Grade 6 Adding Fractions Worksheets | Free Printables | Math ... - Free Printable

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

1. Find a Common Denominator: If the denominators of the fractions are different, we need to find a common denominator so that we can subtract the numerators directly.
2. Adjust the Fractions: Rewrite each fraction with the common denominator.
3. Subtract the Numerators: Subtract the numerators while keeping the common denominator.
4. Simplify the Result: Simplify the resulting fraction if possible.

Let's solve each problem step by step.

---

Problem 1: $\frac{3}{6} - \frac{1}{7}$

- Step 1: Find the least common denominator (LCD) of 6 and 7. The LCD is 42.
- Step 2: Rewrite the fractions with the common denominator:
$$
\frac{3}{6} = \frac{3 \times 7}{6 \times 7} = \frac{21}{42}, \quad \frac{1}{7} = \frac{1 \times 6}{7 \times 6} = \frac{6}{42}
$$
- Step 3: Subtract the numerators:
$$
\frac{21}{42} - \frac{6}{42} = \frac{21 - 6}{42} = \frac{15}{42}
$$
- Step 4: Simplify the fraction:
$$
\frac{15}{42} = \frac{5}{14}
$$
- Answer: $\frac{5}{14}$

---

Problem 2: $\frac{4}{5} - \frac{2}{3}$

- Step 1: Find the LCD of 5 and 3. The LCD is 15.
- Step 2: Rewrite the fractions with the common denominator:
$$
\frac{4}{5} = \frac{4 \times 3}{5 \times 3} = \frac{12}{15}, \quad \frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15}
$$
- Step 3: Subtract the numerators:
$$
\frac{12}{15} - \frac{10}{15} = \frac{12 - 10}{15} = \frac{2}{15}
$$
- Step 4: The fraction is already simplified.
- Answer: $\frac{2}{15}$

---

Problem 3: $\frac{1}{4} - \frac{1}{5}$

- Step 1: Find the LCD of 4 and 5. The LCD is 20.
- Step 2: Rewrite the fractions with the common denominator:
$$
\frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}, \quad \frac{1}{5} = \frac{1 \times 4}{5 \times 4} = \frac{4}{20}
$$
- Step 3: Subtract the numerators:
$$
\frac{5}{20} - \frac{4}{20} = \frac{5 - 4}{20} = \frac{1}{20}
$$
- Step 4: The fraction is already simplified.
- Answer: $\frac{1}{20}$

---

Problem 4: $\frac{5}{6} - \frac{5}{11}$

- Step 1: Find the LCD of 6 and 11. The LCD is 66.
- Step 2: Rewrite the fractions with the common denominator:
$$
\frac{5}{6} = \frac{5 \times 11}{6 \times 11} = \frac{55}{66}, \quad \frac{5}{11} = \frac{5 \times 6}{11 \times 6} = \frac{30}{66}
$$
- Step 3: Subtract the numerators:
$$
\frac{55}{66} - \frac{30}{66} = \frac{55 - 30}{66} = \frac{25}{66}
$$
- Step 4: The fraction is already simplified.
- Answer: $\frac{25}{66}$

---

Problem 5: $\frac{5}{12} - \frac{3}{8}$

- Step 1: Find the LCD of 12 and 8. The LCD is 24.
- Step 2: Rewrite the fractions with the common denominator:
$$
\frac{5}{12} = \frac{5 \times 2}{12 \times 2} = \frac{10}{24}, \quad \frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24}
$$
- Step 3: Subtract the numerators:
$$
\frac{10}{24} - \frac{9}{24} = \frac{10 - 9}{24} = \frac{1}{24}
$$
- Step 4: The fraction is already simplified.
- Answer: $\frac{1}{24}$

---

Problem 6: $\frac{7}{8} - \frac{2}{5}$

- Step 1: Find the LCD of 8 and 5. The LCD is 40.
- Step 2: Rewrite the fractions with the common denominator:
$$
\frac{7}{8} = \frac{7 \times 5}{8 \times 5} = \frac{35}{40}, \quad \frac{2}{5} = \frac{2 \times 8}{5 \times 8} = \frac{16}{40}
$$
- Step 3: Subtract the numerators:
$$
\frac{35}{40} - \frac{16}{40} = \frac{35 - 16}{40} = \frac{19}{40}
$$
- Step 4: The fraction is already simplified.
- Answer: $\frac{19}{40}$

---

Problem 7: $\frac{4}{5} - \frac{6}{9}$

- Step 1: Simplify $\frac{6}{9}$ to $\frac{2}{3}$.
- Step 2: Find the LCD of 5 and 3. The LCD is 15.
- Step 3: Rewrite the fractions with the common denominator:
$$
\frac{4}{5} = \frac{4 \times 3}{5 \times 3} = \frac{12}{15}, \quad \frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15}
$$
- Step 4: Subtract the numerators:
$$
\frac{12}{15} - \frac{10}{15} = \frac{12 - 10}{15} = \frac{2}{15}
$$
- Answer: $\frac{2}{15}$

---

Problem 8: $\frac{3}{5} - \frac{3}{10}$

- Step 1: Find the LCD of 5 and 10. The LCD is 10.
- Step 2: Rewrite the fractions with the common denominator:
$$
\frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10}, \quad \frac{3}{10} = \frac{3}{10}
$$
- Step 3: Subtract the numerators:
$$
\frac{6}{10} - \frac{3}{10} = \frac{6 - 3}{10} = \frac{3}{10}
$$
- Answer: $\frac{3}{10}$

---

Problem 9: $\frac{5}{8} - \frac{7}{24}$

- Step 1: Find the LCD of 8 and 24. The LCD is 24.
- Step 2: Rewrite the fractions with the common denominator:
$$
\frac{5}{8} = \frac{5 \times 3}{8 \times 3} = \frac{15}{24}, \quad \frac{7}{24} = \frac{7}{24}
$$
- Step 3: Subtract the numerators:
$$
\frac{15}{24} - \frac{7}{24} = \frac{15 - 7}{24} = \frac{8}{24}
$$
- Step 4: Simplify the fraction:
$$
\frac{8}{24} = \frac{1}{3}
$$
- Answer: $\frac{1}{3}$

---

Problem 10: $\frac{4}{6} - \frac{5}{18}$

- Step 1: Simplify $\frac{4}{6}$ to $\frac{2}{3}$.
- Step 2: Find the LCD of 3 and 18. The LCD is 18.
- Step 3: Rewrite the fractions with the common denominator:
$$
\frac{2}{3} = \frac{2 \times 6}{3 \times 6} = \frac{12}{18}, \quad \frac{5}{18} = \frac{5}{18}
$$
- Step 4: Subtract the numerators:
$$
\frac{12}{18} - \frac{5}{18} = \frac{12 - 5}{18} = \frac{7}{18}
$$
- Answer: $\frac{7}{18}$

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Final Answers

$$
\boxed{
\begin{aligned}
1. & \ \frac{5}{14} \\
2. & \ \frac{2}{15} \\
3. & \ \frac{1}{20} \\
4. & \ \frac{25}{66} \\
5. & \ \frac{1}{24} \\
6. & \ \frac{19}{40} \\
7. & \ \frac{2}{15} \\
8. & \ \frac{3}{10} \\
9. & \ \frac{1}{3} \\
10. & \ \frac{7}{18}
\end{aligned}
}
$$