/8) = 46/8.

Explanation:
In the above-given question,
given that,
5(2/8) + (3/8).
5 x 8 = 40.
40 + 3/8 = 43/8.
43/8 + 3/8 = 46/8.
5(2/8) + (3/8) = 46/8.

d. $$\frac{1}{8}$$ + 6$$\frac{7}{8}$$

6(7/8) + (1/8) = 56/8.

Explanation:
In the above-given question,
given that,
6(7/8) + (1/8).
6 x 8 = 48.
48 + 7/8 = 55/8.
55/8 + 1/8 = 56/8.
6(7/8) + (1/8) = 56/8.

Question 2.
Complete the number sentences.
a. 4$$\frac{7}{8}$$ + _1____ = 5

4(7/8) + 1 = 5.

Explanation:
In the above-given question,
given that,
complete the number sentences.
4(7/8) + 1.
8 x 4 = 32.
32 + 7 = 39.
39 + 1 = 40.
40/8 = 5.

b. 7$$\frac{2}{5}$$ + __3___ = 8

7(2/5) + 3 = 8.

Explanation:
In the above-given question,
given that,
complete the number sentences.
7(2/5) + 3.
7 x 5 = 35.
35 + 2 = 37.
37 + 3 = 40.
40/5 = 8.

c. 3 = 2$$\frac{1}{6}$$ + ___5___

2(1/6) + 5 = 3.

Explanation:
In the above-given question,
given that,
complete the number sentences.
2(1/6) + 5.
2 x 6 = 12.
12 + 1 = 13.
13 + 5 = 18.
18/6 = 3.

d. 12 = 11$$\frac{1}{12}$$ + ___12___

11(1/12) + 12 = 12.

Explanation:
In the above-given question,
given that,
complete the number sentences.
11(1/12) + 12.
11 x 12 = 132.
132 + 12 = 144.
144/12 = 12.

Question 3.
Use a number bond and the arrow way to show how to make one. Solve.

2(3/4) + (2/4) = 13/4.

Explanation:
In the above-given question,
given that,
2(3/4) + (2/4).
2 x 4 = 8.
8 + 3/4 = 11/4.
11/4 + 2/4 = 13/4.
2(3/4) + (2/4) = 13/4.

Question 4.
Solve.
a. 4$$\frac{2}{3}$$ + $$\frac{2}{3}$$

4(2/3) + (2/3) = 16/3.

Explanation:
In the above-given question,
given that,
4(2/3) + (2/3).
3 x 4 = 12.
12 + 2/3 = 14/3.
14/3 + 2/3 = 16/3.
4(2/3) + (2/3) = 16/3.

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

3(3/5) + (4/5) = 22/5.

Explanation:
In the above-given question,
given that,
3(3/5) + (4/5).
3 x 5 = 15.
15 + 3/5 = 18/5.
18/5 + 4/5 = 22/5.
3(3/5) + (4/5) = 22/5.

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

5(4/6) + (5/6) = 39/6.

Explanation:
In the above-given question,
given that,
5(4/6) + (5/6).
5 x 6 = 30.
30 + 4/6 = 34/6.
34/6 + 5/6 = 39/6.
5(4/6) + (5/6) = 39/6.

d. $$\frac{7}{8}$$ + 6$$\frac{4}{8}$$

6(4/8) + (7/8) = 59/8.

Explanation:
In the above-given question,
given that,
6(4/8) + (7/8).
6 x 8 = 48.
48 + 4/8 = 52/8.
52/8 + 7/8 = 59/8.
6(4/8) + (7/8) = 59/8.

e. $$\frac{7}{10}$$ + 7$$\frac{9}{10}$$

7(9/10) + (7/10) = 86/10.

Explanation:
In the above-given question,
given that,
7(9/10) + (7/10).
7 x 10 = 70.
70 + 9/10 = 79/10.
79/10 + 7/10 = 86/10.
7(9/10) + (7/10) = 86/10.

f. 9$$\frac{7}{12}$$ + $$\frac{11}{12}$$

9(7/12) + (11/12) = 126/2.

Explanation:
In the above-given question,
given that,
9(7/12) + (11/12).
9 x 12 = 108.
108 + 7/12 = 115/12.
115/12 + 11/12 = 126/12.
9(7/12) + (11/12) = 126/2.

g. 2$$\frac{70}{100}$$ + $$\frac{87}{100}$$

2(70/100) + (87/100) = 357/100.

Explanation:
In the above-given question,
given that,
2(70/100) + (87/100).
100 x 2 = 200.
200 + 70/100 = 270/100.
270/100 + 87/100 = 357/100.
2(70/100) + (87/100) = 357/100.

h. $$\frac{50}{100}$$ + 16$$\frac{78}{100}$$

16(78/100) + (50/100) = 1728/100.

Explanation:
In the above-given question,
given that,
16(78/100) + (50/100).
100 x 16 = 1600.
1600 + 78/100 = 1678/100.
1678/100 + 50/4 = 1728/100.
16(78/100) + (50/100) = 1728/100.

Question 5.
To solve 7$$\frac{9}{10}$$ + $$\frac{5}{10}$$, Maria thought, “7$$\frac{9}{10}$$ + $$\frac{1}{10}$$ = 8 and 8 + $$\frac{4}{10}$$ = 8 $$\frac{4}{10}$$ .” Paul thought, “7$$\frac{9}{10}$$ + $$\frac{5}{10}$$ = 7 $$\frac{14}{10}$$ = 7 + $$\frac{10}{10}$$ + $$\frac{4}{10}$$ = 8$$\frac{4}{10}$$” Explain why Maria and Paul are both right.

Yes, Maria and Paul are right.

Explanation:
In the above-given question,
given that,
Maria thought,
7$$\frac{9}{10}$$ + $$\frac{1}{10}$$ = 8.
8 + $$\frac{4}{10}$$ = 8$$\frac{4}{10}$$.
7(9/10) + 1/10.
70 + 9/10 + 1/10.
79 + 1/10 = 80/10 = 8.
8 + 4/10 = 84/10.
8 x 4/10 = 84/10.

Eureka Math Grade 4 Module 5 Lesson 30 Exit Ticket Answer Key

Solve.
Question 1.
3$$\frac{2}{5}$$ + __3__ = 4

3(2/5) + 3 = 4.

Explanation:
In the above-given question,
given that,
complete the number sentences.
3(2/5) + 3.
3 x 5 = 15.
15 + 2 = 17.
17 + 3 = 20.
20/5 = 4.

Question 2.
2$$\frac{3}{8}$$ + $$\frac{7}{8}$$

2(3/8) + 7/8 = 26/8.

Explanation:
In the above-given question,
given that,
complete the number sentences.
2(3/8) + 7/8.
2 x 8 = 16.
16 + 3/8 = 19/8.
19/8 + 7/8 = 26/8.
2(3/8) + 7/8 = 26/8.

Question 1.
Solve.
a. 4$$\frac{1}{3}$$ + $$\frac{1}{3}$$

4(1/3) + 1/3 = 14/3.

Explanation:
In the above-given question,
given that,
complete the number sentences.
4(1/3) + 1/3.
4 x 3 = 12.
12 + 1/3 = 13/3.
13/3 + 1/3 = 14/3.
4(1/3) + 1/3 = 14/3.

b. 5$$\frac{1}{4}$$ + $$\frac{2}{4}$$

5(1/4) + 2/4 = 23/4.

Explanation:
In the above-given question,
given that,
complete the number sentences.
5(1/4) + 2/4.
5 x 4 = 20.
20 + 1/4 = 21/4.
21/4 + 2/4 = 23/4.
5(1/4) + 2/4 = 23/4.

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

3(4/6) + 2/6 = 29/8.

Explanation:
In the above-given question,
given that,
complete the number sentences.
3(4/6) + 7/8.
3 x 6 = 18.
18 + 4/6 = 22/6.
22/6 + 7/8 = 29/8.
3(4/6) + 2/6 = 29/8.

d. $$\frac{5}{8}$$ + 7$$\frac{3}{8}$$

7(3/8) + 5/8 = 64/8.

Explanation:
In the above-given question,
given that,
complete the number sentences.
7(3/8) + 5/8.
7 x 8 = 56.
56 + 3/8 = 59/8.
59/8 + 5/8 = 64/8.
7(3/8) + 5/8 = 64/8.

Question 2.
Complete the number sentences.
a. 3$$\frac{5}{6}$$ + __1___ = 4

3(5/6) + 1 = 4.

Explanation:
In the above-given question,
given that,
complete the number sentences.
3(5/6) + 1.
3 x 6 = 18.
18 + 5/6 = 23/6.
1 + 23/6 = 24/6.
24/6 = 4.

b. 5$$\frac{3}{7}$$ + ___4____ = 6

5(3/7) + 4 = 6.

Explanation:
In the above-given question,
given that,
complete the number sentences.
5(3/7) + 4.
5 x 7 = 35.
35 + 3/7 = 38/7.
38/7 + 4 = 42/7.
42/7 = 6.

c. 5 = 4$$\frac{1}{8}$$ + __7____

4(1/8) + 7 = 5.

Explanation:
In the above-given question,
given that,
complete the number sentences.
4(1/8) + 7.
4 x 8 = 32.
32 + 1/8 = 33/8.
7 + 33/8 = 40/8.
40/8 = 5.

d. 15 = 14$$\frac{4}{12}$$ + ___8___

14(4/12) + 8 = 15.

Explanation:
In the above-given question,
given that,
complete the number sentences.
14(4/12) + 8.
14 x 12 = 168.
168 + 4/12 = 172/12.
8 + 172/12 = 180/12.
180/12 = 15.

Question 3.
Draw a number bond and the arrow way to show how to make one. Solve.

5(1/4) + 2/4 = 23/4.

Explanation:
In the above-given question,
given that,
complete the number sentences.
5(1/4) + 2/4.
5 x 4 = 20.
20 + 1/4 = 21/4.
21/4 + 2/4 = 23/4.
5(1/4) + 2/4 = 23/4.

Question 4.
Solve.
a. 2$$\frac{3}{5}$$ + $$\frac{3}{5}$$

2(3/5) + 3/5 = 16/5.

Explanation:
In the above-given question,
given that,
complete the number sentences.
2(3/5) + 3/5.
2 x 5 = 10.
10 + 3/5 = 13/5.
13/5 + 3/5 = 16/5.
2(3/5) + 3/5 = 16/5.

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

3(6/8) + 4/8 = 34/8.

Explanation:
In the above-given question,
given that,
complete the number sentences.
3(6/8) + 4/8.
3 x 8 = 24.
24 + 6/8 = 30/8.
30/8 + 4/8 = 34/8.
3(6/8) + 4/8 = 34/8.

c. 5$$\frac{4}{6}$$ + $$\frac{3}{6}$$

5(4/6) + 3/6 = 37/6.

Explanation:
In the above-given question,
given that,
complete the number sentences.
5(4/6) + 3/6.
5 x 6 = 30.
30 + 4/6 = 34/6.
34/6 + 3/6 = 37/6.
5(4/6) + 3/6 = 37/6.

d. $$\frac{7}{10}$$ + 6$$\frac{6}{10}$$

6(6/10) + 7/10 = 74/10.

Explanation:
In the above-given question,
given that,
complete the number sentences.
6(6/10) + 7/10.
6 x 10 = 60.
60 + 7/10 = 67/10.
67/10 + 7/10 = 74/10.
6(6/10) + 7/10 = 74/10.

e. $$\frac{5}{10}$$ + 8$$\frac{9}{10}$$

8(9/10) + 5/10 = 94/10.

Explanation:
In the above-given question,
given that,
complete the number sentences.
8(9/10) + 5/10.
8 x 10 = 80.
80 + 9/10 = 89/10.
89/10 + 5/10 = 94/10.
8(9/10) + 5/10 = 94/10.

f. 7$$\frac{8}{12}$$ + $$\frac{11}{12}$$

7(8/12) + 11/12 = 103/12.

Explanation:
In the above-given question,
given that,
complete the number sentences.
7(8/12) + 11/12.
7 x 12 = 84.
84 + 8/12 = 92/12.
92/12 + 11/12 = 103/12.
7(8/12) + 11/12 = 103/12.

g. 3$$\frac{90}{100}$$ + $$\frac{58}{100}$$

3(90/100) + 58/100 = 448/100.

Explanation:
In the above-given question,
given that,
complete the number sentences.
3(90/100) + 2/4.
3 x 100 = 300.
300 + 90/100 = 390/100.
390/100 + 58/100 = 448/100.
3(90/100) + 58/100 = 448/100.

h. $$\frac{60}{100}$$ + 14$$\frac{79}{100}$$

14(79/100) + 60/100 = 1539/100.

Explanation:
In the above-given question,
given that,
complete the number sentences.
14(79/100) + 60/100.
14 x 100 = 1400.
1400 + 60/100 = 1460/100.
1460/100 + 79/100 = 1539/100.
14(79/100) + 60/100 = 1539/100.

Question 5.
To solve 4$$\frac{8}{10}$$ + $$\frac{3}{10}$$, Carmen thought, “”4$$\frac{8}{10}$$ + $$\frac{2}{10}$$ = 5, and 5 + $$\frac{1}{10}$$ = 5 $$\frac{1}{10}$$.” Benny thought, “”4$$\frac{8}{10}$$ + $$\frac{3}{10}$$ = 4$$\frac{11}{10}$$ = 4 + $$\frac{10}{10}$$ + $$\frac{1}{10}$$ = 5$$\frac{1}{10}$$.” Explain why Carmen and Benny are both right.