Equivalent Fractions Worksheet - Free Printable

Problem Overview:

The task involves shading circles to demonstrate that two given fractions are equivalent. Equivalent fractions represent the same value but are expressed with different numerators and denominators. The goal is to shade the correct portions of the circles to visually confirm the equivalence.

Solution Approach:

1. Understand Equivalent Fractions: Two fractions are equivalent if they can be simplified or expanded to have the same value. For example, \( \frac{1}{2} = \frac{2}{4} \) because both represent half of a whole.
2. Shade the Circles:
- For each pair of fractions, determine how many parts of the circle should be shaded to represent each fraction.
- Ensure that the shaded portions of both circles in a pair visually match the equivalence of the fractions.

Step-by-Step Solution:

#### 1. \( \frac{1}{2} = \frac{2}{4} \)
- Left Circle: Shade 1 out of 2 parts.
- Right Circle: Shade 2 out of 4 parts.
- Both represent half of the circle.

#### 2. \( \frac{1}{3} = \frac{3}{9} \)
- Left Circle: Shade 1 out of 3 parts.
- Right Circle: Shade 3 out of 9 parts.
- Both represent one-third of the circle.

#### 3. \( \frac{2}{4} = \frac{4}{8} \)
- Left Circle: Shade 2 out of 4 parts.
- Right Circle: Shade 4 out of 8 parts.
- Both represent half of the circle.

#### 4. \( \frac{1}{2} = \frac{5}{10} \)
- Left Circle: Shade 1 out of 2 parts.
- Right Circle: Shade 5 out of 10 parts.
- Both represent half of the circle.

#### 5. \( \frac{1}{6} = \frac{2}{12} \)
- Left Circle: Shade 1 out of 6 parts.
- Right Circle: Shade 2 out of 12 parts.
- Both represent one-sixth of the circle.

#### 6. \( \frac{6}{9} = \frac{2}{3} \)
- Left Circle: Shade 6 out of 9 parts.
- Right Circle: Shade 2 out of 3 parts.
- Both represent two-thirds of the circle.

#### 7. \( \frac{2}{10} = \frac{1}{5} \)
- Left Circle: Shade 2 out of 10 parts.
- Right Circle: Shade 1 out of 5 parts.
- Both represent one-fifth of the circle.

#### 8. \( \frac{1}{4} = \frac{3}{12} \)
- Left Circle: Shade 1 out of 4 parts.
- Right Circle: Shade 3 out of 12 parts.
- Both represent one-fourth of the circle.

#### 9. \( \frac{2}{3} = \frac{8}{12} \)
- Left Circle: Shade 2 out of 3 parts.
- Right Circle: Shade 8 out of 12 parts.
- Both represent two-thirds of the circle.

#### 10. \( \frac{3}{5} = \frac{6}{10} \)
- Left Circle: Shade 3 out of 5 parts.
- Right Circle: Shade 6 out of 10 parts.
- Both represent three-fifths of the circle.

Final Answer:

The solution involves shading the circles as described above for each pair of fractions. The shaded portions will visually confirm that the fractions are equivalent.

\[
\boxed{\text{Shade the circles as explained for each pair of fractions.}}
\]