Subtraction of mixed fractions worksheet with 12 problems requiring answers in lowest terms.

To solve the problems involving subtracting mixed fractions, we need to follow these steps:

1. Convert mixed fractions to improper fractions.
2. Find a common denominator for the fractions.
3. Subtract the numerators while keeping the denominator the same.
4. Simplify the result to its lowest terms.
5. Convert back to a mixed fraction if necessary.

Let's solve each problem step by step.

---

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

1. Convert to improper fractions:
\[
5 \frac{2}{3} = \frac{5 \times 3 + 2}{3} = \frac{17}{3}
\]
\[
1 \frac{1}{3} = \frac{1 \times 3 + 1}{3} = \frac{4}{3}
\]

2. Subtract the fractions:
\[
\frac{17}{3} - \frac{4}{3} = \frac{17 - 4}{3} = \frac{13}{3}
\]

3. Convert back to a mixed fraction:
\[
\frac{13}{3} = 4 \frac{1}{3}
\]

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

---

Problem 2: \( 3 \frac{1}{3} - 2 \frac{4}{11} \)

1. Convert to improper fractions:
\[
3 \frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{10}{3}
\]
\[
2 \frac{4}{11} = \frac{2 \times 11 + 4}{11} = \frac{26}{11}
\]

2. Find a common denominator (LCM of 3 and 11 is 33):
\[
\frac{10}{3} = \frac{10 \times 11}{3 \times 11} = \frac{110}{33}
\]
\[
\frac{26}{11} = \frac{26 \times 3}{11 \times 3} = \frac{78}{33}
\]

3. Subtract the fractions:
\[
\frac{110}{33} - \frac{78}{33} = \frac{110 - 78}{33} = \frac{32}{33}
\]

Answer: \( \frac{32}{33} \)

---

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

1. Convert to improper fractions:
\[
7 \frac{2}{3} = \frac{7 \times 3 + 2}{3} = \frac{23}{3}
\]
\[
1 \frac{2}{3} = \frac{1 \times 3 + 2}{3} = \frac{5}{3}
\]

2. Subtract the fractions:
\[
\frac{23}{3} - \frac{5}{3} = \frac{23 - 5}{3} = \frac{18}{3} = 6
\]

Answer: \( 6 \)

---

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

1. Convert to improper fractions:
\[
5 \frac{3}{4} = \frac{5 \times 4 + 3}{4} = \frac{23}{4}
\]
\[
5 \frac{1}{2} = \frac{5 \times 2 + 1}{2} = \frac{11}{2}
\]

2. Find a common denominator (LCM of 4 and 2 is 4):
\[
\frac{11}{2} = \frac{11 \times 2}{2 \times 2} = \frac{22}{4}
\]

3. Subtract the fractions:
\[
\frac{23}{4} - \frac{22}{4} = \frac{23 - 22}{4} = \frac{1}{4}
\]

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

---

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

1. Convert to improper fractions:
\[
3 \frac{1}{11} = \frac{3 \times 11 + 1}{11} = \frac{34}{11}
\]
\[
1 \frac{1}{6} = \frac{1 \times 6 + 1}{6} = \frac{7}{6}
\]

2. Find a common denominator (LCM of 11 and 6 is 66):
\[
\frac{34}{11} = \frac{34 \times 6}{11 \times 6} = \frac{204}{66}
\]
\[
\frac{7}{6} = \frac{7 \times 11}{6 \times 11} = \frac{77}{66}
\]

3. Subtract the fractions:
\[
\frac{204}{66} - \frac{77}{66} = \frac{204 - 77}{66} = \frac{127}{66}
\]

4. Convert back to a mixed fraction:
\[
\frac{127}{66} = 1 \frac{61}{66}
\]

Answer: \( 1 \frac{61}{66} \)

---

Problem 6: \( 9 \frac{2}{3} - 3 \frac{1}{3} \)

1. Convert to improper fractions:
\[
9 \frac{2}{3} = \frac{9 \times 3 + 2}{3} = \frac{29}{3}
\]
\[
3 \frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{10}{3}
\]

2. Subtract the fractions:
\[
\frac{29}{3} - \frac{10}{3} = \frac{29 - 10}{3} = \frac{19}{3}
\]

3. Convert back to a mixed fraction:
\[
\frac{19}{3} = 6 \frac{1}{3}
\]

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

---

Problem 7: \( 3 \frac{3}{4} - 1 \frac{5}{8} \)

1. Convert to improper fractions:
\[
3 \frac{3}{4} = \frac{3 \times 4 + 3}{4} = \frac{15}{4}
\]
\[
1 \frac{5}{8} = \frac{1 \times 8 + 5}{8} = \frac{13}{8}
\]

2. Find a common denominator (LCM of 4 and 8 is 8):
\[
\frac{15}{4} = \frac{15 \times 2}{4 \times 2} = \frac{30}{8}
\]

3. Subtract the fractions:
\[
\frac{30}{8} - \frac{13}{8} = \frac{30 - 13}{8} = \frac{17}{8}
\]

4. Convert back to a mixed fraction:
\[
\frac{17}{8} = 2 \frac{1}{8}
\]

Answer: \( 2 \frac{1}{8} \)

---

Problem 8: \( 4 \frac{3}{5} - 2 \frac{5}{6} \)

1. Convert to improper fractions:
\[
4 \frac{3}{5} = \frac{4 \times 5 + 3}{5} = \frac{23}{5}
\]
\[
2 \frac{5}{6} = \frac{2 \times 6 + 5}{6} = \frac{17}{6}
\]

2. Find a common denominator (LCM of 5 and 6 is 30):
\[
\frac{23}{5} = \frac{23 \times 6}{5 \times 6} = \frac{138}{30}
\]
\[
\frac{17}{6} = \frac{17 \times 5}{6 \times 5} = \frac{85}{30}
\]

3. Subtract the fractions:
\[
\frac{138}{30} - \frac{85}{30} = \frac{138 - 85}{30} = \frac{53}{30}
\]

4. Convert back to a mixed fraction:
\[
\frac{53}{30} = 1 \frac{23}{30}
\]

Answer: \( 1 \frac{23}{30} \)

---

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

1. Convert to improper fractions:
\[
4 \frac{7}{9} = \frac{4 \times 9 + 7}{9} = \frac{43}{9}
\]
\[
3 \frac{4}{7} = \frac{3 \times 7 + 4}{7} = \frac{25}{7}
\]

2. Find a common denominator (LCM of 9 and 7 is 63):
\[
\frac{43}{9} = \frac{43 \times 7}{9 \times 7} = \frac{301}{63}
\]
\[
\frac{25}{7} = \frac{25 \times 9}{7 \times 9} = \frac{225}{63}
\]

3. Subtract the fractions:
\[
\frac{301}{63} - \frac{225}{63} = \frac{301 - 225}{63} = \frac{76}{63}
\]

4. Convert back to a mixed fraction:
\[
\frac{76}{63} = 1 \frac{13}{63}
\]

Answer: \( 1 \frac{13}{63} \)

---

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

1. Convert to improper fractions:
\[
3 \frac{1}{5} = \frac{3 \times 5 + 1}{5} = \frac{16}{5}
\]
\[
1 \frac{1}{6} = \frac{1 \times 6 + 1}{6} = \frac{7}{6}
\]

2. Find a common denominator (LCM of 5 and 6 is 30):
\[
\frac{16}{5} = \frac{16 \times 6}{5 \times 6} = \frac{96}{30}
\]
\[
\frac{7}{6} = \frac{7 \times 5}{6 \times 5} = \frac{35}{30}
\]

3. Subtract the fractions:
\[
\frac{96}{30} - \frac{35}{30} = \frac{96 - 35}{30} = \frac{61}{30}
\]

4. Convert back to a mixed fraction:
\[
\frac{61}{30} = 2 \frac{1}{30}
\]

Answer: \( 2 \frac{1}{30} \)

---

Problem 11: \( 5 \frac{1}{6} - 3 \frac{11}{12} \)

1. Convert to improper fractions:
\[
5 \frac{1}{6} = \frac{5 \times 6 + 1}{6} = \frac{31}{6}
\]
\[
3 \frac{11}{12} = \frac{3 \times 12 + 11}{12} = \frac{47}{12}
\]

2. Find a common denominator (LCM of 6 and 12 is 12):
\[
\frac{31}{6} = \frac{31 \times 2}{6 \times 2} = \frac{62}{12}
\]

3. Subtract the fractions:
\[
\frac{62}{12} - \frac{47}{12} = \frac{62 - 47}{12} = \frac{15}{12}
\]

4. Simplify the fraction:
\[
\frac{15}{12} = \frac{5}{4}
\]

5. Convert back to a mixed fraction:
\[
\frac{5}{4} = 1 \frac{1}{4}
\]

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

---

Problem 12: \( 1 \frac{1}{3} - 1 \frac{1}{8} \)

1. Convert to improper fractions:
\[
1 \frac{1}{3} = \frac{1 \times 3 + 1}{3} = \frac{4}{3}
\]
\[
1 \frac{1}{8} = \frac{1 \times 8 + 1}{8} = \frac{9}{8}
\]

2. Find a common denominator (LCM of 3 and 8 is 24):
\[
\frac{4}{3} = \frac{4 \times 8}{3 \times 8} = \frac{32}{24}
\]
\[
\frac{9}{8} = \frac{9 \times 3}{8 \times 3} = \frac{27}{24}
\]

3. Subtract the fractions:
\[
\frac{32}{24} - \frac{27}{24} = \frac{32 - 27}{24} = \frac{5}{24}
\]

Answer: \( \frac{5}{24} \)

---

Final Answers:

\[
\boxed{
\begin{array}{ccc}
1. & 4 \frac{1}{3} & \\
2. & \frac{32}{33} & \\
3. & 6 & \\
4. & \frac{1}{4} & \\
5. & 1 \frac{61}{66} & \\
6. & 6 \frac{1}{3} & \\
7. & 2 \frac{1}{8} & \\
8. & 1 \frac{23}{30} & \\
9. & 1 \frac{13}{63} & \\
10. & 2 \frac{1}{30} & \\
11. & 1 \frac{1}{4} & \\
12. & \frac{5}{24} &
\end{array}
}
\]