Fractions Worksheets | Printable Fractions Worksheets for Teachers - Free Printable

Problem: Subtracting Fractional Inches

The task involves subtracting mixed numbers with fractional parts. To solve these problems, we need to follow these steps:
1. Convert mixed numbers to improper fractions if necessary.
2. Ensure the fractions have a common denominator.
3. Perform the subtraction.
4. Simplify the result and convert back to a mixed number if needed.

Let's solve each problem step by step.

---

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

#### Step 1: Convert to improper fractions
- \( 6 \frac{1}{4} = 6 + \frac{1}{4} = \frac{24}{4} + \frac{1}{4} = \frac{25}{4} \)
- \( 4 \frac{1}{2} = 4 + \frac{1}{2} = \frac{8}{2} + \frac{1}{2} = \frac{9}{2} \)

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

- Convert \( \frac{9}{2} \) to a fraction with denominator 4:
\[
\frac{9}{2} = \frac{9 \times 2}{2 \times 2} = \frac{18}{4}
\]

#### Step 3: Perform the subtraction
\[
\frac{25}{4} - \frac{18}{4} = \frac{25 - 18}{4} = \frac{7}{4}
\]

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

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

---

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

#### Step 1: Convert to improper fractions
- \( 9 \frac{1}{2} = 9 + \frac{1}{2} = \frac{18}{2} + \frac{1}{2} = \frac{19}{2} \)
- \( 1 \frac{1}{4} = 1 + \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4} \)

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

- Convert \( \frac{19}{2} \) to a fraction with denominator 4:
\[
\frac{19}{2} = \frac{19 \times 2}{2 \times 2} = \frac{38}{4}
\]

#### Step 3: Perform the subtraction
\[
\frac{38}{4} - \frac{5}{4} = \frac{38 - 5}{4} = \frac{33}{4}
\]

#### Step 4: Convert back to a mixed number
\[
\frac{33}{4} = 8 \frac{1}{4}
\]

Answer:
\[
\boxed{8 \frac{1}{4}}
\]

---

Problem 3: \( 11 \frac{3}{4} - 7 \frac{1}{4} \)

#### Step 1: Convert to improper fractions
- \( 11 \frac{3}{4} = 11 + \frac{3}{4} = \frac{44}{4} + \frac{3}{4} = \frac{47}{4} \)
- \( 7 \frac{1}{4} = 7 + \frac{1}{4} = \frac{28}{4} + \frac{1}{4} = \frac{29}{4} \)

#### Step 2: Perform the subtraction
\[
\frac{47}{4} - \frac{29}{4} = \frac{47 - 29}{4} = \frac{18}{4}
\]

#### Step 3: Simplify the fraction
\[
\frac{18}{4} = \frac{9}{2}
\]

#### Step 4: Convert back to a mixed number
\[
\frac{9}{2} = 4 \frac{1}{2}
\]

Answer:
\[
\boxed{4 \frac{1}{2}}
\]

---

Problem 4: \( 7 \frac{1}{4} - 5 \frac{5}{16} \)

#### Step 1: Convert to improper fractions
- \( 7 \frac{1}{4} = 7 + \frac{1}{4} = \frac{28}{4} + \frac{1}{4} = \frac{29}{4} \)
- \( 5 \frac{5}{16} = 5 + \frac{5}{16} = \frac{80}{16} + \frac{5}{16} = \frac{85}{16} \)

#### Step 2: Find a common denominator
The denominators are 4 and 16. The LCD is 16.

- Convert \( \frac{29}{4} \) to a fraction with denominator 16:
\[
\frac{29}{4} = \frac{29 \times 4}{4 \times 4} = \frac{116}{16}
\]

#### Step 3: Perform the subtraction
\[
\frac{116}{16} - \frac{85}{16} = \frac{116 - 85}{16} = \frac{31}{16}
\]

#### Step 4: Convert back to a mixed number
\[
\frac{31}{16} = 1 \frac{15}{16}
\]

Answer:
\[
\boxed{1 \frac{15}{16}}
\]

---

Problem 5: \( 7 \frac{1}{2} - 5 \frac{3}{8} \)

#### Step 1: Convert to improper fractions
- \( 7 \frac{1}{2} = 7 + \frac{1}{2} = \frac{14}{2} + \frac{1}{2} = \frac{15}{2} \)
- \( 5 \frac{3}{8} = 5 + \frac{3}{8} = \frac{40}{8} + \frac{3}{8} = \frac{43}{8} \)

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

- Convert \( \frac{15}{2} \) to a fraction with denominator 8:
\[
\frac{15}{2} = \frac{15 \times 4}{2 \times 4} = \frac{60}{8}
\]

#### Step 3: Perform the subtraction
\[
\frac{60}{8} - \frac{43}{8} = \frac{60 - 43}{8} = \frac{17}{8}
\]

#### Step 4: Convert back to a mixed number
\[
\frac{17}{8} = 2 \frac{1}{8}
\]

Answer:
\[
\boxed{2 \frac{1}{8}}
\]

---

Problem 6: \( 7 \frac{9}{16} - 3 \frac{3}{4} \)

#### Step 1: Convert to improper fractions
- \( 7 \frac{9}{16} = 7 + \frac{9}{16} = \frac{112}{16} + \frac{9}{16} = \frac{121}{16} \)
- \( 3 \frac{3}{4} = 3 + \frac{3}{4} = \frac{12}{4} + \frac{3}{4} = \frac{15}{4} \)

#### Step 2: Find a common denominator
The denominators are 16 and 4. The LCD is 16.

- Convert \( \frac{15}{4} \) to a fraction with denominator 16:
\[
\frac{15}{4} = \frac{15 \times 4}{4 \times 4} = \frac{60}{16}
\]

#### Step 3: Perform the subtraction
\[
\frac{121}{16} - \frac{60}{16} = \frac{121 - 60}{16} = \frac{61}{16}
\]

#### Step 4: Convert back to a mixed number
\[
\frac{61}{16} = 3 \frac{13}{16}
\]

Answer:
\[
\boxed{3 \frac{13}{16}}
\]

---

Problem 7: \( 5 \frac{13}{16} - 2 \frac{1}{8} \)

#### Step 1: Convert to improper fractions
- \( 5 \frac{13}{16} = 5 + \frac{13}{16} = \frac{80}{16} + \frac{13}{16} = \frac{93}{16} \)
- \( 2 \frac{1}{8} = 2 + \frac{1}{8} = \frac{16}{8} + \frac{1}{8} = \frac{17}{8} \)

#### Step 2: Find a common denominator
The denominators are 16 and 8. The LCD is 16.

- Convert \( \frac{17}{8} \) to a fraction with denominator 16:
\[
\frac{17}{8} = \frac{17 \times 2}{8 \times 2} = \frac{34}{16}
\]

#### Step 3: Perform the subtraction
\[
\frac{93}{16} - \frac{34}{16} = \frac{93 - 34}{16} = \frac{59}{16}
\]

#### Step 4: Convert back to a mixed number
\[
\frac{59}{16} = 3 \frac{11}{16}
\]

Answer:
\[
\boxed{3 \frac{11}{16}}
\]

---

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

#### Step 1: Convert to improper fractions
- \( 4 \frac{3}{8} = 4 + \frac{3}{8} = \frac{32}{8} + \frac{3}{8} = \frac{35}{8} \)
- \( 2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} \)

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

- Convert \( \frac{5}{2} \) to a fraction with denominator 8:
\[
\frac{5}{2} = \frac{5 \times 4}{2 \times 4} = \frac{20}{8}
\]

#### Step 3: Perform the subtraction
\[
\frac{35}{8} - \frac{20}{8} = \frac{35 - 20}{8} = \frac{15}{8}
\]

#### Step 4: Convert back to a mixed number
\[
\frac{15}{8} = 1 \frac{7}{8}
\]

Answer:
\[
\boxed{1 \frac{7}{8}}
\]

---

Problem 9: \( 7 \frac{3}{16} - 5 \frac{5}{8} \)

#### Step 1: Convert to improper fractions
- \( 7 \frac{3}{16} = 7 + \frac{3}{16} = \frac{112}{16} + \frac{3}{16} = \frac{115}{16} \)
- \( 5 \frac{5}{8} = 5 + \frac{5}{8} = \frac{40}{8} + \frac{5}{8} = \frac{45}{8} \)

#### Step 2: Find a common denominator
The denominators are 16 and 8. The LCD is 16.

- Convert \( \frac{45}{8} \) to a fraction with denominator 16:
\[
\frac{45}{8} = \frac{45 \times 2}{8 \times 2} = \frac{90}{16}
\]

#### Step 3: Perform the subtraction
\[
\frac{115}{16} - \frac{90}{16} = \frac{115 - 90}{16} = \frac{25}{16}
\]

#### Step 4: Convert back to a mixed number
\[
\frac{25}{16} = 1 \frac{9}{16}
\]

Answer:
\[
\boxed{1 \frac{9}{16}}
\]

---

Problem 10: \( 11 \frac{1}{2} - 5 \frac{1}{2} \)

#### Step 1: Convert to improper fractions
- \( 11 \frac{1}{2} = 11 + \frac{1}{2} = \frac{22}{2} + \frac{1}{2} = \frac{23}{2} \)
- \( 5 \frac{1}{2} = 5 + \frac{1}{2} = \frac{10}{2} + \frac{1}{2} = \frac{11}{2} \)

#### Step 2: Perform the subtraction
\[
\frac{23}{2} - \frac{11}{2} = \frac{23 - 11}{2} = \frac{12}{2}
\]

#### Step 3: Simplify the fraction
\[
\frac{12}{2} = 6
\]

Answer:
\[
\boxed{6}
\]

---

Final Answers:

1. \( \boxed{1 \frac{3}{4}} \)
2. \( \boxed{8 \frac{1}{4}} \)
3. \( \boxed{4 \frac{1}{2}} \)
4. \( \boxed{1 \frac{15}{16}} \)
5. \( \boxed{2 \frac{1}{8}} \)
6. \( \boxed{3 \frac{13}{16}} \)
7. \( \boxed{3 \frac{11}{16}} \)
8. \( \boxed{1 \frac{7}{8}} \)
9. \( \boxed{1 \frac{9}{16}} \)
10. \( \boxed{6} \)