# Spectrum Math Grade 4 Chapter 6 Lesson 11 Answer Key Adding Mixed Numerals with Like Denominators

This handy Spectrum Math Grade 4 Answer Key Chapter 6 Lesson 6.11 Adding Mixed Numerals with Like Denominators provides detailed answers for the workbook questions.

## Spectrum Math Grade 4 Chapter 6 Lesson 6.11 Adding Mixed Numerals with Like Denominators Answers Key

$$\frac{4}{9}$$ + $$\frac{2}{9}$$ = $$\frac{6}{9}$$
3 + 2 = 5
Reduce to simplest form. $$\frac{6}{9} \div \frac{3}{3}$$ = $$\frac{2}{3}$$

Question 1.
a.

9

Explanation:
$$\frac{4}{7}$$ + $$\frac{3}{7}$$ = $$\frac{7}{7}$$ = 1
3 + 5 = 8
Therefore, 8 + 1 = 9

b.

15

Explanation:
$$\frac{4}{9}$$ + $$\frac{5}{9}$$ = $$\frac{9}{9}$$ = 1
6 + 8 = 14
Hence, 14 + 1 = 15

c.

10$$\frac{1}{3}$$

Explanation:
$$\frac{1}{6}$$ + $$\frac{1}{6}$$ = $$\frac{2}{6}$$
7 + 3 = 10
Reduce to simplest form.
$$\frac{2}{6} \div \frac{2}{2}$$ = $$\frac{1}{3}$$
Hence, 10$$\frac{1}{3}$$

d.

7$$\frac{1}{5}$$

Explanation:
$$\frac{2}{5}$$ + $$\frac{4}{5}$$ = $$\frac{6}{5}$$
2 + 4 = 6
6 $$\frac{6}{5}$$ = $$\frac{36}{5}$$
Reduce to simplest form.
7$$\frac{1}{5}$$

e.

11$$\frac{10}{11}$$

Explanation:
$$\frac{2}{11}$$ + $$\frac{8}{11}$$ = $$\frac{10}{11}$$
3 + 8 = 11
Hence, 11 $$\frac{10}{11}$$

Question 2.
a.

12$$\frac{1}{5}$$

Explanation:
$$\frac{3}{10}$$ + $$\frac{9}{10}$$ = $$\frac{12}{10}$$
$$\frac{12}{10} \div \frac{2}{2}$$ = $$\frac{6}{5}$$
9 + 2 = 11
Reduce to simplest form.
11$$\frac{6}{5}$$ = $$\frac{61}{5}$$ = 12$$\frac{1}{5}$$

b.

9$$\frac{1}{4}$$

Explanation:
$$\frac{1}{8}$$ + $$\frac{3}{8}$$ = $$\frac{4}{8}$$
5 + 4 = 9
Reduce to simplest form.
$$\frac{4}{8} \div \frac{4}{4}$$ = $$\frac{1}{4}$$
Hence, 9 $$\frac{1}{4}$$

c.

5$$\frac{1}{7}$$

Explanation:
$$\frac{6}{7}$$ + $$\frac{2}{7}$$ = $$\frac{8}{7}$$
1 + 3 = 4
So, 4 $$\frac{8}{7}$$ = $$\frac{36}{7}$$
Reduce to simplest form.
5 $$\frac{1}{7}$$

d.

15$$\frac{1}{2}$$

Explanation:
$$\frac{3}{4}$$ + $$\frac{3}{4}$$ = $$\frac{6}{4}$$
Reduce to simplest form.
$$\frac{6}{4} \div \frac{2}{2}$$ = $$\frac{3}{2}$$
8 + 6 = 14
So, 14$$\frac{3}{2}$$ = $$\frac{31}{2}$$
Reduce to simplest form.
15$$\frac{1}{2}$$

e.

9$$\frac{4}{9}$$

Explanation:
$$\frac{2}{9}$$ + $$\frac{2}{9}$$ = $$\frac{4}{9}$$
2 + 7 = 9
So, 9$$\frac{4}{9}$$

Question 3.
a.

7$$\frac{7}{11}$$

Explanation:
$$\frac{4}{11}$$ + $$\frac{3}{11}$$ = $$\frac{7}{11}$$
6 + 1 = 7
So, 7$$\frac{7}{11}$$

b.

8

Explanation:
$$\frac{1}{10}$$ + $$\frac{9}{10}$$ = $$\frac{10}{10}$$ = 1
3 + 4 = 7
So, 7 + 1 = 8

c.

12$$\frac{2}{3}$$

Explanation:
$$\frac{5}{6}$$ + $$\frac{5}{6}$$ = $$\frac{10}{6}$$
6 + 5 = 11
So, 11 $$\frac{10}{6}$$
Reduce to simplest form.
$$\frac{76}{6}$$ = 12$$\frac{2}{3}$$

d.

13$$\frac{3}{4}$$

Explanation:
$$\frac{3}{8}$$ + $$\frac{3}{8}$$ = $$\frac{6}{8}$$
5 + 8 = 13
Reduce to simplest form.
$$\frac{6}{8} \div \frac{2}{2}$$ = $$\frac{3}{4}$$
Therefore, 13$$\frac{3}{4}$$

e.

8$$\frac{2}{7}$$

Explanation:
$$\frac{5}{7}$$ + $$\frac{4}{7}$$ = $$\frac{9}{7}$$
1 + 6 = 7
So, 7 $$\frac{9}{7}$$
Reduce to simplest form.
$$\frac{58}{7}$$ = 8$$\frac{2}{7}$$

Question 4.
a.

10$$\frac{5}{6}$$

Explanation:
$$\frac{11}{12}$$ + $$\frac{11}{12}$$ = $$\frac{22}{12}$$
Reduce to simplest form.
$$\frac{22}{12} \div \frac{2}{2}$$ = $$\frac{11}{6}$$
2 + 7 = 9
Hence, 9 $$\frac{11}{6}$$
Reduce to simplest form.
$$\frac{65}{6}$$ = 10$$\frac{5}{6}$$

b.

16$$\frac{4}{5}$$

Explanation:
$$\frac{3}{5}$$ + $$\frac{1}{5}$$ = $$\frac{4}{5}$$
8 + 8 = 16
So, 16$$\frac{4}{5}$$

c.

14

Explanation:
$$\frac{5}{12}$$ + $$\frac{7}{12}$$ = $$\frac{12}{12}$$ = 1
9 + 4 = 13
So, 13 + 1 = 14

d.

8$$\frac{2}{3}$$

Explanation:
$$\frac{8}{9}$$ + $$\frac{7}{9}$$ = $$\frac{15}{9}$$
2 + 5 = 7
Reduce to simplest form.
$$\frac{15}{9} \div \frac{3}{3}$$ = $$\frac{5}{3}$$
Therefore, 7$$\frac{5}{3}$$
Reduce to simplest form.
$$\frac{26}{3}$$ = 8$$\frac{2}{3}$$

e.

14$$\frac{4}{5}$$

Explanation:
$$\frac{9}{10}$$ + $$\frac{9}{10}$$ = $$\frac{18}{10}$$
$$\frac{18}{10} \div \frac{2}{2}$$ = $$\frac{9}{5}$$
So, 13$$\frac{9}{5}$$
= $$\frac{74}{5}$$
= 14$$\frac{4}{5}$$