Adding and Subtracting Fractions - Worksheet | Maths Year 3 - Free Printable

Problem: Adding Fractions Worksheet

The task is to add the given fractions and shade the diagrams to help visualize the solutions. Let's solve each problem step by step.

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#### 1. $\frac{1}{5} + \frac{1}{5}$
- Both fractions have the same denominator (5).
- Add the numerators: $1 + 1 = 2$.
- The denominator remains the same: $5$.
- Result: $\frac{2}{5}$.

Shading: Shade 2 out of 5 parts in the circle.

Answer: $\boxed{\frac{2}{5}}$

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#### 2. $\frac{3}{7} + \frac{2}{7}$
- Both fractions have the same denominator (7).
- Add the numerators: $3 + 2 = 5$.
- The denominator remains the same: $7$.
- Result: $\frac{5}{7}$.

Shading: Shade 5 out of 7 parts in the circle.

Answer: $\boxed{\frac{5}{7}}$

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#### 3. $\frac{3}{5} + \frac{1}{5}$
- Both fractions have the same denominator (5).
- Add the numerators: $3 + 1 = 4$.
- The denominator remains the same: $5$.
- Result: $\frac{4}{5}$.

Shading: Shade 4 out of 5 parts in the circle.

Answer: $\boxed{\frac{4}{5}}$

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#### 4. $\frac{5}{10} + \frac{4}{10}$
- Both fractions have the same denominator (10).
- Add the numerators: $5 + 4 = 9$.
- The denominator remains the same: $10$.
- Result: $\frac{9}{10}$.

Shading: Shade 9 out of 10 parts in the circle.

Answer: $\boxed{\frac{9}{10}}$

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#### 5. $\frac{2}{6} + \frac{3}{6}$
- Both fractions have the same denominator (6).
- Add the numerators: $2 + 3 = 5$.
- The denominator remains the same: $6$.
- Result: $\frac{5}{6}$.

Shading: Shade 5 out of 6 parts in the circle.

Answer: $\boxed{\frac{5}{6}}$

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#### 6. $\frac{4}{8} + \frac{3}{8}$
- Both fractions have the same denominator (8).
- Add the numerators: $4 + 3 = 7$.
- The denominator remains the same: $8$.
- Result: $\frac{7}{8}$.

Shading: Shade 7 out of 8 parts in the circle.

Answer: $\boxed{\frac{7}{8}}$

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#### 7. $\frac{8}{15} + \frac{5}{15}$
- Both fractions have the same denominator (15).
- Add the numerators: $8 + 5 = 13$.
- The denominator remains the same: $15$.
- Result: $\frac{13}{15}$.

Shading: Shade 13 out of 15 parts in the circle.

Answer: $\boxed{\frac{13}{15}}$

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#### 8. $\frac{7}{12} + \frac{3}{12}$
- Both fractions have the same denominator (12).
- Add the numerators: $7 + 3 = 10$.
- The denominator remains the same: $12$.
- Result: $\frac{10}{12}$.
- Simplify the fraction: $\frac{10}{12} = \frac{5}{6}$ (divide numerator and denominator by 2).

Shading: Shade 10 out of 12 parts in the circle.

Answer: $\boxed{\frac{5}{6}}$

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Final Answers:

1. $\boxed{\frac{2}{5}}$
2. $\boxed{\frac{5}{7}}$
3. $\boxed{\frac{4}{5}}$
4. $\boxed{\frac{9}{10}}$
5. $\boxed{\frac{5}{6}}$
6. $\boxed{\frac{7}{8}}$
7. $\boxed{\frac{13}{15}}$
8. $\boxed{\frac{5}{6}}$

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Explanation:

- When adding fractions with the same denominator, simply add the numerators and keep the denominator the same.
- Shading the diagrams helps visualize the addition process and ensures accuracy.
- Always simplify the final fraction if possible.

Final Answer Boxed:
$$
\boxed{\frac{2}{5}, \frac{5}{7}, \frac{4}{5}, \frac{9}{10}, \frac{5}{6}, \frac{7}{8}, \frac{13}{15}, \frac{5}{6}}
$$