Worksheet for subtracting improper fractions and converting results to mixed numbers.

To solve the problems involving subtraction of improper fractions, we need to follow these steps:

1. Find a common denominator for the fractions.
2. Rewrite each fraction with the common denominator.
3. Subtract the numerators while keeping the denominator the same.
4. Simplify the result, if possible.
5. Convert the result to a mixed number if it is an improper fraction.

Let's solve each problem step by step.

---

Problem 1:

$$
\frac{11}{4} - \frac{5}{3}
$$

#### Step 1: Find the common denominator
The denominators are 4 and 3. The least common denominator (LCD) is 12.

#### Step 2: Rewrite each fraction with the common denominator
$$
\frac{11}{4} = \frac{11 \times 3}{4 \times 3} = \frac{33}{12}
$$
$$
\frac{5}{3} = \frac{5 \times 4}{3 \times 4} = \frac{20}{12}
$$

#### Step 3: Subtract the numerators
$$
\frac{33}{12} - \frac{20}{12} = \frac{33 - 20}{12} = \frac{13}{12}
$$

#### Step 4: Simplify and convert to a mixed number
$$
\frac{13}{12} = 1 \frac{1}{12}
$$

Answer:
$$
\boxed{1 \frac{1}{12}}
$$

---

Problem 2:

$$
\frac{12}{5} - \frac{3}{2}
$$

#### Step 1: Find the common denominator
The denominators are 5 and 2. The LCD is 10.

#### Step 2: Rewrite each fraction with the common denominator
$$
\frac{12}{5} = \frac{12 \times 2}{5 \times 2} = \frac{24}{10}
$$
$$
\frac{3}{2} = \frac{3 \times 5}{2 \times 5} = \frac{15}{10}
$$

#### Step 3: Subtract the numerators
$$
\frac{24}{10} - \frac{15}{10} = \frac{24 - 15}{10} = \frac{9}{10}
$$

#### Step 4: Simplify
$$
\frac{9}{10}
$$

Answer:
$$
\boxed{\frac{9}{10}}
$$

---

Problem 3:

$$
\frac{9}{2} - \frac{8}{3}
$$

#### Step 1: Find the common denominator
The denominators are 2 and 3. The LCD is 6.

#### Step 2: Rewrite each fraction with the common denominator
$$
\frac{9}{2} = \frac{9 \times 3}{2 \times 3} = \frac{27}{6}
$$
$$
\frac{8}{3} = \frac{8 \times 2}{3 \times 2} = \frac{16}{6}
$$

#### Step 3: Subtract the numerators
$$
\frac{27}{6} - \frac{16}{6} = \frac{27 - 16}{6} = \frac{11}{6}
$$

#### Step 4: Convert to a mixed number
$$
\frac{11}{6} = 1 \frac{5}{6}
$$

Answer:
$$
\boxed{1 \frac{5}{6}}
$$

---

Problem 4:

$$
\frac{11}{3} - \frac{5}{4}
$$

#### Step 1: Find the common denominator
The denominators are 3 and 4. The LCD is 12.

#### Step 2: Rewrite each fraction with the common denominator
$$
\frac{11}{3} = \frac{11 \times 4}{3 \times 4} = \frac{44}{12}
$$
$$
\frac{5}{4} = \frac{5 \times 3}{4 \times 3} = \frac{15}{12}
$$

#### Step 3: Subtract the numerators
$$
\frac{44}{12} - \frac{15}{12} = \frac{44 - 15}{12} = \frac{29}{12}
$$

#### Step 4: Convert to a mixed number
$$
\frac{29}{12} = 2 \frac{5}{12}
$$

Answer:
$$
\boxed{2 \frac{5}{12}}
$$

---

Problem 5:

$$
\frac{13}{4} - \frac{6}{5}
$$

#### Step 1: Find the common denominator
The denominators are 4 and 5. The LCD is 20.

#### Step 2: Rewrite each fraction with the common denominator
$$
\frac{13}{4} = \frac{13 \times 5}{4 \times 5} = \frac{65}{20}
$$
$$
\frac{6}{5} = \frac{6 \times 4}{5 \times 4} = \frac{24}{20}
$$

#### Step 3: Subtract the numerators
$$
\frac{65}{20} - \frac{24}{20} = \frac{65 - 24}{20} = \frac{41}{20}
$$

#### Step 4: Convert to a mixed number
$$
\frac{41}{20} = 2 \frac{1}{20}
$$

Answer:
$$
\boxed{2 \frac{1}{20}}
$$

---

Problem 6:

$$
\frac{21}{6} - \frac{13}{12}
$$

#### Step 1: Find the common denominator
The denominators are 6 and 12. The LCD is 12.

#### Step 2: Rewrite each fraction with the common denominator
$$
\frac{21}{6} = \frac{21 \times 2}{6 \times 2} = \frac{42}{12}
$$
$$
\frac{13}{12} = \frac{13}{12}
$$

#### Step 3: Subtract the numerators
$$
\frac{42}{12} - \frac{13}{12} = \frac{42 - 13}{12} = \frac{29}{12}
$$

#### Step 4: Convert to a mixed number
$$
\frac{29}{12} = 2 \frac{5}{12}
$$

Answer:
$$
\boxed{2 \frac{5}{12}}
$$

---

Problem 7:

$$
\frac{25}{7} - \frac{5}{3}
$$

#### Step 1: Find the common denominator
The denominators are 7 and 3. The LCD is 21.

#### Step 2: Rewrite each fraction with the common denominator
$$
\frac{25}{7} = \frac{25 \times 3}{7 \times 3} = \frac{75}{21}
$$
$$
\frac{5}{3} = \frac{5 \times 7}{3 \times 7} = \frac{35}{21}
$$

#### Step 3: Subtract the numerators
$$
\frac{75}{21} - \frac{35}{21} = \frac{75 - 35}{21} = \frac{40}{21}
$$

#### Step 4: Convert to a mixed number
$$
\frac{40}{21} = 1 \frac{19}{21}
$$

Answer:
$$
\boxed{1 \frac{19}{21}}
$$

---

Problem 8:

$$
\frac{11}{4} - \frac{7}{6}
$$

#### Step 1: Find the common denominator
The denominators are 4 and 6. The LCD is 12.

#### Step 2: Rewrite each fraction with the common denominator
$$
\frac{11}{4} = \frac{11 \times 3}{4 \times 3} = \frac{33}{12}
$$
$$
\frac{7}{6} = \frac{7 \times 2}{6 \times 2} = \frac{14}{12}
$$

#### Step 3: Subtract the numerators
$$
\frac{33}{12} - \frac{14}{12} = \frac{33 - 14}{12} = \frac{19}{12}
$$

#### Step 4: Convert to a mixed number
$$
\frac{19}{12} = 1 \frac{7}{12}
$$

Answer:
$$
\boxed{1 \frac{7}{12}}
$$

---

Problem 9:

$$
\frac{22}{3} - \frac{14}{9}
$$

#### Step 1: Find the common denominator
The denominators are 3 and 9. The LCD is 9.

#### Step 2: Rewrite each fraction with the common denominator
$$
\frac{22}{3} = \frac{22 \times 3}{3 \times 3} = \frac{66}{9}
$$
$$
\frac{14}{9} = \frac{14}{9}
$$

#### Step 3: Subtract the numerators
$$
\frac{66}{9} - \frac{14}{9} = \frac{66 - 14}{9} = \frac{52}{9}
$$

#### Step 4: Convert to a mixed number
$$
\frac{52}{9} = 5 \frac{7}{9}
$$

Answer:
$$
\boxed{5 \frac{7}{9}}
$$

---

Problem 10:

$$
\frac{12}{5} - \frac{9}{8}
$$

#### Step 1: Find the common denominator
The denominators are 5 and 8. The LCD is 40.

#### Step 2: Rewrite each fraction with the common denominator
$$
\frac{12}{5} = \frac{12 \times 8}{5 \times 8} = \frac{96}{40}
$$
$$
\frac{9}{8} = \frac{9 \times 5}{8 \times 5} = \frac{45}{40}
$$

#### Step 3: Subtract the numerators
$$
\frac{96}{40} - \frac{45}{40} = \frac{96 - 45}{40} = \frac{51}{40}
$$

#### Step 4: Convert to a mixed number
$$
\frac{51}{40} = 1 \frac{11}{40}
$$

Answer:
$$
\boxed{1 \frac{11}{40}}
$$

---

Final Answers:

1. $\boxed{1 \frac{1}{12}}$
2. $\boxed{\frac{9}{10}}$
3. $\boxed{1 \frac{5}{6}}$
4. $\boxed{2 \frac{5}{12}}$
5. $\boxed{2 \frac{1}{20}}$
6. $\boxed{2 \frac{5}{12}}$
7. $\boxed{1 \frac{19}{21}}$
8. $\boxed{1 \frac{7}{12}}$
9. $\boxed{5 \frac{7}{9}}$
10. $\boxed{1 \frac{11}{40}}$