Equivalent Fractions - Worksheet | Math 2nd Grade - Free Printable

Problem Overview:

The task involves identifying equivalent fractions based on the shaded portions of bar diagrams and then drawing a new bar diagram to represent a different equivalent fraction for each given problem.

Solution Approach:

1. Identify the given fractions: For each pair of bar diagrams, determine the fraction represented by the shaded portion.
2. Find equivalent fractions: Use the concept that equivalent fractions have the same value but are expressed with different numerators and denominators.
3. Draw a new bar diagram: Create a new bar diagram that represents a different equivalent fraction for each problem.

Step-by-Step Solution:

#### Problem 1:
- Top Bar: 2 out of 4 parts are shaded. The fraction is \( \frac{2}{4} \).
- Bottom Bar: 4 out of 8 parts are shaded. The fraction is \( \frac{4}{8} \).
- Equivalent Fraction: Both fractions simplify to \( \frac{1}{2} \).
- New Bar Diagram: Draw a bar divided into 6 parts, with 3 parts shaded (representing \( \frac{3}{6} \)).

#### Problem 2:
- Top Bar: 3 out of 5 parts are shaded. The fraction is \( \frac{3}{5} \).
- Bottom Bar: 6 out of 10 parts are shaded. The fraction is \( \frac{6}{10} \).
- Equivalent Fraction: Both fractions simplify to \( \frac{3}{5} \).
- New Bar Diagram: Draw a bar divided into 15 parts, with 9 parts shaded (representing \( \frac{9}{15} \)).

#### Problem 3:
- Top Bar: 2 out of 6 parts are shaded. The fraction is \( \frac{2}{6} \).
- Bottom Bar: 1 out of 3 parts are shaded. The fraction is \( \frac{1}{3} \).
- Equivalent Fraction: Both fractions simplify to \( \frac{1}{3} \).
- New Bar Diagram: Draw a bar divided into 9 parts, with 3 parts shaded (representing \( \frac{3}{9} \)).

#### Problem 4:
- Top Bar: 4 out of 6 parts are shaded. The fraction is \( \frac{4}{6} \).
- Bottom Bar: 8 out of 12 parts are shaded. The fraction is \( \frac{8}{12} \).
- Equivalent Fraction: Both fractions simplify to \( \frac{2}{3} \).
- New Bar Diagram: Draw a bar divided into 9 parts, with 6 parts shaded (representing \( \frac{6}{9} \)).

#### Problem 5:
- Top Bar: 2 out of 8 parts are shaded. The fraction is \( \frac{2}{8} \).
- Bottom Bar: 4 out of 16 parts are shaded. The fraction is \( \frac{4}{16} \).
- Equivalent Fraction: Both fractions simplify to \( \frac{1}{4} \).
- New Bar Diagram: Draw a bar divided into 12 parts, with 3 parts shaded (representing \( \frac{3}{12} \)).

#### Problem 6:
- Top Bar: 5 out of 8 parts are shaded. The fraction is \( \frac{5}{8} \).
- Bottom Bar: 10 out of 16 parts are shaded. The fraction is \( \frac{10}{16} \).
- Equivalent Fraction: Both fractions simplify to \( \frac{5}{8} \).
- New Bar Diagram: Draw a bar divided into 24 parts, with 15 parts shaded (representing \( \frac{15}{24} \)).

Final Answer:

For each problem, the new bar diagrams representing different equivalent fractions are as follows:

1. New bar: 6 parts total, 3 shaded (representing \( \frac{3}{6} \)).
2. New bar: 15 parts total, 9 shaded (representing \( \frac{9}{15} \)).
3. New bar: 9 parts total, 3 shaded (representing \( \frac{3}{9} \)).
4. New bar: 9 parts total, 6 shaded (representing \( \frac{6}{9} \)).
5. New bar: 12 parts total, 3 shaded (representing \( \frac{3}{12} \)).
6. New bar: 24 parts total, 15 shaded (representing \( \frac{15}{24} \)).

\[
\boxed{
\begin{array}{c}
\text{1. } \frac{3}{6} \\
\text{2. } \frac{9}{15} \\
\text{3. } \frac{3}{9} \\
\text{4. } \frac{6}{9} \\
\text{5. } \frac{3}{12} \\
\text{6. } \frac{15}{24} \\
\end{array}
}
\]