Free equivalent fractions worksheets with visual models - Free Printable

Problem Description:

The worksheet provided is about Equivalent Fractions. Each question shows two fractions represented visually using shaded circles and bars. The task is to determine the numerical value of each fraction and confirm whether they are equivalent.

Solution Approach:

1. Understand the Visual Representation:
- Each circle is divided into equal parts, and some parts are shaded.
- The numerator of the fraction is the number of shaded parts.
- The denominator of the fraction is the total number of parts in the circle.

2. Compare the Fractions:
- For each pair of fractions, calculate their numerical values.
- Simplify the fractions if necessary to check for equivalence.

3. Fill in the Bars:
- The yellow bars below each fraction should represent the simplified form of the fraction (if applicable).

Step-by-Step Solution:

#### 1 a.
- Left Fraction: Circle divided into 4 parts, 2 shaded.
- Numerator = 2, Denominator = 4
- Fraction = \( \frac{2}{4} \)
- Simplified: \( \frac{2}{4} = \frac{1}{2} \)

- Right Fraction: Circle divided into 2 parts, 1 shaded.
- Numerator = 1, Denominator = 2
- Fraction = \( \frac{1}{2} \)

- Both fractions are equivalent: \( \frac{2}{4} = \frac{1}{2} \).

- Bars: Both bars should show \( \frac{1}{2} \).

#### 1 b.
- Left Fraction: Circle divided into 3 parts, 1 shaded.
- Numerator = 1, Denominator = 3
- Fraction = \( \frac{1}{3} \)

- Right Fraction: Circle divided into 6 parts, 2 shaded.
- Numerator = 2, Denominator = 6
- Fraction = \( \frac{2}{6} \)
- Simplified: \( \frac{2}{6} = \frac{1}{3} \)

- Both fractions are equivalent: \( \frac{1}{3} = \frac{2}{6} \).

- Bars: Both bars should show \( \frac{1}{3} \).

#### 2 a.
- Left Fraction: Circle divided into 3 parts, 1 shaded.
- Numerator = 1, Denominator = 3
- Fraction = \( \frac{1}{3} \)

- Right Fraction: Circle divided into 9 parts, 3 shaded.
- Numerator = 3, Denominator = 9
- Fraction = \( \frac{3}{9} \)
- Simplified: \( \frac{3}{9} = \frac{1}{3} \)

- Both fractions are equivalent: \( \frac{1}{3} = \frac{3}{9} \).

- Bars: Both bars should show \( \frac{1}{3} \).

#### 2 b.
- Left Fraction: Circle divided into 8 parts, 2 shaded.
- Numerator = 2, Denominator = 8
- Fraction = \( \frac{2}{8} \)
- Simplified: \( \frac{2}{8} = \frac{1}{4} \)

- Right Fraction: Circle divided into 4 parts, 1 shaded.
- Numerator = 1, Denominator = 4
- Fraction = \( \frac{1}{4} \)

- Both fractions are equivalent: \( \frac{2}{8} = \frac{1}{4} \).

- Bars: Both bars should show \( \frac{1}{4} \).

#### 3 a.
- Left Fraction: Circle divided into 8 parts, 2 shaded.
- Numerator = 2, Denominator = 8
- Fraction = \( \frac{2}{8} \)
- Simplified: \( \frac{2}{8} = \frac{1}{4} \)

- Right Fraction: Circle divided into 4 parts, 1 shaded.
- Numerator = 1, Denominator = 4
- Fraction = \( \frac{1}{4} \)

- Both fractions are equivalent: \( \frac{2}{8} = \frac{1}{4} \).

- Bars: Both bars should show \( \frac{1}{4} \).

#### 3 b.
- Left Fraction: Circle divided into 10 parts, 2 shaded.
- Numerator = 2, Denominator = 10
- Fraction = \( \frac{2}{10} \)
- Simplified: \( \frac{2}{10} = \frac{1}{5} \)

- Right Fraction: Circle divided into 5 parts, 1 shaded.
- Numerator = 1, Denominator = 5
- Fraction = \( \frac{1}{5} \)

- Both fractions are equivalent: \( \frac{2}{10} = \frac{1}{5} \).

- Bars: Both bars should show \( \frac{1}{5} \).

#### 4 a.
- Left Fraction: Circle divided into 8 parts, 4 shaded.
- Numerator = 4, Denominator = 8
- Fraction = \( \frac{4}{8} \)
- Simplified: \( \frac{4}{8} = \frac{1}{2} \)

- Right Fraction: Circle divided into 3 parts, 2 shaded.
- Numerator = 2, Denominator = 3
- Fraction = \( \frac{2}{3} \)

- These fractions are not equivalent.

- Bars: The left bar should show \( \frac{1}{2} \), and the right bar should show \( \frac{2}{3} \).

#### 4 b.
- Left Fraction: Circle divided into 4 parts, 2 shaded.
- Numerator = 2, Denominator = 4
- Fraction = \( \frac{2}{4} \)
- Simplified: \( \frac{2}{4} = \frac{1}{2} \)

- Right Fraction: Circle divided into 8 parts, 4 shaded.
- Numerator = 4, Denominator = 8
- Fraction = \( \frac{4}{8} \)
- Simplified: \( \frac{4}{8} = \frac{1}{2} \)

- Both fractions are equivalent: \( \frac{2}{4} = \frac{4}{8} \).

- Bars: Both bars should show \( \frac{1}{2} \).

#### 5 a.
- Left Fraction: Circle divided into 10 parts, 5 shaded.
- Numerator = 5, Denominator = 10
- Fraction = \( \frac{5}{10} \)
- Simplified: \( \frac{5}{10} = \frac{1}{2} \)

- Right Fraction: Circle divided into 6 parts, 3 shaded.
- Numerator = 3, Denominator = 6
- Fraction = \( \frac{3}{6} \)
- Simplified: \( \frac{3}{6} = \frac{1}{2} \)

- Both fractions are equivalent: \( \frac{5}{10} = \frac{3}{6} \).

- Bars: Both bars should show \( \frac{1}{2} \).

#### 5 b.
- Left Fraction: Circle divided into 2 parts, 1 shaded.
- Numerator = 1, Denominator = 2
- Fraction = \( \frac{1}{2} \)

- Right Fraction: Circle divided into 6 parts, 3 shaded.
- Numerator = 3, Denominator = 6
- Fraction = \( \frac{3}{6} \)
- Simplified: \( \frac{3}{6} = \frac{1}{2} \)

- Both fractions are equivalent: \( \frac{1}{2} = \frac{3}{6} \).

- Bars: Both bars should show \( \frac{1}{2} \).

Final Answer:

\[
\boxed{
\begin{array}{ll}
1 \text{ a. } & \frac{1}{2} = \frac{1}{2} \\
1 \text{ b. } & \frac{1}{3} = \frac{1}{3} \\
2 \text{ a. } & \frac{1}{3} = \frac{1}{3} \\
2 \text{ b. } & \frac{1}{4} = \frac{1}{4} \\
3 \text{ a. } & \frac{1}{4} = \frac{1}{4} \\
3 \text{ b. } & \frac{1}{5} = \frac{1}{5} \\
4 \text{ a. } & \frac{1}{2} \neq \frac{2}{3} \\
4 \text{ b. } & \frac{1}{2} = \frac{1}{2} \\
5 \text{ a. } & \frac{1}{2} = \frac{1}{2} \\
5 \text{ b. } & \frac{1}{2} = \frac{1}{2} \\
\end{array}
}
\]