Adding and Subtracting Fractions Worksheets with Answer Key - Free Printable

To solve the problems involving adding and subtracting mixed fractions, we need to follow these steps:

1. Convert mixed fractions to improper fractions (if necessary).
2. Find a common denominator for the fractions.
3. Perform the addition or subtraction.
4. Simplify the result (convert back to a mixed fraction if needed).

Let's solve each problem step by step.

---

Problem 1: \( 7 \frac{1}{2} + 1 \frac{7}{8} \)

#### Step 1: Convert to improper fractions
- \( 7 \frac{1}{2} = 7 + \frac{1}{2} = \frac{14}{2} + \frac{1}{2} = \frac{15}{2} \)
- \( 1 \frac{7}{8} = 1 + \frac{7}{8} = \frac{8}{8} + \frac{7}{8} = \frac{15}{8} \)

#### Step 2: Find a common denominator
The denominators are 2 and 8. The least common denominator (LCD) is 8.

- Convert \( \frac{15}{2} \) to a fraction with denominator 8:
\[
\frac{15}{2} = \frac{15 \times 4}{2 \times 4} = \frac{60}{8}
\]

#### Step 3: Add the fractions
\[
\frac{60}{8} + \frac{15}{8} = \frac{60 + 15}{8} = \frac{75}{8}
\]

#### Step 4: Convert back to a mixed fraction
\[
\frac{75}{8} = 9 \frac{3}{8}
\]

Answer:
\[
\boxed{9 \frac{3}{8}}
\]

---

Problem 2: \( 9 \frac{1}{6} - 4 \frac{1}{2} \)

#### Step 1: Convert to improper fractions
- \( 9 \frac{1}{6} = 9 + \frac{1}{6} = \frac{54}{6} + \frac{1}{6} = \frac{55}{6} \)
- \( 4 \frac{1}{2} = 4 + \frac{1}{2} = \frac{8}{2} + \frac{1}{2} = \frac{9}{2} \)

#### Step 2: Find a common denominator
The denominators are 6 and 2. The LCD is 6.

- Convert \( \frac{9}{2} \) to a fraction with denominator 6:
\[
\frac{9}{2} = \frac{9 \times 3}{2 \times 3} = \frac{27}{6}
\]

#### Step 3: Subtract the fractions
\[
\frac{55}{6} - \frac{27}{6} = \frac{55 - 27}{6} = \frac{28}{6}
\]

#### Step 4: Simplify and convert back to a mixed fraction
\[
\frac{28}{6} = \frac{14}{3} = 4 \frac{2}{3}
\]

Answer:
\[
\boxed{4 \frac{2}{3}}
\]

---

Problem 3: \( 6 \frac{1}{3} + 2 \frac{5}{6} \)

#### Step 1: Convert to improper fractions
- \( 6 \frac{1}{3} = 6 + \frac{1}{3} = \frac{18}{3} + \frac{1}{3} = \frac{19}{3} \)
- \( 2 \frac{5}{6} = 2 + \frac{5}{6} = \frac{12}{6} + \frac{5}{6} = \frac{17}{6} \)

#### Step 2: Find a common denominator
The denominators are 3 and 6. The LCD is 6.

- Convert \( \frac{19}{3} \) to a fraction with denominator 6:
\[
\frac{19}{3} = \frac{19 \times 2}{3 \times 2} = \frac{38}{6}
\]

#### Step 3: Add the fractions
\[
\frac{38}{6} + \frac{17}{6} = \frac{38 + 17}{6} = \frac{55}{6}
\]

#### Step 4: Convert back to a mixed fraction
\[
\frac{55}{6} = 9 \frac{1}{6}
\]

Answer:
\[
\boxed{9 \frac{1}{6}}
\]

---

Problem 4: \( 4 \frac{4}{5} - 3 \frac{1}{6} \)

#### Step 1: Convert to improper fractions
- \( 4 \frac{4}{5} = 4 + \frac{4}{5} = \frac{20}{5} + \frac{4}{5} = \frac{24}{5} \)
- \( 3 \frac{1}{6} = 3 + \frac{1}{6} = \frac{18}{6} + \frac{1}{6} = \frac{19}{6} \)

#### Step 2: Find a common denominator
The denominators are 5 and 6. The LCD is 30.

- Convert \( \frac{24}{5} \) to a fraction with denominator 30:
\[
\frac{24}{5} = \frac{24 \times 6}{5 \times 6} = \frac{144}{30}
\]
- Convert \( \frac{19}{6} \) to a fraction with denominator 30:
\[
\frac{19}{6} = \frac{19 \times 5}{6 \times 5} = \frac{95}{30}
\]

#### Step 3: Subtract the fractions
\[
\frac{144}{30} - \frac{95}{30} = \frac{144 - 95}{30} = \frac{49}{30}
\]

#### Step 4: Convert back to a mixed fraction
\[
\frac{49}{30} = 1 \frac{19}{30}
\]

Answer:
\[
\boxed{1 \frac{19}{30}}
\]

---

Problem 5: \( 2 \frac{1}{2} + 3 \frac{1}{4} \)

#### Step 1: Convert to improper fractions
- \( 2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} \)
- \( 3 \frac{1}{4} = 3 + \frac{1}{4} = \frac{12}{4} + \frac{1}{4} = \frac{13}{4} \)

#### Step 2: Find a common denominator
The denominators are 2 and 4. The LCD is 4.

- Convert \( \frac{5}{2} \) to a fraction with denominator 4:
\[
\frac{5}{2} = \frac{5 \times 2}{2 \times 2} = \frac{10}{4}
\]

#### Step 3: Add the fractions
\[
\frac{10}{4} + \frac{13}{4} = \frac{10 + 13}{4} = \frac{23}{4}
\]

#### Step 4: Convert back to a mixed fraction
\[
\frac{23}{4} = 5 \frac{3}{4}
\]

Answer:
\[
\boxed{5 \frac{3}{4}}
\]

---

Problem 6: \( 4 \frac{4}{7} - 2 \frac{2}{5} \)

#### Step 1: Convert to improper fractions
- \( 4 \frac{4}{7} = 4 + \frac{4}{7} = \frac{28}{7} + \frac{4}{7} = \frac{32}{7} \)
- \( 2 \frac{2}{5} = 2 + \frac{2}{5} = \frac{10}{5} + \frac{2}{5} = \frac{12}{5} \)

#### Step 2: Find a common denominator
The denominators are 7 and 5. The LCD is 35.

- Convert \( \frac{32}{7} \) to a fraction with denominator 35:
\[
\frac{32}{7} = \frac{32 \times 5}{7 \times 5} = \frac{160}{35}
\]
- Convert \( \frac{12}{5} \) to a fraction with denominator 35:
\[
\frac{12}{5} = \frac{12 \times 7}{5 \times 7} = \frac{84}{35}
\]

#### Step 3: Subtract the fractions
\[
\frac{160}{35} - \frac{84}{35} = \frac{160 - 84}{35} = \frac{76}{35}
\]

#### Step 4: Convert back to a mixed fraction
\[
\frac{76}{35} = 2 \frac{6}{35}
\]

Answer:
\[
\boxed{2 \frac{6}{35}}
\]

---

Problem 7: \( 3 \frac{7}{12} + 2 \frac{1}{8} \)

#### Step 1: Convert to improper fractions
- \( 3 \frac{7}{12} = 3 + \frac{7}{12} = \frac{36}{12} + \frac{7}{12} = \frac{43}{12} \)
- \( 2 \frac{1}{8} = 2 + \frac{1}{8} = \frac{16}{8} + \frac{1}{8} = \frac{17}{8} \)

#### Step 2: Find a common denominator
The denominators are 12 and 8. The LCD is 24.

- Convert \( \frac{43}{12} \) to a fraction with denominator 24:
\[
\frac{43}{12} = \frac{43 \times 2}{12 \times 2} = \frac{86}{24}
\]
- Convert \( \frac{17}{8} \) to a fraction with denominator 24:
\[
\frac{17}{8} = \frac{17 \times 3}{8 \times 3} = \frac{51}{24}
\]

#### Step 3: Add the fractions
\[
\frac{86}{24} + \frac{51}{24} = \frac{86 + 51}{24} = \frac{137}{24}
\]

#### Step 4: Convert back to a mixed fraction
\[
\frac{137}{24} = 5 \frac{17}{24}
\]

Answer:
\[
\boxed{5 \frac{17}{24}}
\]

---

Problem 8: \( 5 \frac{1}{5} - 3 \frac{5}{7} \)

#### Step 1: Convert to improper fractions
- \( 5 \frac{1}{5} = 5 + \frac{1}{5} = \frac{25}{5} + \frac{1}{5} = \frac{26}{5} \)
- \( 3 \frac{5}{7} = 3 + \frac{5}{7} = \frac{21}{7} + \frac{5}{7} = \frac{26}{7} \)

#### Step 2: Find a common denominator
The denominators are 5 and 7. The LCD is 35.

- Convert \( \frac{26}{5} \) to a fraction with denominator 35:
\[
\frac{26}{5} = \frac{26 \times 7}{5 \times 7} = \frac{182}{35}
\]
- Convert \( \frac{26}{7} \) to a fraction with denominator 35:
\[
\frac{26}{7} = \frac{26 \times 5}{7 \times 5} = \frac{130}{35}
\]

#### Step 3: Subtract the fractions
\[
\frac{182}{35} - \frac{130}{35} = \frac{182 - 130}{35} = \frac{52}{35}
\]

#### Step 4: Convert back to a mixed fraction
\[
\frac{52}{35} = 1 \frac{17}{35}
\]

Answer:
\[
\boxed{1 \frac{17}{35}}
\]

---

Problem 9: \( 4 \frac{2}{5} + 3 \frac{5}{6} \)

#### Step 1: Convert to improper fractions
- \( 4 \frac{2}{5} = 4 + \frac{2}{5} = \frac{20}{5} + \frac{2}{5} = \frac{22}{5} \)
- \( 3 \frac{5}{6} = 3 + \frac{5}{6} = \frac{18}{6} + \frac{5}{6} = \frac{23}{6} \)

#### Step 2: Find a common denominator
The denominators are 5 and 6. The LCD is 30.

- Convert \( \frac{22}{5} \) to a fraction with denominator 30:
\[
\frac{22}{5} = \frac{22 \times 6}{5 \times 6} = \frac{132}{30}
\]
- Convert \( \frac{23}{6} \) to a fraction with denominator 30:
\[
\frac{23}{6} = \frac{23 \times 5}{6 \times 5} = \frac{115}{30}
\]

#### Step 3: Add the fractions
\[
\frac{132}{30} + \frac{115}{30} = \frac{132 + 115}{30} = \frac{247}{30}
\]

#### Step 4: Convert back to a mixed fraction
\[
\frac{247}{30} = 8 \frac{7}{30}
\]

Answer:
\[
\boxed{8 \frac{7}{30}}
\]

---

Problem 10: \( 3 \frac{1}{10} - 1 \frac{6}{8} \)

#### Step 1: Convert to improper fractions
- \( 3 \frac{1}{10} = 3 + \frac{1}{10} = \frac{30}{10} + \frac{1}{10} = \frac{31}{10} \)
- \( 1 \frac{6}{8} = 1 + \frac{6}{8} = \frac{8}{8} + \frac{6}{8} = \frac{14}{8} \)

#### Step 2: Simplify \( \frac{14}{8} \)
\[
\frac{14}{8} = \frac{7}{4}
\]

#### Step 3: Find a common denominator
The denominators are 10 and 4. The LCD is 20.

- Convert \( \frac{31}{10} \) to a fraction with denominator 20:
\[
\frac{31}{10} = \frac{31 \times 2}{10 \times 2} = \frac{62}{20}
\]
- Convert \( \frac{7}{4} \) to a fraction with denominator 20:
\[
\frac{7}{4} = \frac{7 \times 5}{4 \times 5} = \frac{35}{20}
\]

#### Step 4: Subtract the fractions
\[
\frac{62}{20} - \frac{35}{20} = \frac{62 - 35}{20} = \frac{27}{20}
\]

#### Step 5: Convert back to a mixed fraction
\[
\frac{27}{20} = 1 \frac{7}{20}
\]

Answer:
\[
\boxed{1 \frac{7}{20}}
\]

---

Problem 11: \( 6 \frac{7}{8} + 9 \frac{3}{9} \)

#### Step 1: Simplify \( 9 \frac{3}{9} \)
\[
9 \frac{3}{9} = 9 + \frac{3}{9} = 9 + \frac{1}{3} = 9 \frac{1}{3}
\]

#### Step 2: Convert to improper fractions
- \( 6 \frac{7}{8} = 6 + \frac{7}{8} = \frac{48}{8} + \frac{7}{8} = \frac{55}{8} \)
- \( 9 \frac{1}{3} = 9 + \frac{1}{3} = \frac{27}{3} + \frac{1}{3} = \frac{28}{3} \)

#### Step 3: Find a common denominator
The denominators are 8 and 3. The LCD is 24.

- Convert \( \frac{55}{8} \) to a fraction with denominator 24:
\[
\frac{55}{8} = \frac{55 \times 3}{8 \times 3} = \frac{165}{24}
\]
- Convert \( \frac{28}{3} \) to a fraction with denominator 24:
\[
\frac{28}{3} = \frac{28 \times 8}{3 \times 8} = \frac{224}{24}
\]

#### Step 4: Add the fractions
\[
\frac{165}{24} + \frac{224}{24} = \frac{165 + 224}{24} = \frac{389}{24}
\]

#### Step 5: Convert back to a mixed fraction
\[
\frac{389}{24} = 16 \frac{5}{24}
\]

Answer:
\[
\boxed{16 \frac{5}{24}}
\]

---

Problem 12: \( 7 \frac{1}{2} - 4 \frac{7}{8} \)

#### Step 1: Convert to improper fractions
- \( 7 \frac{1}{2} = 7 + \frac{1}{2} = \frac{14}{2} + \frac{1}{2} = \frac{15}{2} \)
- \( 4 \frac{7}{8} = 4 + \frac{7}{8} = \frac{32}{8} + \frac{7}{8} = \frac{39}{8} \)

#### Step 2: Find a common denominator
The denominators are 2 and 8. The LCD is 8.

- Convert \( \frac{15}{2} \) to a fraction with denominator 8:
\[
\frac{15}{2} = \frac{15 \times 4}{2 \times 4} = \frac{60}{8}
\]

#### Step 3: Subtract the fractions
\[
\frac{60}{8} - \frac{39}{8} = \frac{60 - 39}{8} = \frac{21}{8}
\]

#### Step 4: Convert back to a mixed fraction
\[
\frac{21}{8} = 2 \frac{5}{8}
\]

Answer:
\[
\boxed{2 \frac{5}{8}}
\]

---

Final Answers:

\[
\boxed{
\begin{aligned}
1. & \ 9 \frac{3}{8} \\
2. & \ 4 \frac{2}{3} \\
3. & \ 9 \frac{1}{6} \\
4. & \ 1 \frac{19}{30} \\
5. & \ 5 \frac{3}{4} \\
6. & \ 2 \frac{6}{35} \\
7. & \ 5 \frac{17}{24} \\
8. & \ 1 \frac{17}{35} \\
9. & \ 8 \frac{7}{30} \\
10. & \ 1 \frac{7}{20} \\
11. & \ 16 \frac{5}{24} \\
12. & \ 2 \frac{5}{8}
\end{aligned}
}
\]