Mixed number subtraction practice problems for students.

To solve the problems involving the subtraction of 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 fractions and simplify the result.
4. Convert back to a mixed number if needed.

Let's solve each problem step by step.

---

Problem 1: \( 16 \frac{3}{9} - 10 \frac{2}{5} \)

#### Step 1: Simplify the fractions
- \( \frac{3}{9} = \frac{1}{3} \)
- So, \( 16 \frac{3}{9} = 16 \frac{1}{3} \)

#### Step 2: Convert to improper fractions
- \( 16 \frac{1}{3} = \frac{16 \times 3 + 1}{3} = \frac{48 + 1}{3} = \frac{49}{3} \)
- \( 10 \frac{2}{5} = \frac{10 \times 5 + 2}{5} = \frac{50 + 2}{5} = \frac{52}{5} \)

#### Step 3: Find a common denominator
- The denominators are 3 and 5. The least common denominator (LCD) is 15.
- Convert \( \frac{49}{3} \) to a fraction with denominator 15:
\[
\frac{49}{3} = \frac{49 \times 5}{3 \times 5} = \frac{245}{15}
\]
- Convert \( \frac{52}{5} \) to a fraction with denominator 15:
\[
\frac{52}{5} = \frac{52 \times 3}{5 \times 3} = \frac{156}{15}
\]

#### Step 4: Subtract the fractions
\[
\frac{245}{15} - \frac{156}{15} = \frac{245 - 156}{15} = \frac{89}{15}
\]

#### Step 5: Convert back to a mixed number
- \( \frac{89}{15} = 5 \frac{14}{15} \)

Answer:
\[
\boxed{5 \frac{14}{15}}
\]

---

Problem 2: \( 7 \frac{5}{12} - 2 \frac{1}{2} \)

#### Step 1: Convert to improper fractions
- \( 7 \frac{5}{12} = \frac{7 \times 12 + 5}{12} = \frac{84 + 5}{12} = \frac{89}{12} \)
- \( 2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2} \)

#### Step 2: Find a common denominator
- The denominators are 12 and 2. The LCD is 12.
- Convert \( \frac{5}{2} \) to a fraction with denominator 12:
\[
\frac{5}{2} = \frac{5 \times 6}{2 \times 6} = \frac{30}{12}
\]

#### Step 3: Subtract the fractions
\[
\frac{89}{12} - \frac{30}{12} = \frac{89 - 30}{12} = \frac{59}{12}
\]

#### Step 4: Convert back to a mixed number
- \( \frac{59}{12} = 4 \frac{11}{12} \)

Answer:
\[
\boxed{4 \frac{11}{12}}
\]

---

Problem 3: \( 8 \frac{9}{10} - 3 \frac{2}{3} \)

#### Step 1: Convert to improper fractions
- \( 8 \frac{9}{10} = \frac{8 \times 10 + 9}{10} = \frac{80 + 9}{10} = \frac{89}{10} \)
- \( 3 \frac{2}{3} = \frac{3 \times 3 + 2}{3} = \frac{9 + 2}{3} = \frac{11}{3} \)

#### Step 2: Find a common denominator
- The denominators are 10 and 3. The LCD is 30.
- Convert \( \frac{89}{10} \) to a fraction with denominator 30:
\[
\frac{89}{10} = \frac{89 \times 3}{10 \times 3} = \frac{267}{30}
\]
- Convert \( \frac{11}{3} \) to a fraction with denominator 30:
\[
\frac{11}{3} = \frac{11 \times 10}{3 \times 10} = \frac{110}{30}
\]

#### Step 3: Subtract the fractions
\[
\frac{267}{30} - \frac{110}{30} = \frac{267 - 110}{30} = \frac{157}{30}
\]

#### Step 4: Convert back to a mixed number
- \( \frac{157}{30} = 5 \frac{7}{30} \)

Answer:
\[
\boxed{5 \frac{7}{30}}
\]

---

Problem 4: \( 19 \frac{2}{3} - 11 \frac{5}{8} \)

#### Step 1: Convert to improper fractions
- \( 19 \frac{2}{3} = \frac{19 \times 3 + 2}{3} = \frac{57 + 2}{3} = \frac{59}{3} \)
- \( 11 \frac{5}{8} = \frac{11 \times 8 + 5}{8} = \frac{88 + 5}{8} = \frac{93}{8} \)

#### Step 2: Find a common denominator
- The denominators are 3 and 8. The LCD is 24.
- Convert \( \frac{59}{3} \) to a fraction with denominator 24:
\[
\frac{59}{3} = \frac{59 \times 8}{3 \times 8} = \frac{472}{24}
\]
- Convert \( \frac{93}{8} \) to a fraction with denominator 24:
\[
\frac{93}{8} = \frac{93 \times 3}{8 \times 3} = \frac{279}{24}
\]

#### Step 3: Subtract the fractions
\[
\frac{472}{24} - \frac{279}{24} = \frac{472 - 279}{24} = \frac{193}{24}
\]

#### Step 4: Convert back to a mixed number
- \( \frac{193}{24} = 8 \frac{1}{24} \)

Answer:
\[
\boxed{8 \frac{1}{24}}
\]

---

Problem 5: \( 13 \frac{1}{8} - 12 \frac{10}{12} \)

#### Step 1: Simplify the fractions
- \( \frac{10}{12} = \frac{5}{6} \)
- So, \( 12 \frac{10}{12} = 12 \frac{5}{6} \)

#### Step 2: Convert to improper fractions
- \( 13 \frac{1}{8} = \frac{13 \times 8 + 1}{8} = \frac{104 + 1}{8} = \frac{105}{8} \)
- \( 12 \frac{5}{6} = \frac{12 \times 6 + 5}{6} = \frac{72 + 5}{6} = \frac{77}{6} \)

#### Step 3: Find a common denominator
- The denominators are 8 and 6. The LCD is 24.
- Convert \( \frac{105}{8} \) to a fraction with denominator 24:
\[
\frac{105}{8} = \frac{105 \times 3}{8 \times 3} = \frac{315}{24}
\]
- Convert \( \frac{77}{6} \) to a fraction with denominator 24:
\[
\frac{77}{6} = \frac{77 \times 4}{6 \times 4} = \frac{308}{24}
\]

#### Step 4: Subtract the fractions
\[
\frac{315}{24} - \frac{308}{24} = \frac{315 - 308}{24} = \frac{7}{24}
\]

Answer:
\[
\boxed{\frac{7}{24}}
\]

---

Problem 6: \( 18 \frac{1}{2} - 17 \frac{2}{8} \)

#### Step 1: Simplify the fractions
- \( \frac{2}{8} = \frac{1}{4} \)
- So, \( 17 \frac{2}{8} = 17 \frac{1}{4} \)

#### Step 2: Convert to improper fractions
- \( 18 \frac{1}{2} = \frac{18 \times 2 + 1}{2} = \frac{36 + 1}{2} = \frac{37}{2} \)
- \( 17 \frac{1}{4} = \frac{17 \times 4 + 1}{4} = \frac{68 + 1}{4} = \frac{69}{4} \)

#### Step 3: Find a common denominator
- The denominators are 2 and 4. The LCD is 4.
- Convert \( \frac{37}{2} \) to a fraction with denominator 4:
\[
\frac{37}{2} = \frac{37 \times 2}{2 \times 2} = \frac{74}{4}
\]

#### Step 4: Subtract the fractions
\[
\frac{74}{4} - \frac{69}{4} = \frac{74 - 69}{4} = \frac{5}{4}
\]

#### Step 5: Convert back to a mixed number
- \( \frac{5}{4} = 1 \frac{1}{4} \)

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

---

Problem 7: \( 14 \frac{4}{10} - 13 \frac{1}{3} \)

#### Step 1: Simplify the fractions
- \( \frac{4}{10} = \frac{2}{5} \)
- So, \( 14 \frac{4}{10} = 14 \frac{2}{5} \)

#### Step 2: Convert to improper fractions
- \( 14 \frac{2}{5} = \frac{14 \times 5 + 2}{5} = \frac{70 + 2}{5} = \frac{72}{5} \)
- \( 13 \frac{1}{3} = \frac{13 \times 3 + 1}{3} = \frac{39 + 1}{3} = \frac{40}{3} \)

#### Step 3: Find a common denominator
- The denominators are 5 and 3. The LCD is 15.
- Convert \( \frac{72}{5} \) to a fraction with denominator 15:
\[
\frac{72}{5} = \frac{72 \times 3}{5 \times 3} = \frac{216}{15}
\]
- Convert \( \frac{40}{3} \) to a fraction with denominator 15:
\[
\frac{40}{3} = \frac{40 \times 5}{3 \times 5} = \frac{200}{15}
\]

#### Step 4: Subtract the fractions
\[
\frac{216}{15} - \frac{200}{15} = \frac{216 - 200}{15} = \frac{16}{15}
\]

#### Step 5: Convert back to a mixed number
- \( \frac{16}{15} = 1 \frac{1}{15} \)

Answer:
\[
\boxed{1 \frac{1}{15}}
\]

---

Problem 8: \( 19 \frac{7}{12} - 19 \frac{1}{5} \)

#### Step 1: Convert to improper fractions
- \( 19 \frac{7}{12} = \frac{19 \times 12 + 7}{12} = \frac{228 + 7}{12} = \frac{235}{12} \)
- \( 19 \frac{1}{5} = \frac{19 \times 5 + 1}{5} = \frac{95 + 1}{5} = \frac{96}{5} \)

#### Step 2: Find a common denominator
- The denominators are 12 and 5. The LCD is 60.
- Convert \( \frac{235}{12} \) to a fraction with denominator 60:
\[
\frac{235}{12} = \frac{235 \times 5}{12 \times 5} = \frac{1175}{60}
\]
- Convert \( \frac{96}{5} \) to a fraction with denominator 60:
\[
\frac{96}{5} = \frac{96 \times 12}{5 \times 12} = \frac{1152}{60}
\]

#### Step 3: Subtract the fractions
\[
\frac{1175}{60} - \frac{1152}{60} = \frac{1175 - 1152}{60} = \frac{23}{60}
\]

Answer:
\[
\boxed{\frac{23}{60}}
\]

---

Problem 9: \( 20 \frac{3}{4} - 18 \frac{2}{3} \)

#### Step 1: Convert to improper fractions
- \( 20 \frac{3}{4} = \frac{20 \times 4 + 3}{4} = \frac{80 + 3}{4} = \frac{83}{4} \)
- \( 18 \frac{2}{3} = \frac{18 \times 3 + 2}{3} = \frac{54 + 2}{3} = \frac{56}{3} \)

#### Step 2: Find a common denominator
- The denominators are 4 and 3. The LCD is 12.
- Convert \( \frac{83}{4} \) to a fraction with denominator 12:
\[
\frac{83}{4} = \frac{83 \times 3}{4 \times 3} = \frac{249}{12}
\]
- Convert \( \frac{56}{3} \) to a fraction with denominator 12:
\[
\frac{56}{3} = \frac{56 \times 4}{3 \times 4} = \frac{224}{12}
\]

#### Step 3: Subtract the fractions
\[
\frac{249}{12} - \frac{224}{12} = \frac{249 - 224}{12} = \frac{25}{12}
\]

#### Step 4: Convert back to a mixed number
- \( \frac{25}{12} = 2 \frac{1}{12} \)

Answer:
\[
\boxed{2 \frac{1}{12}}
\]

---

Problem 10: \( 19 \frac{7}{10} - 13 \frac{4}{10} \)

#### Step 1: Simplify the fractions
- Both fractions have the same denominator, so no conversion is needed.

#### Step 2: Subtract the whole numbers and fractions separately
- Whole numbers: \( 19 - 13 = 6 \)
- Fractions: \( \frac{7}{10} - \frac{4}{10} = \frac{7 - 4}{10} = \frac{3}{10} \)

#### Step 3: Combine the results
- \( 6 + \frac{3}{10} = 6 \frac{3}{10} \)

Answer:
\[
\boxed{6 \frac{3}{10}}
\]

---

Problem 11: \( 17 \frac{5}{6} - 1 \frac{3}{5} \)

#### Step 1: Convert to improper fractions
- \( 17 \frac{5}{6} = \frac{17 \times 6 + 5}{6} = \frac{102 + 5}{6} = \frac{107}{6} \)
- \( 1 \frac{3}{5} = \frac{1 \times 5 + 3}{5} = \frac{5 + 3}{5} = \frac{8}{5} \)

#### Step 2: Find a common denominator
- The denominators are 6 and 5. The LCD is 30.
- Convert \( \frac{107}{6} \) to a fraction with denominator 30:
\[
\frac{107}{6} = \frac{107 \times 5}{6 \times 5} = \frac{535}{30}
\]
- Convert \( \frac{8}{5} \) to a fraction with denominator 30:
\[
\frac{8}{5} = \frac{8 \times 6}{5 \times 6} = \frac{48}{30}
\]

#### Step 3: Subtract the fractions
\[
\frac{535}{30} - \frac{48}{30} = \frac{535 - 48}{30} = \frac{487}{30}
\]

#### Step 4: Convert back to a mixed number
- \( \frac{487}{30} = 16 \frac{7}{30} \)

Answer:
\[
\boxed{16 \frac{7}{30}}
\]

---

Problem 12: \( 9 \frac{1}{5} - 5 \frac{4}{6} \)

#### Step 1: Simplify the fractions
- \( \frac{4}{6} = \frac{2}{3} \)
- So, \( 5 \frac{4}{6} = 5 \frac{2}{3} \)

#### Step 2: Convert to improper fractions
- \( 9 \frac{1}{5} = \frac{9 \times 5 + 1}{5} = \frac{45 + 1}{5} = \frac{46}{5} \)
- \( 5 \frac{2}{3} = \frac{5 \times 3 + 2}{3} = \frac{15 + 2}{3} = \frac{17}{3} \)

#### Step 3: Find a common denominator
- The denominators are 5 and 3. The LCD is 15.
- Convert \( \frac{46}{5} \) to a fraction with denominator 15:
\[
\frac{46}{5} = \frac{46 \times 3}{5 \times 3} = \frac{138}{15}
\]
- Convert \( \frac{17}{3} \) to a fraction with denominator 15:
\[
\frac{17}{3} = \frac{17 \times 5}{3 \times 5} = \frac{85}{15}
\]

#### Step 4: Subtract the fractions
\[
\frac{138}{15} - \frac{85}{15} = \frac{138 - 85}{15} = \frac{53}{15}
\]

#### Step 5: Convert back to a mixed number
- \( \frac{53}{15} = 3 \frac{8}{15} \)

Answer:
\[
\boxed{3 \frac{8}{15}}
\]

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & 5 \frac{14}{15} \\
2. & 4 \frac{11}{12} \\
3. & 5 \frac{7}{30} \\
4. & 8 \frac{1}{24} \\
5. & \frac{7}{24} \\
6. & 1 \frac{1}{4} \\
7. & 1 \frac{1}{15} \\
8. & \frac{23}{60} \\
9. & 2 \frac{1}{12} \\
10. & 6 \frac{3}{10} \\
11. & 16 \frac{7}{30} \\
12. & 3 \frac{8}{15}
\end{array}
}
\]