Equivalent fractions with numerators & denominators missing - Free Printable

Problem Overview:

The task involves identifying equivalent fractions based on the shaded portions of pie charts. Equivalent fractions are fractions that represent the same value but are expressed with different numerators and denominators. For example, \( \frac{1}{2} \) and \( \frac{2}{4} \) are equivalent.

Solution Approach:

1. Count the Total Slices: Determine the total number of slices in each pie chart.
2. Count the Shaded Slices: Count how many slices are shaded in each pie chart.
3. Write the Fraction: Write the fraction as \( \frac{\text{shaded slices}}{\text{total slices}} \).
4. Find Equivalent Fractions: Simplify or expand the fraction to find an equivalent form.

Step-by-Step Solutions:

#### Problem 1:
- Left Pie Chart: 3 shaded out of 5 slices.
- Right Pie Chart: 6 shaded out of 10 slices.
- Equivalent Fraction: \( \frac{3}{5} = \frac{6}{10} \).

#### Problem 2:
- Left Pie Chart: 2 shaded out of 4 slices.
- Right Pie Chart: 4 shaded out of 8 slices.
- Equivalent Fraction: \( \frac{2}{4} = \frac{4}{8} \).

#### Problem 3:
- Left Pie Chart: 1 shaded out of 2 slices.
- Right Pie Chart: 5 shaded out of 10 slices.
- Equivalent Fraction: \( \frac{1}{2} = \frac{5}{10} \).

#### Problem 4:
- Left Pie Chart: 1 shaded out of 4 slices.
- Right Pie Chart: 2 shaded out of 8 slices.
- Equivalent Fraction: \( \frac{1}{4} = \frac{2}{8} \).

#### Problem 5:
- Left Pie Chart: 3 shaded out of 4 slices.
- Right Pie Chart: 6 shaded out of 8 slices.
- Equivalent Fraction: \( \frac{3}{4} = \frac{6}{8} \).

#### Problem 6:
- Left Pie Chart: 3 shaded out of 4 slices.
- Right Pie Chart: 6 shaded out of 8 slices.
- Equivalent Fraction: \( \frac{3}{4} = \frac{6}{8} \).

#### Problem 7:
- Left Pie Chart: 4 shaded out of 10 slices.
- Right Pie Chart: 2 shaded out of 5 slices.
- Equivalent Fraction: \( \frac{4}{10} = \frac{2}{5} \).

#### Problem 8:
- Left Pie Chart: 1 shaded out of 2 slices.
- Right Pie Chart: 2 shaded out of 4 slices.
- Equivalent Fraction: \( \frac{1}{2} = \frac{2}{4} \).

#### Problem 9:
- Left Pie Chart: 5 shaded out of 10 slices.
- Right Pie Chart: 10 shaded out of 20 slices.
- Equivalent Fraction: \( \frac{5}{10} = \frac{10}{20} \).

#### Problem 10:
- Left Pie Chart: 2 shaded out of 10 slices.
- Right Pie Chart: 4 shaded out of 20 slices.
- Equivalent Fraction: \( \frac{2}{10} = \frac{4}{20} \).

#### Problem 11:
- Left Pie Chart: 5 shaded out of 8 slices.
- Right Pie Chart: 10 shaded out of 16 slices.
- Equivalent Fraction: \( \frac{5}{8} = \frac{10}{16} \).

#### Problem 12:
- Left Pie Chart: 3 shaded out of 10 slices.
- Right Pie Chart: 6 shaded out of 20 slices.
- Equivalent Fraction: \( \frac{3}{10} = \frac{6}{20} \).

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & \frac{3}{5} = \frac{6}{10} \\
2. & \frac{2}{4} = \frac{4}{8} \\
3. & \frac{1}{2} = \frac{5}{10} \\
4. & \frac{1}{4} = \frac{2}{8} \\
5. & \frac{3}{4} = \frac{6}{8} \\
6. & \frac{3}{4} = \frac{6}{8} \\
7. & \frac{4}{10} = \frac{2}{5} \\
8. & \frac{1}{2} = \frac{2}{4} \\
9. & \frac{5}{10} = \frac{10}{20} \\
10. & \frac{2}{10} = \frac{4}{20} \\
11. & \frac{5}{8} = \frac{10}{16} \\
12. & \frac{3}{10} = \frac{6}{20} \\
\end{array}
}
\]