# Spectrum Math Grade 5 Chapter 5 Lesson 5 Answer Key Subtracting Mixed Numbers

Practice with the help of Spectrum Math Grade 5 Answer Key Chapter 5 Lesson 5.5 Subtracting Mixed Numbers regularly and improve your accuracy in solving questions.

## Spectrum Math Grade 5 Chapter 5 Lesson 5.5 Subtracting Mixed Numbers Answers Key

Rename fractions to have common denominators.
Subtract the fractions, then subtract the whole numbers.
Write the difference in simplest form.

Subtract. Write answers in simplest form.

Question 1.
a.

4$$\frac{2}{3}$$ – 2$$\frac{1}{6}$$
4 + $$\frac{2}{3}$$ – 2 – $$\frac{1}{6}$$
4 – 2 = 2
$$\frac{2}{3}$$ – $$\frac{1}{6}$$
LCD is 6
$$\frac{4}{6}$$ – $$\frac{1}{6}$$ = $$\frac{3}{6}$$ = $$\frac{1}{2}$$
2 + $$\frac{1}{2}$$ = 2$$\frac{1}{2}$$

b.

7$$\frac{7}{8}$$ – 2$$\frac{3}{4}$$
7 + $$\frac{7}{8}$$ – 2 – $$\frac{3}{4}$$
7 – 2 = 5
$$\frac{7}{8}$$ – $$\frac{3}{4}$$
LCD is 8
$$\frac{7}{8}$$ – $$\frac{6}{8}$$ = $$\frac{1}{8}$$
5 + $$\frac{1}{8}$$ = 5$$\frac{1}{8}$$

c.

8$$\frac{9}{10}$$ – 6$$\frac{2}{5}$$
8 + $$\frac{9}{10}$$ – 6 – $$\frac{2}{5}$$
8 – 6 = 2
$$\frac{9}{10}$$ – $$\frac{2}{5}$$
LCD is 10
$$\frac{9}{10}$$ – $$\frac{4}{10}$$ = $$\frac{5}{10}$$ = $$\frac{1}{2}$$
2 + $$\frac{1}{2}$$ = 2$$\frac{1}{2}$$

d.

8$$\frac{3}{4}$$ – 4$$\frac{3}{8}$$
8 + $$\frac{3}{4}$$ – 4 – $$\frac{3}{8}$$
8 – 4 = 4
$$\frac{3}{4}$$ – $$\frac{3}{8}$$
LCD is 8.
$$\frac{6}{8}$$ – $$\frac{3}{8}$$ = $$\frac{3}{8}$$
4 + $$\frac{3}{8}$$ = 4$$\frac{3}{8}$$

e.

3$$\frac{1}{3}$$ – 2$$\frac{2}{9}$$
3 + $$\frac{1}{3}$$ – 2 – $$\frac{2}{9}$$
3 – 2 = 1
$$\frac{1}{3}$$ – $$\frac{2}{9}$$
LCD is 9.
$$\frac{3}{9}$$ – $$\frac{2}{9}$$ = $$\frac{1}{9}$$
1 + $$\frac{1}{9}$$ = 1$$\frac{1}{9}$$

Question 2.
a.

6$$\frac{5}{8}$$ – 4$$\frac{3}{7}$$
6 + $$\frac{5}{8}$$ – 4 – $$\frac{3}{7}$$
6 – 4 = 2
$$\frac{5}{8}$$ – $$\frac{3}{7}$$
LCD is 56
$$\frac{35}{56}$$ – $$\frac{24}{56}$$ = $$\frac{11}{56}$$
2 + $$\frac{11}{56}$$ = 2$$\frac{11}{56}$$

b.

5$$\frac{1}{2}$$ – 1$$\frac{1}{6}$$
5 + $$\frac{1}{2}$$ – 1 – $$\frac{1}{6}$$
5 – 1 = 4
$$\frac{1}{2}$$ – $$\frac{1}{6}$$
LCD is 6.
$$\frac{3}{6}$$ – $$\frac{1}{6}$$ = $$\frac{2}{6}$$ = $$\frac{1}{3}$$
4 + $$\frac{1}{3}$$ = 4$$\frac{1}{3}$$

c.

9$$\frac{7}{8}$$ – 4$$\frac{2}{5}$$
9 + $$\frac{7}{8}$$ – 4 – $$\frac{2}{5}$$
9 – 4 = 5
$$\frac{7}{8}$$ – $$\frac{2}{5}$$
LCD is 40
$$\frac{35}{40}$$ – $$\frac{16}{40}$$ = $$\frac{19}{40}$$
5 + $$\frac{19}{40}$$ = 5$$\frac{19}{40}$$

d.

9$$\frac{5}{9}$$ – 3$$\frac{1}{3}$$
9 + $$\frac{5}{9}$$ – 3 – $$\frac{1}{3}$$
9 – 3 = 6
$$\frac{5}{9}$$ – $$\frac{1}{3}$$
LCD is 9
$$\frac{5}{9}$$ – $$\frac{3}{9}$$ = $$\frac{2}{9}$$
6 + $$\frac{2}{9}$$ = 6$$\frac{2}{9}$$

e.

7$$\frac{7}{10}$$ – 4$$\frac{4}{7}$$
7 + $$\frac{7}{10}$$ – 4 – $$\frac{4}{7}$$
7 – 4 = 3
$$\frac{7}{10}$$ – $$\frac{4}{7}$$
LCD is 70.
$$\frac{49}{70}$$ – $$\frac{40}{70}$$ = $$\frac{9}{70}$$
3 + $$\frac{9}{70}$$ = 3$$\frac{9}{70}$$

Question 3.
a.

8$$\frac{8}{12}$$ – 2$$\frac{3}{4}$$
8 + $$\frac{8}{12}$$ – 2 – $$\frac{3}{4}$$
8 – 2 = 6
$$\frac{8}{12}$$ – $$\frac{3}{4}$$
LCD is 12
$$\frac{8}{12}$$ – $$\frac{9}{12}$$ = –$$\frac{1}{12}$$
6 – $$\frac{1}{12}$$ = 5$$\frac{11}{12}$$

b.

9$$\frac{3}{10}$$ – 6$$\frac{1}{8}$$
9 + $$\frac{3}{10}$$ – 6 – $$\frac{1}{8}$$
9 – 6 = 3
$$\frac{3}{10}$$ – $$\frac{1}{8}$$
LCD is 40
$$\frac{12}{40}$$ – $$\frac{5}{40}$$ = $$\frac{7}{40}$$
3 + $$\frac{7}{40}$$ = 3$$\frac{7}{40}$$

c.

8$$\frac{4}{6}$$ – 5$$\frac{2}{8}$$
8 + $$\frac{4}{6}$$ – 5 – $$\frac{2}{8}$$
8 – 5 = 3
$$\frac{4}{6}$$ – $$\frac{2}{8}$$
LCD is 24
$$\frac{16}{24}$$ – $$\frac{6}{24}$$ = $$\frac{10}{24}$$ = $$\frac{5}{12}$$
3 + $$\frac{5}{12}$$ = 3$$\frac{5}{12}$$

d.

6$$\frac{6}{7}$$ – 3$$\frac{3}{5}$$
6 + $$\frac{6}{7}$$ – 3 – $$\frac{3}{5}$$
6 – 3 = 3
$$\frac{6}{7}$$ – $$\frac{3}{5}$$
LCD is 35
$$\frac{30}{35}$$ – $$\frac{21}{35}$$ = $$\frac{9}{35}$$
3 + $$\frac{9}{35}$$ = 3$$\frac{9}{35}$$

e.

5$$\frac{5}{6}$$ – 3$$\frac{1}{12}$$
5 + $$\frac{5}{6}$$ – 3 – $$\frac{1}{12}$$
5 – 3 = 2
$$\frac{5}{6}$$ – $$\frac{1}{12}$$
LCD is 6.
$$\frac{5}{6}$$ – $$\frac{3}{6}$$ = $$\frac{2}{6}$$ = $$\frac{1}{3}$$
2 + $$\frac{1}{3}$$ = 2$$\frac{1}{3}$$

Subtract. Write answers in simplest form.

Question 1.
a.

4 – $$\frac{3}{8}$$ = 3$$\frac{5}{8}$$

b.

5$$\frac{5}{6}$$ – 1$$\frac{1}{3}$$
5 + $$\frac{5}{6}$$ – 1 – $$\frac{1}{3}$$
5 – 1 = 4
$$\frac{5}{6}$$ – $$\frac{1}{3}$$
LCD is 6.
$$\frac{5}{6}$$ – $$\frac{2}{6}$$ = $$\frac{3}{6}$$ = $$\frac{1}{2}$$
4 + $$\frac{1}{2}$$ = 4$$\frac{1}{2}$$

c.

8 – 3$$\frac{5}{8}$$
8 – 3 – $$\frac{5}{8}$$
8 – 3 = 5
5 – $$\frac{5}{8}$$ = 4$$\frac{3}{8}$$

d.

4$$\frac{3}{5}$$ – $$\frac{3}{10}$$
4 + $$\frac{3}{5}$$ – $$\frac{3}{10}$$
$$\frac{3}{5}$$ – $$\frac{3}{10}$$
LCD is 10
$$\frac{6}{10}$$ – $$\frac{3}{10}$$ = $$\frac{3}{10}$$
4 + $$\frac{3}{10}$$ = 4$$\frac{3}{10}$$

Question 2.
a.

5$$\frac{3}{4}$$ – 4$$\frac{5}{8}$$
5 + $$\frac{3}{4}$$ – 4 – $$\frac{5}{8}$$
5 – 4 = 1
$$\frac{3}{4}$$ – $$\frac{5}{8}$$
LCD is 8.
$$\frac{6}{8}$$ – $$\frac{5}{8}$$ = $$\frac{1}{8}$$
1 + $$\frac{1}{8}$$ = 1$$\frac{1}{8}$$

b.

8$$\frac{2}{3}$$ – 4$$\frac{1}{6}$$
8 + $$\frac{2}{3}$$ – 4 – $$\frac{1}{6}$$
8 – 4 = 4
$$\frac{2}{3}$$ – $$\frac{1}{6}$$
LCD is 6
$$\frac{4}{6}$$ – $$\frac{1}{6}$$ = $$\frac{3}{6}$$ = $$\frac{1}{2}$$
4 + $$\frac{1}{2}$$ = 4$$\frac{1}{2}$$

c.

5$$\frac{5}{6}$$ – 3$$\frac{3}{4}$$
5 + $$\frac{5}{6}$$ – 3 – $$\frac{3}{4}$$
5 – 3 = 2
$$\frac{5}{6}$$ – $$\frac{3}{4}$$
LCD is 12
$$\frac{10}{12}$$ – $$\frac{9}{12}$$ = $$\frac{1}{12}$$
2 + $$\frac{1}{12}$$ = 2$$\frac{1}{12}$$

d.

7$$\frac{4}{5}$$ – 2$$\frac{1}{2}$$
7 + $$\frac{4}{5}$$ – 2 – $$\frac{1}{2}$$
7 – 2 = 5
$$\frac{4}{5}$$ – $$\frac{1}{2}$$
LCD is 10
$$\frac{8}{10}$$ – $$\frac{5}{10}$$ = $$\frac{3}{10}$$
5 + $$\frac{3}{10}$$ = 5$$\frac{3}{10}$$

Question 3.
a.

5$$\frac{3}{8}$$ – 2$$\frac{7}{8}$$
5 + $$\frac{3}{8}$$ – 2 – $$\frac{7}{8}$$
5 – 2 = 3
$$\frac{3}{8}$$ – $$\frac{7}{8}$$ = –$$\frac{1}{2}$$
3 – $$\frac{1}{2}$$ = 2$$\frac{1}{2}$$

b.

3$$\frac{1}{4}$$ – 2$$\frac{3}{4}$$
3 + $$\frac{1}{4}$$ – 2 – $$\frac{3}{4}$$
3 – 2 = 1
$$\frac{1}{4}$$ – $$\frac{3}{4}$$ = –$$\frac{1}{2}$$
1 – $$\frac{1}{2}$$ = $$\frac{1}{2}$$

c.

8$$\frac{2}{5}$$ – 3$$\frac{4}{5}$$
8 + $$\frac{2}{5}$$ – 3 – $$\frac{4}{5}$$
8 – 3 = 5
$$\frac{2}{5}$$ – $$\frac{4}{5}$$ = –$$\frac{2}{5}$$
5 – $$\frac{2}{5}$$ = 4$$\frac{3}{5}$$

d.

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

Question 4.
a.

4$$\frac{3}{4}$$ – 2$$\frac{7}{8}$$
4 + $$\frac{3}{4}$$ – 2 – $$\frac{7}{8}$$
4 – 2 = 2
$$\frac{3}{4}$$ – $$\frac{7}{8}$$
LCD is 8
$$\frac{6}{8}$$ – $$\frac{7}{8}$$ = –$$\frac{1}{8}$$
2 – $$\frac{1}{8}$$ = 1$$\frac{7}{8}$$

b.

6$$\frac{1}{2}$$ – 3$$\frac{2}{3}$$
6 + $$\frac{1}{2}$$ – 3 – $$\frac{2}{3}$$
6 – 3 = 3
$$\frac{1}{2}$$ – $$\frac{2}{3}$$
LCD is 6.
$$\frac{3}{6}$$ – $$\frac{4}{6}$$ = –$$\frac{1}{6}$$
3 – $$\frac{1}{6}$$ = 2$$\frac{5}{6}$$

c.

5 – 2$$\frac{3}{3}$$
5 – 3 = 2

d.

3 – $$\frac{5}{6}$$ = 2$$\frac{1}{6}$$

Question 5.
a.

2$$\frac{1}{2}$$ – 1$$\frac{4}{11}$$
2 + $$\frac{1}{2}$$ – 1 – $$\frac{4}{11}$$
2 – 1 = 1
$$\frac{1}{2}$$ – $$\frac{4}{11}$$
$$\frac{11}{22}$$ – $$\frac{8}{22}$$ = $$\frac{3}{22}$$
1 + $$\frac{3}{22}$$ = 1$$\frac{3}{22}$$

b.

5$$\frac{7}{10}$$ – 2$$\frac{3}{8}$$
5 + $$\frac{7}{10}$$ – 2 – $$\frac{3}{8}$$
5 – 2 = 3
$$\frac{7}{10}$$ – $$\frac{3}{8}$$
LCD is 40
$$\frac{28}{40}$$ – $$\frac{15}{40}$$ = $$\frac{13}{40}$$
3 + $$\frac{13}{40}$$ = 3$$\frac{13}{40}$$

c.

9$$\frac{7}{8}$$ – 8$$\frac{2}{9}$$
9 + $$\frac{7}{8}$$ – 8 – $$\frac{2}{9}$$
9 – 8 = 1
$$\frac{7}{8}$$ – $$\frac{2}{9}$$
LCD is 72
$$\frac{63}{72}$$ – $$\frac{16}{72}$$ = $$\frac{47}{72}$$
1 + $$\frac{47}{72}$$ = 1$$\frac{47}{72}$$

d.

7$$\frac{3}{4}$$ – 6$$\frac{7}{12}$$
7 + $$\frac{3}{4}$$ – 6 – $$\frac{7}{12}$$
$$\frac{3}{4}$$ – $$\frac{7}{12}$$
$$\frac{9}{12}$$ – $$\frac{7}{12}$$ = $$\frac{2}{12}$$ = $$\frac{1}{6}$$
1 + $$\frac{1}{6}$$ = 1$$\frac{1}{6}$$