## Engage NY Eureka Math 4th Grade Module 6 Lesson 13 Answer Key

### Eureka Math Grade 4 Module 6 Lesson 13 Problem Set Answer Key

Question 1.
Solve. Convert tenths to hundredths before finding the sum. Rewrite the complete number sentence in decimal form. Problems 1(a) and 1(b) are partially completed for you.
a. 2$$\frac{1}{10}$$ + $$\frac{3}{100}$$ = 2$$\frac{10}{100}$$ + $$\frac{3}{100}$$ = ___2.13____
2.1 + 0.03 = __2.13_____

2.1 + 0.03 = 2.13.

Explanation:
In the above-given question,
given that,
2$$\frac{1}{10}$$ + $$\frac{3}{100}$$.
2$$\frac{10}{100}$$ + $$\frac{3}{100}$$.
2 + 1/10 = 2 + 0.1 = 2.1.
3/100 = 0.03.
2.1 + 0.03.
2.13.

b. 2$$\frac{1}{10}$$ + 5$$\frac{3}{100}$$ = 2$$\frac{10}{100}$$ + 5$$\frac{3}{100}$$ = _7.13_____

2.1 + 5.03 = 7.13.

Explanation:
In the above-given question,
given that,
2$$\frac{1}{10}$$ + 5$$\frac{3}{100}$$.
2$$\frac{10}{100}$$ +5 $$\frac{3}{100}$$.
2 + 1/10 = 2 + 0.1 = 2.1.
5 + 3/100 = 5 + 0.03 = 5.03.
2.1 + 5.03.
7.13.

c. 3$$\frac{24}{100}$$ + $$\frac{7}{10}$$

0.7 + 3.24 = 3.94.

Explanation:
In the above-given question,
given that,
$$\frac{7}{10}$$ + 3$$\frac{24}{100}$$.
$$\frac{70}{100}$$ + 3$$\frac{24}{100}$$.
7/10 = 0.7 = 0.7.
3 + 24/100 = 3 + 0.24 = 3.24.
0.7 + 3.24.
3.94.

d. 3$$\frac{24}{100}$$ + 8$$\frac{7}{10}$$

8.7 + 3.24 = 11.94.

Explanation:
In the above-given question,
given that,
8$$\frac{7}{10}$$ + 3$$\frac{24}{100}$$.
8$$\frac{70}{100}$$ + 3$$\frac{24}{100}$$.
8 + 7/10 = 8 + 0.7 = 8.7.
3 + 24/100 = 3 + 0.24 = 3.24.
8.7 + 3.24.
11.94.

Question 2.
Solve. Then, rewrite the complete number sentence in decimal form.
a. 6$$\frac{9}{10}$$ + 1$$\frac{10}{100}$$
b. 9$$\frac{9}{10}$$ + 2$$\frac{45}{100}$$
c. 2$$\frac{4}{10}$$ + 8$$\frac{90}{100}$$
d. 6$$\frac{37}{100}$$ + 7$$\frac{7}{10}$$

a. 7.91.

Explanation:
In the above-given question,
given that,
6$$\frac{9}{10}$$ + 1$$\frac{10}{100}$$.
6 + 9/10 = 6 + 0.9 = 6.9.
1 + 10/100 = 1 + 0.01 = 1.01.
6.9 + 1.01.
7.91.

b. 11.115.

Explanation:
In the above-given question,
given that,
9$$\frac{9}{10}$$ + 2$$\frac{45}{100}$$.
9 + 9/10 = 9 + 0.9 = 9.9.
2 + 45/100 = 2 + 0.45 = 2.45.
9.9 + 2.45.
11. 115.

c. 10.49.

Explanation:
In the above-given question,
given that,
2$$\frac{4}{10}$$ + 8$$\frac{90}{100}$$.
2 + 4/10 = 2 + 0.4 = 2.4.
8 + 90/100 = 8 + 0.09 = 8.09.
2.4 + 8.09.
10.49.

d. 13.107.

Explanation:
In the above-given question,
given that,
7$$\frac{7}{10}$$ + 6$$\frac{37}{100}$$.
7 + 7/10 = 7 + 0.7 = 7.7.
6 + 37/100 = 6 + 0.37 = 6.37.
7.7 + 6.37.
13.107.

Question 3.
Solve by rewriting the number sentence in fraction form. After solving, rewrite the complete number sentence in decimal form.
a. 6.4 + 5.3
b. 6.62 + 2.98
c. 2.1 + 0.94
d. 2.1 + 5.94
e. 5.7 + 4.92
f. 5.68 + 4.9
g. 4.8 + 3.27
h. 17.6 + 3.59

a. 11.7.

Explanation:
In the above-given question,
given that,
6$$\frac{4}{10}$$ + 5$$\frac{3}{10}$$.
6 + 4/10 = 6 + 0.4 = 6.4.
5 + 3/10 = 5 + 0.3 = 5.3.
6.4 + 5.3.
11.7.

b. 8.1510.

Explanation:
In the above-given question,
given that,
6$$\frac{9}{10}$$ + 2$$\frac{98}{100}$$.
6 + 62/100 = 6 + 0.62 = 6.62.
2 + 98/100 = 2 + 0.98 = 2.98.
6.62 + 2.98.
8.1510.

c. 2.104.

Explanation:
In the above-given question,
given that,
2$$\frac{1}{10}$$ + $$\frac{94}{100}$$.
2 + 1/10 = 2 + 0.1 = 2.1.
94/100 =  0.94 = 0.94.
2.1 + 0.94.
2.104.

d. 7.104.

Explanation:
In the above-given question,
given that,
2$$\frac{1}{10}$$ + 5$$\frac{94}{100}$$.
2 + 1/10 = 2 + 0.1 = 2.1.
5 + 94/100 = 5 + 0.94 = 5.94.
2.1 + 5.94.
7.104.

e. 9.162.

Explanation:
In the above-given question,
given that,
5$$\frac{7}{10}$$ + 4$$\frac{92}{100}$$.
5 + 7/10 = 5 + 0.7 = 5.7.
4 + 92/100 = 4 + 0.92 = 4.92.
5.7 + 4.92.
9.162.

f. 4.9 + 5.68.

Explanation:
In the above-given question,
given that,
4$$\frac{9}{10}$$ + 5$$\frac{68}{100}$$.
4 + 9/10 = 4 + 0.9 = 4.9.
5 + 68/100 = 5 + 0.68 = 5.68.
4.9 + 5.68.

g. 4.8 + 3.27.

Explanation:
In the above-given question,
given that,
4$$\frac{8}{10}$$ + 3$$\frac{27}{100}$$.
4 + 8/10 = 4 + 0.8 = 4.8.
3 + 27/100 = 3 + 0.27 = 3.27.
4.8 + 3.27.

h. 17.6 + 3.59.

Explanation:
In the above-given question,
given that,
17$$\frac{6}{10}$$ + 3$$\frac{59}{100}$$.
17 + 6/10 = 17 + 0.6 = 17.6.
3 + 59/100 = 3 + 0.59 = 3.59.
17.6 + 3.59.

Eureka Math Grade 4 Module 6 Lesson 13 Exit Ticket Answer Key

Solve by rewriting the number sentence in fraction form. After solving, rewrite the complete number sentence in decimal form.
Question 1.
7.3 + 0.95

8.25.

Explanation:
In the above-given question,
given that,
7$$\frac{3}{10}$$ + $$\frac{95}{100}$$.
7 + 3/10 = 7 + 0.3 = 7.3.
0 + 95/100 = 0 + 0.95 = 0.95.
7.3 + 0.95.

Question 2.
8.29 + 5.9

14.19.

Explanation:
In the above-given question,
given that,
5$$\frac{9}{10}$$ + 8$$\frac{29}{100}$$.
5 + 9/10 = 5 + 0.9 = 5.9.
8 + 29/100 = 8 + 0.29 = 8.29.
5.9 + 8.29.
14.19.

Question 1.
Solve. Convert tenths to hundredths before finding the sum. Rewrite the complete number sentence in decimal form. Problems 1(a) and 1(b) are partially completed for you.
a. 5$$\frac{2}{10}$$ + $$\frac{7}{100}$$ = 5$$\frac{20}{100}$$ + $$\frac{7}{100}$$ = ___5.27_____
5.2 + 0.07 = __5.27____

5.2 + 0.07 = 5.27.

Explanation:
In the above-given question,
given that,
5$$\frac{2}{10}$$ + $$\frac{7}{100}$$.
5$$\frac{20}{100}$$ + $$\frac{7}{100}$$.
5 + 2/10 = 5 + 0.2 = 5.2.
7/100 = 0.07.
5.2 + 0.07.
5.27.

b. 5$$\frac{2}{10}$$ + 3$$\frac{7}{100}$$ = 8$$\frac{20}{100}$$ + $$\frac{7}{100}$$ = ___8.27_____

5.2 + 3.07 = 8.27.

Explanation:
In the above-given question,
given that,
5$$\frac{2}{10}$$ +3 $$\frac{7}{100}$$.
5$$\frac{20}{100}$$ +3 $$\frac{7}{100}$$.
5 + 20/100 = 5 + 0.2 = 5.2.
7/100 = 0.07 + 3 = 3.07.
5.2 + 3.07.
8.27.

c. 6$$\frac{5}{10}$$ + $$\frac{1}{100}$$

6.5 + 0.01 = 6.51.

Explanation:
In the above-given question,
given that,
6$$\frac{5}{10}$$ + $$\frac{1}{100}$$.
6$$\frac{50}{100}$$ + $$\frac{1}{100}$$.
6 + 5/10 = 6 + 0.5 = 6.5.
1/100 = 0.01.
6.5 + 0.01.
6.51.

d. 6$$\frac{5}{10}$$ + 7$$\frac{1}{100}$$

2.1 + 0.03 = 2.13.

Explanation:
In the above-given question,
given that,
6$$\frac{5}{10}$$ + 7$$\frac{1}{100}$$.
6$$\frac{50}{100}$$ +7 $$\frac{1}{100}$$.
6 + 5/10 = 6 + 0.5 = 6.5.
7 + 1/100 = 0.01 + 7.
6.5 + 0.07.
6.57.

Question 2.
Solve. Then, rewrite the complete number sentence in decimal form.
a. 4$$\frac{9}{10}$$ + 5$$\frac{10}{10}$$
b. 8$$\frac{7}{10}$$ + 2$$\frac{65}{100}$$
c. 7$$\frac{3}{10}$$ + 6$$\frac{87}{100}$$
d. 5$$\frac{48}{100}$$ + 7$$\frac{8}{10}$$

4.9 + 6 = 10.9.

Explanation:
In the above-given question,
given that,
4$$\frac{9}{10}$$ + 5$$\frac{10}{10}$$.
4$$\frac{90}{100}$$ + 5$$\frac{100}{100}$$.
4 + 9/10 = 4 + 0.9 = 4.9.
5 + 10/10 = 6.
4.9 + 6.
10.9.

8.7 + 2.65 = 11.35.

Explanation:
In the above-given question,
given that,
8$$\frac{7}{10}$$ + 2 $$\frac{65}{100}$$.
8$$\frac{70}{100}$$ + 2$$\frac{65}{100}$$.
8 + 7/10 = 8 + 0.7 = 8.7.
2 + 65/100 = 2 + 0.65 = 2.65.
8.7 + 2.65.
11.35.

7.3 + 0.87 = 8.17.

Explanation:
In the above-given question,
given that,
7$$\frac{3}{10}$$ +6 $$\frac{87}{100}$$.
7$$\frac{30}{100}$$ +6 $$\frac{87}{100}$$.
7 + 3/10 = 7 + 0.3 = 7.3.
6 + 87/100 = 6 + 0.87.
7.3 + 0.87.
8.17.

7.8 + 0.48 = 8.28.

Explanation:
In the above-given question,
given that,
7$$\frac{8}{10}$$ + 5$$\frac{48}{100}$$.
7$$\frac{80}{100}$$ + 5$$\frac{48}{100}$$.
7 + 8/10 = 7 + 0.8 = 7.8.
48/100 = 0.48.
7.8 + 0.48.
8.28.

Question 3.
Solve by rewriting the number sentence in fraction form. After solving, rewrite the complete number sentence in decimal form.
a. 2.1 + 0.87 = 2$$\frac{1}{10}$$ + $$\frac{87}{100}$$
b. 7.2 + 2.67 = 7$$\frac{2}{10}$$ + 2$$\frac{67}{100}$$
c. 7.3 + 1.8 = 7$$\frac{3}{10}$$ +1 $$\frac{8}{10}$$
d. 7.3 + 1.86 = 7$$\frac{3}{10}$$ + 1 $$\frac{86}{100}$$
e. 6.07 + 3.93 = 6$$\frac{7}{100}$$ + 3$$\frac{93}{100}$$
f. 6.87 + 3.9 = 3$$\frac{9}{10}$$ +6 $$\frac{87}{100}$$
g. 8.6 + 4.67 = 8$$\frac{6}{10}$$ + 4$$\frac{67}{100}$$
h. 18.62 + 14.7 = 14$$\frac{7}{10}$$ + 18$$\frac{62}{100}$$

a. 7$$\frac{2}{10}$$ +2 $$\frac{67}{100}$$.

Explanation:
In the above-given question,
given that,
7$$\frac{2}{10}$$ +2 $$\frac{67}{100}$$.
7 + 2/10 = 7 + 0.2 = 7.2.
2 + 67/100 = 2 + 0.67.
7.2 + 0.67.
7.87.

b. 2$$\frac{1}{10}$$ + $$\frac{87}{100}$$.

Explanation:
In the above-given question,
given that,
2$$\frac{1}{10}$$ + $$\frac{87}{100}$$.
2 + 1/10 = 2 + 0.1 = 2.1.
87/100 =  0.87.
2.1 + 0.87.
2.97.

c. 7$$\frac{3}{10}$$ +1 $$\frac{8}{10}$$.

Explanation:
In the above-given question,
given that,
7$$\frac{3}{10}$$ + 1$$\frac{87}{100}$$.
7 + 3/10 = 7 + 0.3 = 7.3.
1 + 87/100 = 1 +0.87.= 1.87
7.3 + 1.87.
9.17.

d. 7$$\frac{3}{10}$$ + 1$$\frac{86}{100}$$.

Explanation:
In the above-given question,
given that,
7$$\frac{3}{10}$$ + 1$$\frac{86}{100}$$.
7 + 3/10 = 7 + 0.3 = 7.3.
86/100 = 1 + 0.86.
7 .3+ 1.86.
9.16.

e. 6$$\frac{7}{100}$$ +3 $$\frac{93}{100}$$.

Explanation:
In the above-given question,
given that,
6$$\frac{7}{100}$$ +3 $$\frac{93}{100}$$.
6 + 7/100 = 6 + 0.07 = 6.07.
3 + 93/100 = 3 + 0.93.
6.07 + 0.93.
7.00.

f. 3$$\frac{9}{10}$$ +6 $$\frac{87}{100}$$.

Explanation:
In the above-given question,
given that,
3$$\frac{9}{10}$$ +6 $$\frac{87}{100}$$.
3 + 9/10 = 3 + 0.9 = 3.9.
6 + 87/100 =  6 + 0.87 = 6.87.
3.9 + 6.87.
10.77.

g. 8$$\frac{6}{10}$$ + 4$$\frac{67}{100}$$.

Explanation:
In the above-given question,
given that,
8$$\frac{6}{10}$$ +4 $$\frac{67}{100}$$.
8 + 6/10 = 8 + 0.6 = 8.6.
67/100 = 4 + 0.67 = 4.67.
8.6 + 4.67.
13.27.

h. 14$$\frac{7}{10}$$ +18 $$\frac{62}{100}$$.
14$$\frac{7}{10}$$ +18 $$\frac{62}{100}$$.