Grade 6 Adding Mixed Numbers Worksheets | Math Worksheets - 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 numerators while keeping the denominator the same.
4. Simplify the result if possible, and convert back to a mixed number if needed.

Let's solve each problem step by step.

---

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

#### Step 1: Convert to improper fractions
- \( 6 \frac{1}{3} = 6 + \frac{1}{3} = \frac{18}{3} + \frac{1}{3} = \frac{19}{3} \)
- \( 3 \frac{1}{12} = 3 + \frac{1}{12} = \frac{36}{12} + \frac{1}{12} = \frac{37}{12} \)

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

- Convert \( \frac{19}{3} \) to a fraction with denominator 12:
\[
\frac{19}{3} = \frac{19 \times 4}{3 \times 4} = \frac{76}{12}
\]

#### Step 3: Subtract the fractions
\[
\frac{76}{12} - \frac{37}{12} = \frac{76 - 37}{12} = \frac{39}{12}
\]

#### Step 4: Simplify and convert to a mixed number
- Simplify \( \frac{39}{12} \):
\[
\frac{39}{12} = \frac{13}{4}
\]
- Convert \( \frac{13}{4} \) to a mixed number:
\[
\frac{13}{4} = 3 \frac{1}{4}
\]

Answer: \( 3 \frac{1}{4} \)

---

Problem 2: \( 7 \frac{3}{4} - 1 \frac{2}{4} \)

#### Step 1: Convert to improper fractions
- \( 7 \frac{3}{4} = 7 + \frac{3}{4} = \frac{28}{4} + \frac{3}{4} = \frac{31}{4} \)
- \( 1 \frac{2}{4} = 1 + \frac{2}{4} = \frac{4}{4} + \frac{2}{4} = \frac{6}{4} \)

#### Step 2: Subtract the fractions
\[
\frac{31}{4} - \frac{6}{4} = \frac{31 - 6}{4} = \frac{25}{4}
\]

#### Step 3: Convert to a mixed number
\[
\frac{25}{4} = 6 \frac{1}{4}
\]

Answer: \( 6 \frac{1}{4} \)

---

Problem 3: \( 9 \frac{5}{6} - 3 \frac{1}{18} \)

#### Step 1: Convert to improper fractions
- \( 9 \frac{5}{6} = 9 + \frac{5}{6} = \frac{54}{6} + \frac{5}{6} = \frac{59}{6} \)
- \( 3 \frac{1}{18} = 3 + \frac{1}{18} = \frac{54}{18} + \frac{1}{18} = \frac{55}{18} \)

#### Step 2: Find a common denominator
The denominators are 6 and 18. The LCD is 18.

- Convert \( \frac{59}{6} \) to a fraction with denominator 18:
\[
\frac{59}{6} = \frac{59 \times 3}{6 \times 3} = \frac{177}{18}
\]

#### Step 3: Subtract the fractions
\[
\frac{177}{18} - \frac{55}{18} = \frac{177 - 55}{18} = \frac{122}{18}
\]

#### Step 4: Simplify and convert to a mixed number
- Simplify \( \frac{122}{18} \):
\[
\frac{122}{18} = \frac{61}{9}
\]
- Convert \( \frac{61}{9} \) to a mixed number:
\[
\frac{61}{9} = 6 \frac{7}{9}
\]

Answer: \( 6 \frac{7}{9} \)

---

Problem 4: \( 5 \frac{8}{9} - 3 \frac{5}{9} \)

#### Step 1: Convert to improper fractions
- \( 5 \frac{8}{9} = 5 + \frac{8}{9} = \frac{45}{9} + \frac{8}{9} = \frac{53}{9} \)
- \( 3 \frac{5}{9} = 3 + \frac{5}{9} = \frac{27}{9} + \frac{5}{9} = \frac{32}{9} \)

#### Step 2: Subtract the fractions
\[
\frac{53}{9} - \frac{32}{9} = \frac{53 - 32}{9} = \frac{21}{9}
\]

#### Step 3: Simplify and convert to a mixed number
- Simplify \( \frac{21}{9} \):
\[
\frac{21}{9} = \frac{7}{3}
\]
- Convert \( \frac{7}{3} \) to a mixed number:
\[
\frac{7}{3} = 2 \frac{1}{3}
\]

Answer: \( 2 \frac{1}{3} \)

---

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

#### Step 1: Convert to improper fractions
- \( 3 \frac{3}{4} = 3 + \frac{3}{4} = \frac{12}{4} + \frac{3}{4} = \frac{15}{4} \)
- \( 3 \frac{5}{8} = 3 + \frac{5}{8} = \frac{24}{8} + \frac{5}{8} = \frac{29}{8} \)

#### Step 2: Find a common denominator
The denominators are 4 and 8. The LCD is 8.

- Convert \( \frac{15}{4} \) to a fraction with denominator 8:
\[
\frac{15}{4} = \frac{15 \times 2}{4 \times 2} = \frac{30}{8}
\]

#### Step 3: Subtract the fractions
\[
\frac{30}{8} - \frac{29}{8} = \frac{30 - 29}{8} = \frac{1}{8}
\]

Answer: \( \frac{1}{8} \)

---

Problem 6: \( 4 \frac{2}{3} - 3 \frac{2}{5} \)

#### Step 1: Convert to improper fractions
- \( 4 \frac{2}{3} = 4 + \frac{2}{3} = \frac{12}{3} + \frac{2}{3} = \frac{14}{3} \)
- \( 3 \frac{2}{5} = 3 + \frac{2}{5} = \frac{15}{5} + \frac{2}{5} = \frac{17}{5} \)

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

- Convert \( \frac{14}{3} \) to a fraction with denominator 15:
\[
\frac{14}{3} = \frac{14 \times 5}{3 \times 5} = \frac{70}{15}
\]
- Convert \( \frac{17}{5} \) to a fraction with denominator 15:
\[
\frac{17}{5} = \frac{17 \times 3}{5 \times 3} = \frac{51}{15}
\]

#### Step 3: Subtract the fractions
\[
\frac{70}{15} - \frac{51}{15} = \frac{70 - 51}{15} = \frac{19}{15}
\]

#### Step 4: Convert to a mixed number
\[
\frac{19}{15} = 1 \frac{4}{15}
\]

Answer: \( 1 \frac{4}{15} \)

---

Problem 7: \( 11 \frac{5}{6} - 5 \frac{1}{2} \)

#### Step 1: Convert to improper fractions
- \( 11 \frac{5}{6} = 11 + \frac{5}{6} = \frac{66}{6} + \frac{5}{6} = \frac{71}{6} \)
- \( 5 \frac{1}{2} = 5 + \frac{1}{2} = \frac{10}{2} + \frac{1}{2} = \frac{11}{2} \)

#### Step 2: Find a common denominator
The denominators are 6 and 2. The LCD is 6.

- Convert \( \frac{11}{2} \) to a fraction with denominator 6:
\[
\frac{11}{2} = \frac{11 \times 3}{2 \times 3} = \frac{33}{6}
\]

#### Step 3: Subtract the fractions
\[
\frac{71}{6} - \frac{33}{6} = \frac{71 - 33}{6} = \frac{38}{6}
\]

#### Step 4: Simplify and convert to a mixed number
- Simplify \( \frac{38}{6} \):
\[
\frac{38}{6} = \frac{19}{3}
\]
- Convert \( \frac{19}{3} \) to a mixed number:
\[
\frac{19}{3} = 6 \frac{1}{3}
\]

Answer: \( 6 \frac{1}{3} \)

---

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

#### Step 1: Convert to improper fractions
- \( 8 \frac{1}{5} = 8 + \frac{1}{5} = \frac{40}{5} + \frac{1}{5} = \frac{41}{5} \)
- \( 1 \frac{1}{8} = 1 + \frac{1}{8} = \frac{8}{8} + \frac{1}{8} = \frac{9}{8} \)

#### Step 2: Find a common denominator
The denominators are 5 and 8. The LCD is 40.

- Convert \( \frac{41}{5} \) to a fraction with denominator 40:
\[
\frac{41}{5} = \frac{41 \times 8}{5 \times 8} = \frac{328}{40}
\]
- Convert \( \frac{9}{8} \) to a fraction with denominator 40:
\[
\frac{9}{8} = \frac{9 \times 5}{8 \times 5} = \frac{45}{40}
\]

#### Step 3: Subtract the fractions
\[
\frac{328}{40} - \frac{45}{40} = \frac{328 - 45}{40} = \frac{283}{40}
\]

#### Step 4: Convert to a mixed number
\[
\frac{283}{40} = 7 \frac{3}{40}
\]

Answer: \( 7 \frac{3}{40} \)

---

Problem 9: \( 3 \frac{2}{7} - 3 \frac{1}{14} \)

#### Step 1: Convert to improper fractions
- \( 3 \frac{2}{7} = 3 + \frac{2}{7} = \frac{21}{7} + \frac{2}{7} = \frac{23}{7} \)
- \( 3 \frac{1}{14} = 3 + \frac{1}{14} = \frac{42}{14} + \frac{1}{14} = \frac{43}{14} \)

#### Step 2: Find a common denominator
The denominators are 7 and 14. The LCD is 14.

- Convert \( \frac{23}{7} \) to a fraction with denominator 14:
\[
\frac{23}{7} = \frac{23 \times 2}{7 \times 2} = \frac{46}{14}
\]

#### Step 3: Subtract the fractions
\[
\frac{46}{14} - \frac{43}{14} = \frac{46 - 43}{14} = \frac{3}{14}
\]

Answer: \( \frac{3}{14} \)

---

Problem 10: \( 10 \frac{1}{3} - 4 \frac{4}{21} \)

#### Step 1: Convert to improper fractions
- \( 10 \frac{1}{3} = 10 + \frac{1}{3} = \frac{30}{3} + \frac{1}{3} = \frac{31}{3} \)
- \( 4 \frac{4}{21} = 4 + \frac{4}{21} = \frac{84}{21} + \frac{4}{21} = \frac{88}{21} \)

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

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

#### Step 3: Subtract the fractions
\[
\frac{217}{21} - \frac{88}{21} = \frac{217 - 88}{21} = \frac{129}{21}
\]

#### Step 4: Simplify and convert to a mixed number
- Simplify \( \frac{129}{21} \):
\[
\frac{129}{21} = \frac{43}{7}
\]
- Convert \( \frac{43}{7} \) to a mixed number:
\[
\frac{43}{7} = 6 \frac{1}{7}
\]

Answer: \( 6 \frac{1}{7} \)

---

Final Answers

\[
\boxed{
\begin{array}{ll}
1. & 3 \frac{1}{4} \\
2. & 6 \frac{1}{4} \\
3. & 6 \frac{7}{9} \\
4. & 2 \frac{1}{3} \\
5. & \frac{1}{8} \\
6. & 1 \frac{4}{15} \\
7. & 6 \frac{1}{3} \\
8. & 7 \frac{3}{40} \\
9. & \frac{3}{14} \\
10. & 6 \frac{1}{7} \\
\end{array}
}
\]