Subtracting Unlike fractions worksheets - Math Worksheets ... - Free Printable

To solve the given problems, we need to subtract mixed fractions. The general steps are:

1. Convert mixed fractions to improper fractions if necessary.
2. Ensure the fractions have a common denominator.
3. Subtract the numerators while keeping the denominator the same.
4. Simplify the result if possible.
5. Convert back to a mixed fraction if needed.

Let's solve each problem step by step.

---

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

#### Step 1: Convert to improper fractions
- \( 2 \frac{4}{6} = 2 + \frac{4}{6} = \frac{12}{6} + \frac{4}{6} = \frac{16}{6} \)
- \( 2 \frac{1}{5} = 2 + \frac{1}{5} = \frac{10}{5} + \frac{1}{5} = \frac{11}{5} \)

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

- Convert \( \frac{16}{6} \) to a fraction with denominator 30:
\[
\frac{16}{6} = \frac{16 \times 5}{6 \times 5} = \frac{80}{30}
\]
- Convert \( \frac{11}{5} \) to a fraction with denominator 30:
\[
\frac{11}{5} = \frac{11 \times 6}{5 \times 6} = \frac{66}{30}
\]

#### Step 3: Subtract the fractions
\[
\frac{80}{30} - \frac{66}{30} = \frac{80 - 66}{30} = \frac{14}{30}
\]

#### Step 4: Simplify the fraction
\[
\frac{14}{30} = \frac{7}{15}
\]

#### Final Answer:
\[
\boxed{\frac{7}{15}}
\]

---

Problem 2: \( 10 \frac{3}{8} - 8 \frac{5}{8} \)

#### Step 1: Convert to improper fractions
- \( 10 \frac{3}{8} = 10 + \frac{3}{8} = \frac{80}{8} + \frac{3}{8} = \frac{83}{8} \)
- \( 8 \frac{5}{8} = 8 + \frac{5}{8} = \frac{64}{8} + \frac{5}{8} = \frac{69}{8} \)

#### Step 2: Subtract the fractions
\[
\frac{83}{8} - \frac{69}{8} = \frac{83 - 69}{8} = \frac{14}{8}
\]

#### Step 3: Simplify the fraction
\[
\frac{14}{8} = \frac{7}{4}
\]

#### Step 4: Convert back to a mixed fraction
\[
\frac{7}{4} = 1 \frac{3}{4}
\]

#### Final Answer:
\[
\boxed{1 \frac{3}{4}}
\]

---

Problem 3: \( 7 \frac{1}{9} - 5 \frac{8}{9} \)

#### Step 1: Convert to improper fractions
- \( 7 \frac{1}{9} = 7 + \frac{1}{9} = \frac{63}{9} + \frac{1}{9} = \frac{64}{9} \)
- \( 5 \frac{8}{9} = 5 + \frac{8}{9} = \frac{45}{9} + \frac{8}{9} = \frac{53}{9} \)

#### Step 2: Subtract the fractions
\[
\frac{64}{9} - \frac{53}{9} = \frac{64 - 53}{9} = \frac{11}{9}
\]

#### Step 3: Convert back to a mixed fraction
\[
\frac{11}{9} = 1 \frac{2}{9}
\]

#### Final Answer:
\[
\boxed{1 \frac{2}{9}}
\]

---

Problem 4: \( 9 \frac{2}{3} - 9 \frac{3}{12} \)

#### Step 1: Simplify the second fraction
\[
\frac{3}{12} = \frac{1}{4}
\]
So, the problem becomes:
\[
9 \frac{2}{3} - 9 \frac{1}{4}
\]

#### Step 2: Convert to improper fractions
- \( 9 \frac{2}{3} = 9 + \frac{2}{3} = \frac{27}{3} + \frac{2}{3} = \frac{29}{3} \)
- \( 9 \frac{1}{4} = 9 + \frac{1}{4} = \frac{36}{4} + \frac{1}{4} = \frac{37}{4} \)

#### Step 3: Find a common denominator
The denominators are 3 and 4. The LCD is 12.

- Convert \( \frac{29}{3} \) to a fraction with denominator 12:
\[
\frac{29}{3} = \frac{29 \times 4}{3 \times 4} = \frac{116}{12}
\]
- Convert \( \frac{37}{4} \) to a fraction with denominator 12:
\[
\frac{37}{4} = \frac{37 \times 3}{4 \times 3} = \frac{111}{12}
\]

#### Step 4: Subtract the fractions
\[
\frac{116}{12} - \frac{111}{12} = \frac{116 - 111}{12} = \frac{5}{12}
\]

#### Final Answer:
\[
\boxed{\frac{5}{12}}
\]

---

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

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

#### Step 2: Subtract the fractions
\[
\frac{20}{3} - \frac{4}{3} = \frac{20 - 4}{3} = \frac{16}{3}
\]

#### Step 3: Convert back to a mixed fraction
\[
\frac{16}{3} = 5 \frac{1}{3}
\]

#### Final Answer:
\[
\boxed{5 \frac{1}{3}}
\]

---

Problem 6: \( 9 \frac{2}{5} - 1 \frac{2}{11} \)

#### Step 1: Convert to improper fractions
- \( 9 \frac{2}{5} = 9 + \frac{2}{5} = \frac{45}{5} + \frac{2}{5} = \frac{47}{5} \)
- \( 1 \frac{2}{11} = 1 + \frac{2}{11} = \frac{11}{11} + \frac{2}{11} = \frac{13}{11} \)

#### Step 2: Find a common denominator
The denominators are 5 and 11. The LCD is 55.

- Convert \( \frac{47}{5} \) to a fraction with denominator 55:
\[
\frac{47}{5} = \frac{47 \times 11}{5 \times 11} = \frac{517}{55}
\]
- Convert \( \frac{13}{11} \) to a fraction with denominator 55:
\[
\frac{13}{11} = \frac{13 \times 5}{11 \times 5} = \frac{65}{55}
\]

#### Step 3: Subtract the fractions
\[
\frac{517}{55} - \frac{65}{55} = \frac{517 - 65}{55} = \frac{452}{55}
\]

#### Step 4: Convert back to a mixed fraction
\[
\frac{452}{55} = 8 \frac{12}{55}
\]

#### Final Answer:
\[
\boxed{8 \frac{12}{55}}
\]

---

Problem 7: \( 10 \frac{10}{12} - 10 \frac{1}{2} \)

#### Step 1: Simplify the fractions
- \( \frac{10}{12} = \frac{5}{6} \)
- \( \frac{1}{2} = \frac{3}{6} \)
So, the problem becomes:
\[
10 \frac{5}{6} - 10 \frac{3}{6}
\]

#### Step 2: Subtract the fractions
\[
10 \frac{5}{6} - 10 \frac{3}{6} = \frac{5}{6} - \frac{3}{6} = \frac{5 - 3}{6} = \frac{2}{6}
\]

#### Step 3: Simplify the fraction
\[
\frac{2}{6} = \frac{1}{3}
\]

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

---

Problem 8: \( 10 \frac{8}{9} - 6 \frac{6}{10} \)

#### Step 1: Simplify the second fraction
\[
\frac{6}{10} = \frac{3}{5}
\]
So, the problem becomes:
\[
10 \frac{8}{9} - 6 \frac{3}{5}
\]

#### Step 2: Convert to improper fractions
- \( 10 \frac{8}{9} = 10 + \frac{8}{9} = \frac{90}{9} + \frac{8}{9} = \frac{98}{9} \)
- \( 6 \frac{3}{5} = 6 + \frac{3}{5} = \frac{30}{5} + \frac{3}{5} = \frac{33}{5} \)

#### Step 3: Find a common denominator
The denominators are 9 and 5. The LCD is 45.

- Convert \( \frac{98}{9} \) to a fraction with denominator 45:
\[
\frac{98}{9} = \frac{98 \times 5}{9 \times 5} = \frac{490}{45}
\]
- Convert \( \frac{33}{5} \) to a fraction with denominator 45:
\[
\frac{33}{5} = \frac{33 \times 9}{5 \times 9} = \frac{297}{45}
\]

#### Step 4: Subtract the fractions
\[
\frac{490}{45} - \frac{297}{45} = \frac{490 - 297}{45} = \frac{193}{45}
\]

#### Step 5: Convert back to a mixed fraction
\[
\frac{193}{45} = 4 \frac{13}{45}
\]

#### Final Answer:
\[
\boxed{4 \frac{13}{45}}
\]

---

Problem 9: \( 8 \frac{1}{2} - 4 \frac{2}{3} \)

#### Step 1: Convert to improper fractions
- \( 8 \frac{1}{2} = 8 + \frac{1}{2} = \frac{16}{2} + \frac{1}{2} = \frac{17}{2} \)
- \( 4 \frac{2}{3} = 4 + \frac{2}{3} = \frac{12}{3} + \frac{2}{3} = \frac{14}{3} \)

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

- Convert \( \frac{17}{2} \) to a fraction with denominator 6:
\[
\frac{17}{2} = \frac{17 \times 3}{2 \times 3} = \frac{51}{6}
\]
- Convert \( \frac{14}{3} \) to a fraction with denominator 6:
\[
\frac{14}{3} = \frac{14 \times 2}{3 \times 2} = \frac{28}{6}
\]

#### Step 3: Subtract the fractions
\[
\frac{51}{6} - \frac{28}{6} = \frac{51 - 28}{6} = \frac{23}{6}
\]

#### Step 4: Convert back to a mixed fraction
\[
\frac{23}{6} = 3 \frac{5}{6}
\]

#### Final Answer:
\[
\boxed{3 \frac{5}{6}}
\]

---

Problem 10: \( 1 \frac{11}{12} - 1 \frac{1}{8} \)

#### Step 1: Convert to improper fractions
- \( 1 \frac{11}{12} = 1 + \frac{11}{12} = \frac{12}{12} + \frac{11}{12} = \frac{23}{12} \)
- \( 1 \frac{1}{8} = 1 + \frac{1}{8} = \frac{8}{8} + \frac{1}{8} = \frac{9}{8} \)

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

- Convert \( \frac{23}{12} \) to a fraction with denominator 24:
\[
\frac{23}{12} = \frac{23 \times 2}{12 \times 2} = \frac{46}{24}
\]
- Convert \( \frac{9}{8} \) to a fraction with denominator 24:
\[
\frac{9}{8} = \frac{9 \times 3}{8 \times 3} = \frac{27}{24}
\]

#### Step 3: Subtract the fractions
\[
\frac{46}{24} - \frac{27}{24} = \frac{46 - 27}{24} = \frac{19}{24}
\]

#### Final Answer:
\[
\boxed{\frac{19}{24}}
\]

---

Final Answers:

1. \(\boxed{\frac{7}{15}}\)
2. \(\boxed{1 \frac{3}{4}}\)
3. \(\boxed{1 \frac{2}{9}}\)
4. \(\boxed{\frac{5}{12}}\)
5. \(\boxed{5 \frac{1}{3}}\)
6. \(\boxed{8 \frac{12}{55}}\)
7. \(\boxed{\frac{1}{3}}\)
8. \(\boxed{4 \frac{13}{45}}\)
9. \(\boxed{3 \frac{5}{6}}\)
10. \(\boxed{\frac{19}{24}}\)