Grade 3 Math Worksheets: Identify equivalent fractions | Worsheets library - Free Printable

Problem Overview:

The task involves identifying and writing equivalent fractions based on the shaded portions of circles. Each circle is divided into equal parts, and some parts are shaded. The goal is to determine the fraction represented by the shaded portion in each circle and find an equivalent fraction.

Solution Approach:

1. Determine the Fraction for Each Circle:
- Count the total number of equal parts in the circle.
- Count the number of shaded parts.
- Write the fraction as \( \frac{\text{shaded parts}}{\text{total parts}} \).

2. Find Equivalent Fractions:
- Equivalent fractions are fractions that represent the same value but have different numerators and denominators.
- To find an equivalent fraction, multiply or divide both the numerator and the denominator by the same non-zero number.

3. Match the Equivalent Fractions:
- Compare the fractions from the left and right columns to identify pairs of equivalent fractions.

Step-by-Step Solution:

#### Problem 1:
- Left Circle:
- Total parts: 4
- Shaded parts: 2
- Fraction: \( \frac{2}{4} \)
- Right Circle:
- Total parts: 8
- Shaded parts: 4
- Fraction: \( \frac{4}{8} \)
- Equivalent Fraction: Both \( \frac{2}{4} \) and \( \frac{4}{8} \) simplify to \( \frac{1}{2} \).

#### Problem 2:
- Left Circle:
- Total parts: 2
- Shaded parts: 1
- Fraction: \( \frac{1}{2} \)
- Right Circle:
- Total parts: 10
- Shaded parts: 5
- Fraction: \( \frac{5}{10} \)
- Equivalent Fraction: Both \( \frac{1}{2} \) and \( \frac{5}{10} \) simplify to \( \frac{1}{2} \).

#### Problem 3:
- Left Circle:
- Total parts: 6
- Shaded parts: 3
- Fraction: \( \frac{3}{6} \)
- Right Circle:
- Total parts: 8
- Shaded parts: 4
- Fraction: \( \frac{4}{8} \)
- Equivalent Fraction: Both \( \frac{3}{6} \) and \( \frac{4}{8} \) simplify to \( \frac{1}{2} \).

#### Problem 4:
- Left Circle:
- Total parts: 4
- Shaded parts: 3
- Fraction: \( \frac{3}{4} \)
- Right Circle:
- Total parts: 8
- Shaded parts: 6
- Fraction: \( \frac{6}{8} \)
- Equivalent Fraction: Both \( \frac{3}{4} \) and \( \frac{6}{8} \) simplify to \( \frac{3}{4} \).

#### Problem 5:
- Left Circle:
- Total parts: 8
- Shaded parts: 6
- Fraction: \( \frac{6}{8} \)
- Right Circle:
- Total parts: 10
- Shaded parts: 7
- Fraction: \( \frac{7}{10} \)
- Equivalent Fraction: \( \frac{6}{8} \) simplifies to \( \frac{3}{4} \), but \( \frac{7}{10} \) does not simplify further. These are not equivalent.

#### Problem 6:
- Left Circle:
- Total parts: 2
- Shaded parts: 1
- Fraction: \( \frac{1}{2} \)
- Right Circle:
- Total parts: 4
- Shaded parts: 2
- Fraction: \( \frac{2}{4} \)
- Equivalent Fraction: Both \( \frac{1}{2} \) and \( \frac{2}{4} \) simplify to \( \frac{1}{2} \).

#### Problem 7:
- Left Circle:
- Total parts: 4
- Shaded parts: 3
- Fraction: \( \frac{3}{4} \)
- Right Circle:
- Total parts: 8
- Shaded parts: 6
- Fraction: \( \frac{6}{8} \)
- Equivalent Fraction: Both \( \frac{3}{4} \) and \( \frac{6}{8} \) simplify to \( \frac{3}{4} \).

#### Problem 8:
- Left Circle:
- Total parts: 6
- Shaded parts: 4
- Fraction: \( \frac{4}{6} \)
- Right Circle:
- Total parts: 8
- Shaded parts: 6
- Fraction: \( \frac{6}{8} \)
- Equivalent Fraction: Both \( \frac{4}{6} \) and \( \frac{6}{8} \) simplify to \( \frac{2}{3} \).

Final Answer:

\[
\boxed{
\begin{array}{ll}
1. & \frac{2}{4} = \frac{4}{8} \\
2. & \frac{1}{2} = \frac{5}{10} \\
3. & \frac{3}{6} = \frac{4}{8} \\
4. & \frac{3}{4} = \frac{6}{8} \\
5. & \frac{6}{8} \neq \frac{7}{10} \\
6. & \frac{1}{2} = \frac{2}{4} \\
7. & \frac{3}{4} = \frac{6}{8} \\
8. & \frac{4}{6} = \frac{6}{8} \\
\end{array}
}
\]