Equivalent fractions worksheet with fraction circles and instructions to color and fill in missing values.

Problem Overview:

The task involves working with equivalent fractions. Equivalent fractions are fractions that represent the same value but are expressed differently. For example, \( \frac{1}{2} \) and \( \frac{2}{4} \) are equivalent because they both represent half of a whole.

The worksheet provides fraction circles divided into different numbers of parts. The goal is to:
1. Color the fraction circles so that both diagrams in each row are equivalent.
2. Fill in the missing values for the numerators and denominators of the fractions.

Solution Approach:

1. Understand the given example: The first row shows \( \frac{1}{2} = \frac{2}{4} \). This means one-half of a circle is equivalent to two-fourths of a circle.
2. Analyze each row: For each pair of fraction circles, determine how many parts are shaded in each circle and ensure the fractions are equivalent.
3. Fill in the missing values: Write the numerator (number of shaded parts) and the denominator (total number of parts) for each fraction.

Step-by-Step Solution:

#### Row 1 (Already Completed):
- Left circle: \( \frac{1}{2} \)
- Right circle: \( \frac{2}{4} \)

Both circles are correctly shaded to represent equivalent fractions.

#### Row 2:
- Left Circle: The circle is divided into 3 parts, and 1 part is shaded.
- Fraction: \( \frac{1}{3} \)
- Right Circle: The circle is divided into 6 parts. To be equivalent to \( \frac{1}{3} \), we need 2 parts shaded (since \( \frac{1}{3} = \frac{2}{6} \)).
- Fraction: \( \frac{2}{6} \)

So, the completed row is:
\[ \frac{1}{3} = \frac{2}{6} \]

#### Row 3:
- Left Circle: The circle is divided into 4 parts, and 1 part is shaded.
- Fraction: \( \frac{1}{4} \)
- Right Circle: The circle is divided into 8 parts. To be equivalent to \( \frac{1}{4} \), we need 2 parts shaded (since \( \frac{1}{4} = \frac{2}{8} \)).
- Fraction: \( \frac{2}{8} \)

So, the completed row is:
\[ \frac{1}{4} = \frac{2}{8} \]

#### Row 4:
- Left Circle: The circle is divided into 5 parts, and 2 parts are shaded.
- Fraction: \( \frac{2}{5} \)
- Right Circle: The circle is divided into 10 parts. To be equivalent to \( \frac{2}{5} \), we need 4 parts shaded (since \( \frac{2}{5} = \frac{4}{10} \)).
- Fraction: \( \frac{4}{10} \)

So, the completed row is:
\[ \frac{2}{5} = \frac{4}{10} \]

#### Row 5:
- Left Circle: The circle is divided into 6 parts, and 3 parts are shaded.
- Fraction: \( \frac{3}{6} \)
- Right Circle: The circle is divided into 12 parts. To be equivalent to \( \frac{3}{6} \), we need 6 parts shaded (since \( \frac{3}{6} = \frac{6}{12} \)).
- Fraction: \( \frac{6}{12} \)

So, the completed row is:
\[ \frac{3}{6} = \frac{6}{12} \]

#### Row 6:
- Left Circle: The circle is divided into 8 parts, and 4 parts are shaded.
- Fraction: \( \frac{4}{8} \)
- Right Circle: The circle is divided into 16 parts. To be equivalent to \( \frac{4}{8} \), we need 8 parts shaded (since \( \frac{4}{8} = \frac{8}{16} \)).
- Fraction: \( \frac{8}{16} \)

So, the completed row is:
\[ \frac{4}{8} = \frac{8}{16} \]

Final Answer:

\[
\boxed{
\begin{array}{cc}
\frac{1}{3} = \frac{2}{6} \\
\frac{1}{4} = \frac{2}{8} \\
\frac{2}{5} = \frac{4}{10} \\
\frac{3}{6} = \frac{6}{12} \\
\frac{4}{8} = \frac{8}{16}
\end{array}
}
\]