Subtracting Fractions Worksheets - Free Printable

To solve the problems on the "Subtracting Fractions Sheet 3," we need to subtract the given fractions and simplify the answers. Here's a step-by-step explanation for each problem:

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Problem 1:

$$
\frac{7}{4} - \frac{5}{12}
$$

1. Find a common denominator: The denominators are 4 and 12. The least common denominator (LCD) is 12.
2. Adjust the fractions:
- $\frac{7}{4} = \frac{7 \times 3}{4 \times 3} = \frac{21}{12}$
- $\frac{5}{12}$ remains $\frac{5}{12}$.
3. Subtract the fractions:
$$
\frac{21}{12} - \frac{5}{12} = \frac{21 - 5}{12} = \frac{16}{12}
$$
4. Simplify the fraction:
- $\frac{16}{12} = \frac{4}{3}$ (divide numerator and denominator by 4).
5. Convert to a mixed number:
- $\frac{4}{3} = 1 \frac{1}{3}$.

Answer: $\frac{4}{3}$ or $1 \frac{1}{3}$.

---

Problem 2:

$$
\frac{11}{6} - \frac{2}{3}
$$

1. Find a common denominator: The denominators are 6 and 3. The LCD is 6.
2. Adjust the fractions:
- $\frac{11}{6}$ remains $\frac{11}{6}$.
- $\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}$.
3. Subtract the fractions:
$$
\frac{11}{6} - \frac{4}{6} = \frac{11 - 4}{6} = \frac{7}{6}
$$
4. Simplify the fraction: $\frac{7}{6}$ is already in simplest form.
5. Convert to a mixed number:
- $\frac{7}{6} = 1 \frac{1}{6}$.

Answer: $\frac{7}{6}$ or $1 \frac{1}{6}$.

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Problem 3:

$$
\frac{13}{7} - \frac{5}{21}
$$

1. Find a common denominator: The denominators are 7 and 21. The LCD is 21.
2. Adjust the fractions:
- $\frac{13}{7} = \frac{13 \times 3}{7 \times 3} = \frac{39}{21}$.
- $\frac{5}{21}$ remains $\frac{5}{21}$.
3. Subtract the fractions:
$$
\frac{39}{21} - \frac{5}{21} = \frac{39 - 5}{21} = \frac{34}{21}
$$
4. Simplify the fraction: $\frac{34}{21}$ is already in simplest form.
5. Convert to a mixed number:
- $\frac{34}{21} = 1 \frac{13}{21}$.

Answer: $\frac{34}{21}$ or $1 \frac{13}{21}$.

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Problem 4:

$$
\frac{15}{8} - \frac{7}{8}
$$

1. Find a common denominator: The denominators are both 8. The LCD is 8.
2. Subtract the fractions:
$$
\frac{15}{8} - \frac{7}{8} = \frac{15 - 7}{8} = \frac{8}{8}
$$
3. Simplify the fraction:
- $\frac{8}{8} = 1$.

Answer: $1$.

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Problem 5:

$$
\frac{12}{5} - \frac{11}{20}
$$

1. Find a common denominator: The denominators are 5 and 20. The LCD is 20.
2. Adjust the fractions:
- $\frac{12}{5} = \frac{12 \times 4}{5 \times 4} = \frac{48}{20}$.
- $\frac{11}{20}$ remains $\frac{11}{20}$.
3. Subtract the fractions:
$$
\frac{48}{20} - \frac{11}{20} = \frac{48 - 11}{20} = \frac{37}{20}
$$
4. Simplify the fraction: $\frac{37}{20}$ is already in simplest form.
5. Convert to a mixed number:
- $\frac{37}{20} = 1 \frac{17}{20}$.

Answer: $\frac{37}{20}$ or $1 \frac{17}{20}$.

---

Problem 6:

$$
\frac{13}{10} - \frac{7}{30}
$$

1. Find a common denominator: The denominators are 10 and 30. The LCD is 30.
2. Adjust the fractions:
- $\frac{13}{10} = \frac{13 \times 3}{10 \times 3} = \frac{39}{30}$.
- $\frac{7}{30}$ remains $\frac{7}{30}$.
3. Subtract the fractions:
$$
\frac{39}{30} - \frac{7}{30} = \frac{39 - 7}{30} = \frac{32}{30}
$$
4. Simplify the fraction:
- $\frac{32}{30} = \frac{16}{15}$ (divide numerator and denominator by 2).
5. Convert to a mixed number:
- $\frac{16}{15} = 1 \frac{1}{15}$.

Answer: $\frac{16}{15}$ or $1 \frac{1}{15}$.

---

Problem 7:

$$
\frac{14}{9} - \frac{13}{45}
$$

1. Find a common denominator: The denominators are 9 and 45. The LCD is 45.
2. Adjust the fractions:
- $\frac{14}{9} = \frac{14 \times 5}{9 \times 5} = \frac{70}{45}$.
- $\frac{13}{45}$ remains $\frac{13}{45}$.
3. Subtract the fractions:
$$
\frac{70}{45} - \frac{13}{45} = \frac{70 - 13}{45} = \frac{57}{45}
$$
4. Simplify the fraction:
- $\frac{57}{45} = \frac{19}{15}$ (divide numerator and denominator by 3).
5. Convert to a mixed number:
- $\frac{19}{15} = 1 \frac{4}{15}$.

Answer: $\frac{19}{15}$ or $1 \frac{4}{15}$.

---

Problem 8:

$$
\frac{23}{8} - \frac{3}{2}
$$

1. Find a common denominator: The denominators are 8 and 2. The LCD is 8.
2. Adjust the fractions:
- $\frac{23}{8}$ remains $\frac{23}{8}$.
- $\frac{3}{2} = \frac{3 \times 4}{2 \times 4} = \frac{12}{8}$.
3. Subtract the fractions:
$$
\frac{23}{8} - \frac{12}{8} = \frac{23 - 12}{8} = \frac{11}{8}
$$
4. Simplify the fraction: $\frac{11}{8}$ is already in simplest form.
5. Convert to a mixed number:
- $\frac{11}{8} = 1 \frac{3}{8}$.

Answer: $\frac{11}{8}$ or $1 \frac{3}{8}$.

---

Problem 9:

$$
\frac{37}{20} - \frac{7}{20}
$$

1. Find a common denominator: The denominators are both 20. The LCD is 20.
2. Subtract the fractions:
$$
\frac{37}{20} - \frac{7}{20} = \frac{37 - 7}{20} = \frac{30}{20}
$$
3. Simplify the fraction:
- $\frac{30}{20} = \frac{3}{2}$ (divide numerator and denominator by 10).
4. Convert to a mixed number:
- $\frac{3}{2} = 1 \frac{1}{2}$.

Answer: $\frac{3}{2}$ or $1 \frac{1}{2}$.

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Problem 10:

$$
\frac{12}{7} - \frac{22}{35}
$$

1. Find a common denominator: The denominators are 7 and 35. The LCD is 35.
2. Adjust the fractions:
- $\frac{12}{7} = \frac{12 \times 5}{7 \times 5} = \frac{60}{35}$.
- $\frac{22}{35}$ remains $\frac{22}{35}$.
3. Subtract the fractions:
$$
\frac{60}{35} - \frac{22}{35} = \frac{60 - 22}{35} = \frac{38}{35}
$$
4. Simplify the fraction: $\frac{38}{35}$ is already in simplest form.
5. Convert to a mixed number:
- $\frac{38}{35} = 1 \frac{3}{35}$.

Answer: $\frac{38}{35}$ or $1 \frac{3}{35}$.

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Final Answer:

$$
\boxed{\text{See detailed solutions above for all problems.}}
$$