Fractions Worksheets | Printable Fractions Worksheets for Teachers - 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 fractions and simplify the result.
4. Convert back to a mixed number if needed.

Let's solve each problem step by step.

---

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

#### Step 1: Convert mixed numbers to improper fractions
- \( 5 \frac{3}{5} = \frac{5 \times 5 + 3}{5} = \frac{28}{5} \)
- \( 2 \frac{1}{10} = \frac{2 \times 10 + 1}{10} = \frac{21}{10} \)

#### Step 2: Find a common denominator
The denominators are 5 and 10. The least common denominator (LCD) is 10.

- Convert \( \frac{28}{5} \) to a fraction with denominator 10:
\[
\frac{28}{5} = \frac{28 \times 2}{5 \times 2} = \frac{56}{10}
\]

#### Step 3: Subtract the fractions
\[
\frac{56}{10} - \frac{21}{10} = \frac{56 - 21}{10} = \frac{35}{10}
\]

#### Step 4: Simplify and convert back to a mixed number
\[
\frac{35}{10} = \frac{7}{2} = 3 \frac{1}{2}
\]

Answer:
\[
\boxed{3 \frac{1}{2}}
\]

---

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

#### Step 1: Convert mixed numbers to improper fractions
- \( 5 \frac{2}{3} = \frac{5 \times 3 + 2}{3} = \frac{17}{3} \)
- \( 4 \frac{2}{4} = \frac{4 \times 4 + 2}{4} = \frac{18}{4} \)

#### Step 2: Find a common denominator
The denominators are 3 and 4. The least common denominator (LCD) is 12.

- Convert \( \frac{17}{3} \) to a fraction with denominator 12:
\[
\frac{17}{3} = \frac{17 \times 4}{3 \times 4} = \frac{68}{12}
\]
- Convert \( \frac{18}{4} \) to a fraction with denominator 12:
\[
\frac{18}{4} = \frac{18 \times 3}{4 \times 3} = \frac{54}{12}
\]

#### Step 3: Subtract the fractions
\[
\frac{68}{12} - \frac{54}{12} = \frac{68 - 54}{12} = \frac{14}{12}
\]

#### Step 4: Simplify and convert back to a mixed number
\[
\frac{14}{12} = \frac{7}{6} = 1 \frac{1}{6}
\]

Answer:
\[
\boxed{1 \frac{1}{6}}
\]

---

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

#### Step 1: Convert mixed numbers to improper fractions
- \( 5 \frac{3}{4} = \frac{5 \times 4 + 3}{4} = \frac{23}{4} \)
- \( 4 \frac{2}{5} = \frac{4 \times 5 + 2}{5} = \frac{22}{5} \)

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

- Convert \( \frac{23}{4} \) to a fraction with denominator 20:
\[
\frac{23}{4} = \frac{23 \times 5}{4 \times 5} = \frac{115}{20}
\]
- Convert \( \frac{22}{5} \) to a fraction with denominator 20:
\[
\frac{22}{5} = \frac{22 \times 4}{5 \times 4} = \frac{88}{20}
\]

#### Step 3: Subtract the fractions
\[
\frac{115}{20} - \frac{88}{20} = \frac{115 - 88}{20} = \frac{27}{20}
\]

#### Step 4: Simplify and convert back to a mixed number
\[
\frac{27}{20} = 1 \frac{7}{20}
\]

Answer:
\[
\boxed{1 \frac{7}{20}}
\]

---

Problem 4: \( 9 \frac{3}{5} - 1 \frac{2}{4} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 9 \frac{3}{5} = \frac{9 \times 5 + 3}{5} = \frac{48}{5} \)
- \( 1 \frac{2}{4} = \frac{1 \times 4 + 2}{4} = \frac{6}{4} \)

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

- Convert \( \frac{48}{5} \) to a fraction with denominator 20:
\[
\frac{48}{5} = \frac{48 \times 4}{5 \times 4} = \frac{192}{20}
\]
- Convert \( \frac{6}{4} \) to a fraction with denominator 20:
\[
\frac{6}{4} = \frac{6 \times 5}{4 \times 5} = \frac{30}{20}
\]

#### Step 3: Subtract the fractions
\[
\frac{192}{20} - \frac{30}{20} = \frac{192 - 30}{20} = \frac{162}{20}
\]

#### Step 4: Simplify and convert back to a mixed number
\[
\frac{162}{20} = \frac{81}{10} = 8 \frac{1}{10}
\]

Answer:
\[
\boxed{8 \frac{1}{10}}
\]

---

Problem 5: \( 6 \frac{3}{10} - 1 \frac{1}{4} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 6 \frac{3}{10} = \frac{6 \times 10 + 3}{10} = \frac{63}{10} \)
- \( 1 \frac{1}{4} = \frac{1 \times 4 + 1}{4} = \frac{5}{4} \)

#### Step 2: Find a common denominator
The denominators are 10 and 4. The least common denominator (LCD) is 20.

- Convert \( \frac{63}{10} \) to a fraction with denominator 20:
\[
\frac{63}{10} = \frac{63 \times 2}{10 \times 2} = \frac{126}{20}
\]
- Convert \( \frac{5}{4} \) to a fraction with denominator 20:
\[
\frac{5}{4} = \frac{5 \times 5}{4 \times 5} = \frac{25}{20}
\]

#### Step 3: Subtract the fractions
\[
\frac{126}{20} - \frac{25}{20} = \frac{126 - 25}{20} = \frac{101}{20}
\]

#### Step 4: Simplify and convert back to a mixed number
\[
\frac{101}{20} = 5 \frac{1}{20}
\]

Answer:
\[
\boxed{5 \frac{1}{20}}
\]

---

Problem 6: \( 9 \frac{1}{4} - 3 \frac{1}{5} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 9 \frac{1}{4} = \frac{9 \times 4 + 1}{4} = \frac{37}{4} \)
- \( 3 \frac{1}{5} = \frac{3 \times 5 + 1}{5} = \frac{16}{5} \)

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

- Convert \( \frac{37}{4} \) to a fraction with denominator 20:
\[
\frac{37}{4} = \frac{37 \times 5}{4 \times 5} = \frac{185}{20}
\]
- Convert \( \frac{16}{5} \) to a fraction with denominator 20:
\[
\frac{16}{5} = \frac{16 \times 4}{5 \times 4} = \frac{64}{20}
\]

#### Step 3: Subtract the fractions
\[
\frac{185}{20} - \frac{64}{20} = \frac{185 - 64}{20} = \frac{121}{20}
\]

#### Step 4: Simplify and convert back to a mixed number
\[
\frac{121}{20} = 6 \frac{1}{20}
\]

Answer:
\[
\boxed{6 \frac{1}{20}}
\]

---

Problem 7: \( 9 \frac{1}{3} - 4 \frac{1}{5} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 9 \frac{1}{3} = \frac{9 \times 3 + 1}{3} = \frac{28}{3} \)
- \( 4 \frac{1}{5} = \frac{4 \times 5 + 1}{5} = \frac{21}{5} \)

#### Step 2: Find a common denominator
The denominators are 3 and 5. The least common denominator (LCD) is 15.

- Convert \( \frac{28}{3} \) to a fraction with denominator 15:
\[
\frac{28}{3} = \frac{28 \times 5}{3 \times 5} = \frac{140}{15}
\]
- Convert \( \frac{21}{5} \) to a fraction with denominator 15:
\[
\frac{21}{5} = \frac{21 \times 3}{5 \times 3} = \frac{63}{15}
\]

#### Step 3: Subtract the fractions
\[
\frac{140}{15} - \frac{63}{15} = \frac{140 - 63}{15} = \frac{77}{15}
\]

#### Step 4: Simplify and convert back to a mixed number
\[
\frac{77}{15} = 5 \frac{2}{15}
\]

Answer:
\[
\boxed{5 \frac{2}{15}}
\]

---

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

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

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

- Convert \( \frac{34}{5} \) to a fraction with denominator 20:
\[
\frac{34}{5} = \frac{34 \times 4}{5 \times 4} = \frac{136}{20}
\]
- Convert \( \frac{5}{4} \) to a fraction with denominator 20:
\[
\frac{5}{4} = \frac{5 \times 5}{4 \times 5} = \frac{25}{20}
\]

#### Step 3: Subtract the fractions
\[
\frac{136}{20} - \frac{25}{20} = \frac{136 - 25}{20} = \frac{111}{20}
\]

#### Step 4: Simplify and convert back to a mixed number
\[
\frac{111}{20} = 5 \frac{11}{20}
\]

Answer:
\[
\boxed{5 \frac{11}{20}}
\]

---

Problem 9: \( 9 \frac{7}{10} - 1 \frac{2}{3} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 9 \frac{7}{10} = \frac{9 \times 10 + 7}{10} = \frac{97}{10} \)
- \( 1 \frac{2}{3} = \frac{1 \times 3 + 2}{3} = \frac{5}{3} \)

#### Step 2: Find a common denominator
The denominators are 10 and 3. The least common denominator (LCD) is 30.

- Convert \( \frac{97}{10} \) to a fraction with denominator 30:
\[
\frac{97}{10} = \frac{97 \times 3}{10 \times 3} = \frac{291}{30}
\]
- Convert \( \frac{5}{3} \) to a fraction with denominator 30:
\[
\frac{5}{3} = \frac{5 \times 10}{3 \times 10} = \frac{50}{30}
\]

#### Step 3: Subtract the fractions
\[
\frac{291}{30} - \frac{50}{30} = \frac{291 - 50}{30} = \frac{241}{30}
\]

#### Step 4: Simplify and convert back to a mixed number
\[
\frac{241}{30} = 8 \frac{1}{30}
\]

Answer:
\[
\boxed{8 \frac{1}{30}}
\]

---

Problem 10: \( 6 \frac{2}{4} - 3 \frac{4}{10} \)

#### Step 1: Simplify the fractions in the mixed numbers
- \( 6 \frac{2}{4} = 6 \frac{1}{2} \) (since \( \frac{2}{4} = \frac{1}{2} \))
- \( 3 \frac{4}{10} = 3 \frac{2}{5} \) (since \( \frac{4}{10} = \frac{2}{5} \))

#### Step 2: Convert mixed numbers to improper fractions
- \( 6 \frac{1}{2} = \frac{6 \times 2 + 1}{2} = \frac{13}{2} \)
- \( 3 \frac{2}{5} = \frac{3 \times 5 + 2}{5} = \frac{17}{5} \)

#### Step 3: Find a common denominator
The denominators are 2 and 5. The least common denominator (LCD) is 10.

- Convert \( \frac{13}{2} \) to a fraction with denominator 10:
\[
\frac{13}{2} = \frac{13 \times 5}{2 \times 5} = \frac{65}{10}
\]
- Convert \( \frac{17}{5} \) to a fraction with denominator 10:
\[
\frac{17}{5} = \frac{17 \times 2}{5 \times 2} = \frac{34}{10}
\]

#### Step 4: Subtract the fractions
\[
\frac{65}{10} - \frac{34}{10} = \frac{65 - 34}{10} = \frac{31}{10}
\]

#### Step 5: Simplify and convert back to a mixed number
\[
\frac{31}{10} = 3 \frac{1}{10}
\]

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

---

Final Answers:

\[
\boxed{
\begin{aligned}
1) & \ 3 \frac{1}{2} \\
2) & \ 1 \frac{1}{6} \\
3) & \ 1 \frac{7}{20} \\
4) & \ 8 \frac{1}{10} \\
5) & \ 5 \frac{1}{20} \\
6) & \ 6 \frac{1}{20} \\
7) & \ 5 \frac{2}{15} \\
8) & \ 5 \frac{11}{20} \\
9) & \ 8 \frac{1}{30} \\
10) & \ 3 \frac{1}{10}
\end{aligned}
}
\]