Subtraction of Mixed Fractions worksheets - Math Worksheets - Free Printable

To solve the problems involving subtracting mixed numbers, we need to follow these steps:

1. Convert mixed numbers to improper fractions if necessary.
2. Find a common denominator for the fractions.
3. Subtract the numerators while keeping the denominator the same.
4. Simplify the result if possible, and convert back to a mixed number if needed.

Let's solve each problem step by step.

---

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

#### Step 1: Convert mixed numbers to improper fractions
- \( 2 \frac{4}{9} = \frac{2 \times 9 + 4}{9} = \frac{18 + 4}{9} = \frac{22}{9} \)
- \( 1 \frac{4}{6} = \frac{1 \times 6 + 4}{6} = \frac{6 + 4}{6} = \frac{10}{6} \)

#### Step 2: Find a common denominator
The denominators are 9 and 6. The least common denominator (LCD) is 18.

- Convert \( \frac{22}{9} \) to a fraction with denominator 18:
\[
\frac{22}{9} = \frac{22 \times 2}{9 \times 2} = \frac{44}{18}
\]
- Convert \( \frac{10}{6} \) to a fraction with denominator 18:
\[
\frac{10}{6} = \frac{10 \times 3}{6 \times 3} = \frac{30}{18}
\]

#### Step 3: Subtract the fractions
\[
\frac{44}{18} - \frac{30}{18} = \frac{44 - 30}{18} = \frac{14}{18}
\]

#### Step 4: Simplify the result
\[
\frac{14}{18} = \frac{7}{9}
\]

#### Final Answer:
\[
\boxed{\frac{7}{9}}
\]

---

Problem 2: \( 9 \frac{1}{2} - 5 \frac{1}{4} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 9 \frac{1}{2} = \frac{9 \times 2 + 1}{2} = \frac{18 + 1}{2} = \frac{19}{2} \)
- \( 5 \frac{1}{4} = \frac{5 \times 4 + 1}{4} = \frac{20 + 1}{4} = \frac{21}{4} \)

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

- Convert \( \frac{19}{2} \) to a fraction with denominator 4:
\[
\frac{19}{2} = \frac{19 \times 2}{2 \times 2} = \frac{38}{4}
\]
- \( \frac{21}{4} \) already has the denominator 4.

#### Step 3: Subtract the fractions
\[
\frac{38}{4} - \frac{21}{4} = \frac{38 - 21}{4} = \frac{17}{4}
\]

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

#### Final Answer:
\[
\boxed{4 \frac{1}{4}}
\]

---

Problem 3: \( 7 \frac{1}{3} - 4 \frac{1}{6} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 7 \frac{1}{3} = \frac{7 \times 3 + 1}{3} = \frac{21 + 1}{3} = \frac{22}{3} \)
- \( 4 \frac{1}{6} = \frac{4 \times 6 + 1}{6} = \frac{24 + 1}{6} = \frac{25}{6} \)

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

- Convert \( \frac{22}{3} \) to a fraction with denominator 6:
\[
\frac{22}{3} = \frac{22 \times 2}{3 \times 2} = \frac{44}{6}
\]
- \( \frac{25}{6} \) already has the denominator 6.

#### Step 3: Subtract the fractions
\[
\frac{44}{6} - \frac{25}{6} = \frac{44 - 25}{6} = \frac{19}{6}
\]

#### Step 4: Convert back to a mixed number
\[
\frac{19}{6} = 3 \frac{1}{6}
\]

#### Final Answer:
\[
\boxed{3 \frac{1}{6}}
\]

---

Problem 4: \( 7 \frac{1}{2} - 3 \frac{5}{6} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 7 \frac{1}{2} = \frac{7 \times 2 + 1}{2} = \frac{14 + 1}{2} = \frac{15}{2} \)
- \( 3 \frac{5}{6} = \frac{3 \times 6 + 5}{6} = \frac{18 + 5}{6} = \frac{23}{6} \)

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

- Convert \( \frac{15}{2} \) to a fraction with denominator 6:
\[
\frac{15}{2} = \frac{15 \times 3}{2 \times 3} = \frac{45}{6}
\]
- \( \frac{23}{6} \) already has the denominator 6.

#### Step 3: Subtract the fractions
\[
\frac{45}{6} - \frac{23}{6} = \frac{45 - 23}{6} = \frac{22}{6}
\]

#### Step 4: Simplify the result and convert back to a mixed number
\[
\frac{22}{6} = \frac{11}{3} = 3 \frac{2}{3}
\]

#### Final Answer:
\[
\boxed{3 \frac{2}{3}}
\]

---

Problem 5: \( 11 \frac{3}{4} - 5 \frac{1}{4} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 11 \frac{3}{4} = \frac{11 \times 4 + 3}{4} = \frac{44 + 3}{4} = \frac{47}{4} \)
- \( 5 \frac{1}{4} = \frac{5 \times 4 + 1}{4} = \frac{20 + 1}{4} = \frac{21}{4} \)

#### Step 2: Subtract the fractions
\[
\frac{47}{4} - \frac{21}{4} = \frac{47 - 21}{4} = \frac{26}{4}
\]

#### Step 3: Simplify the result and convert back to a mixed number
\[
\frac{26}{4} = \frac{13}{2} = 6 \frac{1}{2}
\]

#### Final Answer:
\[
\boxed{6 \frac{1}{2}}
\]

---

Problem 6: \( 8 \frac{2}{4} - 2 \frac{3}{20} \)

#### Step 1: Simplify and convert mixed numbers to improper fractions
- \( 8 \frac{2}{4} = 8 \frac{1}{2} = \frac{8 \times 2 + 1}{2} = \frac{16 + 1}{2} = \frac{17}{2} \)
- \( 2 \frac{3}{20} = \frac{2 \times 20 + 3}{20} = \frac{40 + 3}{20} = \frac{43}{20} \)

#### Step 2: Find a common denominator
The denominators are 2 and 20. The LCD is 20.

- Convert \( \frac{17}{2} \) to a fraction with denominator 20:
\[
\frac{17}{2} = \frac{17 \times 10}{2 \times 10} = \frac{170}{20}
\]
- \( \frac{43}{20} \) already has the denominator 20.

#### Step 3: Subtract the fractions
\[
\frac{170}{20} - \frac{43}{20} = \frac{170 - 43}{20} = \frac{127}{20}
\]

#### Step 4: Convert back to a mixed number
\[
\frac{127}{20} = 6 \frac{7}{20}
\]

#### Final Answer:
\[
\boxed{6 \frac{7}{20}}
\]

---

Problem 7: \( 12 \frac{2}{3} - 4 \frac{3}{6} \)

#### Step 1: Simplify and convert mixed numbers to improper fractions
- \( 12 \frac{2}{3} = \frac{12 \times 3 + 2}{3} = \frac{36 + 2}{3} = \frac{38}{3} \)
- \( 4 \frac{3}{6} = 4 \frac{1}{2} = \frac{4 \times 2 + 1}{2} = \frac{8 + 1}{2} = \frac{9}{2} \)

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

- Convert \( \frac{38}{3} \) to a fraction with denominator 6:
\[
\frac{38}{3} = \frac{38 \times 2}{3 \times 2} = \frac{76}{6}
\]
- 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
\[
\frac{76}{6} - \frac{27}{6} = \frac{76 - 27}{6} = \frac{49}{6}
\]

#### Step 4: Convert back to a mixed number
\[
\frac{49}{6} = 8 \frac{1}{6}
\]

#### Final Answer:
\[
\boxed{8 \frac{1}{6}}
\]

---

Problem 8: \( 5 \frac{2}{5} - 4 \frac{1}{6} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 5 \frac{2}{5} = \frac{5 \times 5 + 2}{5} = \frac{25 + 2}{5} = \frac{27}{5} \)
- \( 4 \frac{1}{6} = \frac{4 \times 6 + 1}{6} = \frac{24 + 1}{6} = \frac{25}{6} \)

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

- Convert \( \frac{27}{5} \) to a fraction with denominator 30:
\[
\frac{27}{5} = \frac{27 \times 6}{5 \times 6} = \frac{162}{30}
\]
- Convert \( \frac{25}{6} \) to a fraction with denominator 30:
\[
\frac{25}{6} = \frac{25 \times 5}{6 \times 5} = \frac{125}{30}
\]

#### Step 3: Subtract the fractions
\[
\frac{162}{30} - \frac{125}{30} = \frac{162 - 125}{30} = \frac{37}{30}
\]

#### Step 4: Convert back to a mixed number
\[
\frac{37}{30} = 1 \frac{7}{30}
\]

#### Final Answer:
\[
\boxed{1 \frac{7}{30}}
\]

---

Problem 9: \( 6 \frac{4}{5} - 3 \frac{3}{8} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 6 \frac{4}{5} = \frac{6 \times 5 + 4}{5} = \frac{30 + 4}{5} = \frac{34}{5} \)
- \( 3 \frac{3}{8} = \frac{3 \times 8 + 3}{8} = \frac{24 + 3}{8} = \frac{27}{8} \)

#### Step 2: Find a common denominator
The denominators are 5 and 8. The LCD is 40.

- Convert \( \frac{34}{5} \) to a fraction with denominator 40:
\[
\frac{34}{5} = \frac{34 \times 8}{5 \times 8} = \frac{272}{40}
\]
- Convert \( \frac{27}{8} \) to a fraction with denominator 40:
\[
\frac{27}{8} = \frac{27 \times 5}{8 \times 5} = \frac{135}{40}
\]

#### Step 3: Subtract the fractions
\[
\frac{272}{40} - \frac{135}{40} = \frac{272 - 135}{40} = \frac{137}{40}
\]

#### Step 4: Convert back to a mixed number
\[
\frac{137}{40} = 3 \frac{17}{40}
\]

#### Final Answer:
\[
\boxed{3 \frac{17}{40}}
\]

---

Problem 10: \( 9 \frac{2}{3} - 6 \frac{1}{11} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 9 \frac{2}{3} = \frac{9 \times 3 + 2}{3} = \frac{27 + 2}{3} = \frac{29}{3} \)
- \( 6 \frac{1}{11} = \frac{6 \times 11 + 1}{11} = \frac{66 + 1}{11} = \frac{67}{11} \)

#### Step 2: Find a common denominator
The denominators are 3 and 11. The LCD is 33.

- Convert \( \frac{29}{3} \) to a fraction with denominator 33:
\[
\frac{29}{3} = \frac{29 \times 11}{3 \times 11} = \frac{319}{33}
\]
- Convert \( \frac{67}{11} \) to a fraction with denominator 33:
\[
\frac{67}{11} = \frac{67 \times 3}{11 \times 3} = \frac{201}{33}
\]

#### Step 3: Subtract the fractions
\[
\frac{319}{33} - \frac{201}{33} = \frac{319 - 201}{33} = \frac{118}{33}
\]

#### Step 4: Convert back to a mixed number
\[
\frac{118}{33} = 3 \frac{19}{33}
\]

#### Final Answer:
\[
\boxed{3 \frac{19}{33}}
\]

---

Final Answers:

1. \(\boxed{\frac{7}{9}}\)
2. \(\boxed{4 \frac{1}{4}}\)
3. \(\boxed{3 \frac{1}{6}}\)
4. \(\boxed{3 \frac{2}{3}}\)
5. \(\boxed{6 \frac{1}{2}}\)
6. \(\boxed{6 \frac{7}{20}}\)
7. \(\boxed{8 \frac{1}{6}}\)
8. \(\boxed{1 \frac{7}{30}}\)
9. \(\boxed{3 \frac{17}{40}}\)
10. \(\boxed{3 \frac{19}{33}}\)