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.
2. Find a common denominator if necessary.
3. Subtract the fractions.
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: \( 2 \frac{4}{8} - 1 \frac{2}{3} \)

#### Step 1: Convert to improper fractions
- \( 2 \frac{4}{8} = 2 + \frac{4}{8} = \frac{16}{8} + \frac{4}{8} = \frac{20}{8} \)
- \( 1 \frac{2}{3} = 1 + \frac{2}{3} = \frac{3}{3} + \frac{2}{3} = \frac{5}{3} \)

#### Step 2: Find a common denominator
The denominators are 8 and 3. The least common denominator (LCD) is 24.

- Convert \( \frac{20}{8} \) to a fraction with denominator 24:
\[
\frac{20}{8} = \frac{20 \times 3}{8 \times 3} = \frac{60}{24}
\]
- Convert \( \frac{5}{3} \) to a fraction with denominator 24:
\[
\frac{5}{3} = \frac{5 \times 8}{3 \times 8} = \frac{40}{24}
\]

#### Step 3: Subtract the fractions
\[
\frac{60}{24} - \frac{40}{24} = \frac{60 - 40}{24} = \frac{20}{24}
\]

#### Step 4: Simplify the result
\[
\frac{20}{24} = \frac{5}{6}
\]

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

---

Problem 2: \( 8 \frac{6}{10} - 5 \frac{5}{10} \)

#### Step 1: Convert to improper fractions
- \( 8 \frac{6}{10} = 8 + \frac{6}{10} = \frac{80}{10} + \frac{6}{10} = \frac{86}{10} \)
- \( 5 \frac{5}{10} = 5 + \frac{5}{10} = \frac{50}{10} + \frac{5}{10} = \frac{55}{10} \)

#### Step 2: Subtract the fractions
\[
\frac{86}{10} - \frac{55}{10} = \frac{86 - 55}{10} = \frac{31}{10}
\]

#### Step 3: Convert back to a mixed fraction
\[
\frac{31}{10} = 3 \frac{1}{10}
\]

#### Final Answer:
\[
\boxed{3 \frac{1}{10}}
\]

---

Problem 3: \( 10 \frac{1}{3} - 8 \frac{6}{7} \)

#### Step 1: Convert to improper fractions
- \( 10 \frac{1}{3} = 10 + \frac{1}{3} = \frac{30}{3} + \frac{1}{3} = \frac{31}{3} \)
- \( 8 \frac{6}{7} = 8 + \frac{6}{7} = \frac{56}{7} + \frac{6}{7} = \frac{62}{7} \)

#### Step 2: Find a common denominator
The denominators are 3 and 7. The LCD is 21.

- Convert \( \frac{31}{3} \) to a fraction with denominator 21:
\[
\frac{31}{3} = \frac{31 \times 7}{3 \times 7} = \frac{217}{21}
\]
- Convert \( \frac{62}{7} \) to a fraction with denominator 21:
\[
\frac{62}{7} = \frac{62 \times 3}{7 \times 3} = \frac{186}{21}
\]

#### Step 3: Subtract the fractions
\[
\frac{217}{21} - \frac{186}{21} = \frac{217 - 186}{21} = \frac{31}{21}
\]

#### Step 4: Convert back to a mixed fraction
\[
\frac{31}{21} = 1 \frac{10}{21}
\]

#### Final Answer:
\[
\boxed{1 \frac{10}{21}}
\]

---

Problem 4: \( 10 \frac{3}{8} - 9 \frac{3}{6} \)

#### Step 1: Simplify \( \frac{3}{6} \)
\[
\frac{3}{6} = \frac{1}{2}
\]
So, \( 9 \frac{3}{6} = 9 \frac{1}{2} \).

#### Step 2: Convert to improper fractions
- \( 10 \frac{3}{8} = 10 + \frac{3}{8} = \frac{80}{8} + \frac{3}{8} = \frac{83}{8} \)
- \( 9 \frac{1}{2} = 9 + \frac{1}{2} = \frac{18}{2} + \frac{1}{2} = \frac{19}{2} \)

#### Step 3: Find a common denominator
The denominators are 8 and 2. The LCD is 8.

- Convert \( \frac{19}{2} \) to a fraction with denominator 8:
\[
\frac{19}{2} = \frac{19 \times 4}{2 \times 4} = \frac{76}{8}
\]

#### Step 4: Subtract the fractions
\[
\frac{83}{8} - \frac{76}{8} = \frac{83 - 76}{8} = \frac{7}{8}
\]

#### Final Answer:
\[
\boxed{\frac{7}{8}}
\]

---

Problem 5: \( 10 \frac{6}{9} - 10 \frac{2}{12} \)

#### Step 1: Simplify the fractions
- \( \frac{6}{9} = \frac{2}{3} \)
- \( \frac{2}{12} = \frac{1}{6} \)

So, the problem becomes:
\[
10 \frac{2}{3} - 10 \frac{1}{6}
\]

#### Step 2: Convert to improper fractions
- \( 10 \frac{2}{3} = 10 + \frac{2}{3} = \frac{30}{3} + \frac{2}{3} = \frac{32}{3} \)
- \( 10 \frac{1}{6} = 10 + \frac{1}{6} = \frac{60}{6} + \frac{1}{6} = \frac{61}{6} \)

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

- Convert \( \frac{32}{3} \) to a fraction with denominator 6:
\[
\frac{32}{3} = \frac{32 \times 2}{3 \times 2} = \frac{64}{6}
\]

#### Step 4: Subtract the fractions
\[
\frac{64}{6} - \frac{61}{6} = \frac{64 - 61}{6} = \frac{3}{6}
\]

#### Step 5: Simplify the result
\[
\frac{3}{6} = \frac{1}{2}
\]

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

---

Problem 6: \( 7 \frac{10}{12} - 1 \frac{1}{3} \)

#### Step 1: Simplify \( \frac{10}{12} \)
\[
\frac{10}{12} = \frac{5}{6}
\]
So, \( 7 \frac{10}{12} = 7 \frac{5}{6} \).

#### Step 2: Convert to improper fractions
- \( 7 \frac{5}{6} = 7 + \frac{5}{6} = \frac{42}{6} + \frac{5}{6} = \frac{47}{6} \)
- \( 1 \frac{1}{3} = 1 + \frac{1}{3} = \frac{3}{3} + \frac{1}{3} = \frac{4}{3} \)

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

- Convert \( \frac{4}{3} \) to a fraction with denominator 6:
\[
\frac{4}{3} = \frac{4 \times 2}{3 \times 2} = \frac{8}{6}
\]

#### Step 4: Subtract the fractions
\[
\frac{47}{6} - \frac{8}{6} = \frac{47 - 8}{6} = \frac{39}{6}
\]

#### Step 5: Simplify the result
\[
\frac{39}{6} = \frac{13}{2}
\]

#### Step 6: Convert back to a mixed fraction
\[
\frac{13}{2} = 6 \frac{1}{2}
\]

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

---

Problem 7: \( 10 \frac{2}{8} - 7 \frac{2}{4} \)

#### Step 1: Simplify the fractions
- \( \frac{2}{8} = \frac{1}{4} \)
- \( \frac{2}{4} = \frac{1}{2} \)

So, the problem becomes:
\[
10 \frac{1}{4} - 7 \frac{1}{2}
\]

#### Step 2: Convert to improper fractions
- \( 10 \frac{1}{4} = 10 + \frac{1}{4} = \frac{40}{4} + \frac{1}{4} = \frac{41}{4} \)
- \( 7 \frac{1}{2} = 7 + \frac{1}{2} = \frac{14}{2} + \frac{1}{2} = \frac{15}{2} \)

#### Step 3: Find a common denominator
The denominators are 4 and 2. The LCD is 4.

- Convert \( \frac{15}{2} \) to a fraction with denominator 4:
\[
\frac{15}{2} = \frac{15 \times 2}{2 \times 2} = \frac{30}{4}
\]

#### Step 4: Subtract the fractions
\[
\frac{41}{4} - \frac{30}{4} = \frac{41 - 30}{4} = \frac{11}{4}
\]

#### Step 5: Convert back to a mixed fraction
\[
\frac{11}{4} = 2 \frac{3}{4}
\]

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

---

Problem 8: \( 9 \frac{2}{3} - 8 \frac{2}{6} \)

#### Step 1: Simplify \( \frac{2}{6} \)
\[
\frac{2}{6} = \frac{1}{3}
\]
So, \( 8 \frac{2}{6} = 8 \frac{1}{3} \).

#### Step 2: Convert to improper fractions
- \( 9 \frac{2}{3} = 9 + \frac{2}{3} = \frac{27}{3} + \frac{2}{3} = \frac{29}{3} \)
- \( 8 \frac{1}{3} = 8 + \frac{1}{3} = \frac{24}{3} + \frac{1}{3} = \frac{25}{3} \)

#### Step 3: Subtract the fractions
\[
\frac{29}{3} - \frac{25}{3} = \frac{29 - 25}{3} = \frac{4}{3}
\]

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

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

---

Problem 9: \( 9 \frac{3}{4} - 7 \frac{2}{5} \)

#### Step 1: Convert to improper fractions
- \( 9 \frac{3}{4} = 9 + \frac{3}{4} = \frac{36}{4} + \frac{3}{4} = \frac{39}{4} \)
- \( 7 \frac{2}{5} = 7 + \frac{2}{5} = \frac{35}{5} + \frac{2}{5} = \frac{37}{5} \)

#### Step 2: Find a common denominator
The denominators are 4 and 5. The LCD is 20.

- Convert \( \frac{39}{4} \) to a fraction with denominator 20:
\[
\frac{39}{4} = \frac{39 \times 5}{4 \times 5} = \frac{195}{20}
\]
- Convert \( \frac{37}{5} \) to a fraction with denominator 20:
\[
\frac{37}{5} = \frac{37 \times 4}{5 \times 4} = \frac{148}{20}
\]

#### Step 3: Subtract the fractions
\[
\frac{195}{20} - \frac{148}{20} = \frac{195 - 148}{20} = \frac{47}{20}
\]

#### Step 4: Convert back to a mixed fraction
\[
\frac{47}{20} = 2 \frac{7}{20}
\]

#### Final Answer:
\[
\boxed{2 \frac{7}{20}}
\]

---

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

#### Step 1: Simplify \( \frac{8}{10} \)
\[
\frac{8}{10} = \frac{4}{5}
\]
So, \( 1 \frac{8}{10} = 1 \frac{4}{5} \).

#### Step 2: Convert to improper fractions
- \( 1 \frac{4}{5} = 1 + \frac{4}{5} = \frac{5}{5} + \frac{4}{5} = \frac{9}{5} \)
- \( 1 \frac{1}{6} = 1 + \frac{1}{6} = \frac{6}{6} + \frac{1}{6} = \frac{7}{6} \)

#### Step 3: Find a common denominator
The denominators are 5 and 6. The LCD is 30.

- Convert \( \frac{9}{5} \) to a fraction with denominator 30:
\[
\frac{9}{5} = \frac{9 \times 6}{5 \times 6} = \frac{54}{30}
\]
- Convert \( \frac{7}{6} \) to a fraction with denominator 30:
\[
\frac{7}{6} = \frac{7 \times 5}{6 \times 5} = \frac{35}{30}
\]

#### Step 4: Subtract the fractions
\[
\frac{54}{30} - \frac{35}{30} = \frac{54 - 35}{30} = \frac{19}{30}
\]

#### Final Answer:
\[
\boxed{\frac{19}{30}}
\]

---

Final Answers:

1. \(\boxed{\frac{5}{6}}\)
2. \(\boxed{3 \frac{1}{10}}\)
3. \(\boxed{1 \frac{10}{21}}\)
4. \(\boxed{\frac{7}{8}}\)
5. \(\boxed{\frac{1}{2}}\)
6. \(\boxed{6 \frac{1}{2}}\)
7. \(\boxed{2 \frac{3}{4}}\)
8. \(\boxed{1 \frac{1}{3}}\)
9. \(\boxed{2 \frac{7}{20}}\)
10. \(\boxed{\frac{19}{30}}\)