Equivalent Fractions Worksheets Grade 4 | Grade1to6.com - Free Printable

Problem Overview:

The task involves identifying equivalent fractions by analyzing pie charts and writing the equivalent fractions in the provided boxes. Equivalent fractions are fractions that represent the same portion of a whole, even though their numerators and denominators may differ.

Solution Approach:

1. Understand Each Pie Chart: Each pie chart is divided into equal parts, and some parts are shaded. The fraction represented by each pie chart is the number of shaded parts divided by the total number of parts.
2. Identify Equivalent Fractions: Two fractions are equivalent if they represent the same shaded portion of the pie chart. This can be verified by simplifying or expanding the fractions to see if they match.
3. Fill in the Boxes: Write the equivalent fractions in the provided boxes based on the analysis.

Step-by-Step Analysis:

#### First Row:
- Left Pie Chart: The circle is divided into 3 parts, with 2 shaded. The fraction is \( \frac{2}{3} \).
- Right Pie Chart: The circle is divided into 6 parts, with 4 shaded. The fraction is \( \frac{4}{6} \).
- Verification: Simplify \( \frac{4}{6} \) to \( \frac{2}{3} \). They are equivalent.
- Box Filling: Both boxes already have \( \frac{2}{3} \) and \( \frac{4}{6} \).

#### Second Row:
- Left Pie Chart: The circle is divided into 2 parts, with 1 shaded. The fraction is \( \frac{1}{2} \).
- Right Pie Chart: The circle is divided into 4 parts, with 2 shaded. The fraction is \( \frac{2}{4} \).
- Verification: Simplify \( \frac{2}{4} \) to \( \frac{1}{2} \). They are equivalent.
- Box Filling: Write \( \frac{1}{2} \) in both boxes.

#### Third Row:
- Left Pie Chart: The circle is divided into 2 parts, with 1 shaded. The fraction is \( \frac{1}{2} \).
- Right Pie Chart: The circle is divided into 4 parts, with 2 shaded. The fraction is \( \frac{2}{4} \).
- Verification: Simplify \( \frac{2}{4} \) to \( \frac{1}{2} \). They are equivalent.
- Box Filling: Write \( \frac{1}{2} \) in both boxes.

#### Fourth Row:
- Left Pie Chart: The circle is divided into 3 parts, with 1 shaded. The fraction is \( \frac{1}{3} \).
- Right Pie Chart: The circle is divided into 9 parts, with 3 shaded. The fraction is \( \frac{3}{9} \).
- Verification: Simplify \( \frac{3}{9} \) to \( \frac{1}{3} \). They are equivalent.
- Box Filling: Write \( \frac{1}{3} \) in both boxes.

#### Fifth Row:
- Left Pie Chart: The circle is divided into 4 parts, with 1 shaded. The fraction is \( \frac{1}{4} \).
- Right Pie Chart: The circle is divided into 8 parts, with 2 shaded. The fraction is \( \frac{2}{8} \).
- Verification: Simplify \( \frac{2}{8} \) to \( \frac{1}{4} \). They are equivalent.
- Box Filling: Write \( \frac{1}{4} \) in both boxes.

#### Sixth Row:
- Left Pie Chart: The circle is divided into 2 parts, with 1 shaded. The fraction is \( \frac{1}{2} \).
- Right Pie Chart: The circle is divided into 6 parts, with 3 shaded. The fraction is \( \frac{3}{6} \).
- Verification: Simplify \( \frac{3}{6} \) to \( \frac{1}{2} \). They are equivalent.
- Box Filling: Write \( \frac{1}{2} \) in both boxes.

#### Seventh Row:
- Left Pie Chart: The circle is divided into 4 parts, with 3 shaded. The fraction is \( \frac{3}{4} \).
- Right Pie Chart: The circle is divided into 8 parts, with 6 shaded. The fraction is \( \frac{6}{8} \).
- Verification: Simplify \( \frac{6}{8} \) to \( \frac{3}{4} \). They are equivalent.
- Box Filling: Write \( \frac{3}{4} \) in both boxes.

#### Eighth Row:
- Left Pie Chart: The circle is divided into 4 parts, with 2 shaded. The fraction is \( \frac{2}{4} \).
- Right Pie Chart: The circle is divided into 8 parts, with 4 shaded. The fraction is \( \frac{4}{8} \).
- Verification: Simplify \( \frac{2}{4} \) and \( \frac{4}{8} \) to \( \frac{1}{2} \). They are equivalent.
- Box Filling: Write \( \frac{1}{2} \) in both boxes.

Final Answer:

\[
\boxed{
\begin{array}{cc}
\frac{2}{3} & \frac{4}{6} \\
\frac{1}{2} & \frac{2}{4} \\
\frac{1}{2} & \frac{2}{4} \\
\frac{1}{3} & \frac{3}{9} \\
\frac{1}{4} & \frac{2}{8} \\
\frac{1}{2} & \frac{3}{6} \\
\frac{3}{4} & \frac{6}{8} \\
\frac{1}{2} & \frac{4}{8} \\
\end{array}
}
\]