Equivalent Fractions Worksheet with visual fraction models for practice.
Equivalent fractions worksheet with visual representations using circles and rectangles to show fraction equivalency.
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Show Answer Key & Explanations
Step-by-step solution for: Free math worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Free math worksheets
The worksheet provided is about equivalent fractions, where students are asked to identify and write equivalent fractions based on visual representations. Let's solve each problem step by step.
---
- Visual Representation:
- Left: A circle divided into 8 equal parts, with 2 parts shaded.
- Right: A circle divided into 4 equal parts, with 1 part shaded.
- Both have yellow bars below them.
- Fraction Interpretation:
- Left: \( \frac{2}{8} \)
- Right: \( \frac{1}{4} \)
- Solution:
- The fractions \( \frac{2}{8} \) and \( \frac{1}{4} \) are equivalent because \( \frac{2}{8} \) can be simplified by dividing both the numerator and denominator by 2:
\[
\frac{2 \div 2}{8 \div 2} = \frac{1}{4}
\]
- Therefore, the answer is:
\[
\frac{2}{8} = \frac{1}{4}
\]
---
- Visual Representation:
- Left: A circle divided into 6 equal parts, with 3 parts shaded.
- Right: A circle divided into 2 equal parts, with 1 part shaded.
- Both have yellow bars below them.
- Fraction Interpretation:
- Left: \( \frac{3}{6} \)
- Right: \( \frac{1}{2} \)
- Solution:
- The fractions \( \frac{3}{6} \) and \( \frac{1}{2} \) are equivalent because \( \frac{3}{6} \) can be simplified by dividing both the numerator and denominator by 3:
\[
\frac{3 \div 3}{6 \div 3} = \frac{1}{2}
\]
- Therefore, the answer is:
\[
\frac{3}{6} = \frac{1}{2}
\]
---
- Visual Representation:
- Left: A circle divided into 8 equal parts, with 4 parts shaded.
- Right: A circle divided into 3 equal parts, with 2 parts shaded.
- Both have yellow bars below them.
- Fraction Interpretation:
- Left: \( \frac{4}{8} \)
- Right: \( \frac{2}{3} \)
- Solution:
- The fractions \( \frac{4}{8} \) and \( \frac{2}{3} \) are not equivalent. However, if we simplify \( \frac{4}{8} \):
\[
\frac{4 \div 4}{8 \div 4} = \frac{1}{2}
\]
So, \( \frac{4}{8} = \frac{1}{2} \), but \( \frac{1}{2} \neq \frac{2}{3} \).
It seems there might be a misunderstanding in the question. If the right side were \( \frac{2}{4} \) instead of \( \frac{2}{3} \), then it would be equivalent. Assuming the correct interpretation:
\[
\frac{4}{8} = \frac{2}{4}
\]
---
- Visual Representation:
- Left: A circle divided into 8 equal parts, with 4 parts shaded.
- Right: A circle divided into 4 equal parts, with 2 parts shaded.
- Both have yellow bars below them.
- Fraction Interpretation:
- Left: \( \frac{4}{8} \)
- Right: \( \frac{2}{4} \)
- Solution:
- The fractions \( \frac{4}{8} \) and \( \frac{2}{4} \) are equivalent because both can be simplified:
\[
\frac{4 \div 4}{8 \div 4} = \frac{1}{2} \quad \text{and} \quad \frac{2 \div 2}{4 \div 2} = \frac{1}{2}
\]
- Therefore, the answer is:
\[
\frac{4}{8} = \frac{2}{4}
\]
---
- Visual Representation:
- Left: A circle divided into 4 equal parts, with 2 parts shaded.
- Right: A circle divided into 2 equal parts, with 1 part shaded.
- Both have yellow bars below them.
- Fraction Interpretation:
- Left: \( \frac{2}{4} \)
- Right: \( \frac{1}{2} \)
- Solution:
- The fractions \( \frac{2}{4} \) and \( \frac{1}{2} \) are equivalent because \( \frac{2}{4} \) can be simplified:
\[
\frac{2 \div 2}{4 \div 2} = \frac{1}{2}
\]
- Therefore, the answer is:
\[
\frac{2}{4} = \frac{1}{2}
\]
---
- Visual Representation:
- Left: A circle divided into 8 equal parts, with 4 parts shaded.
- Right: A circle divided into 2 equal parts, with 1 part shaded.
- Both have yellow bars below them.
- Fraction Interpretation:
- Left: \( \frac{4}{8} \)
- Right: \( \frac{1}{2} \)
- Solution:
- The fractions \( \frac{4}{8} \) and \( \frac{1}{2} \) are equivalent because \( \frac{4}{8} \) can be simplified:
\[
\frac{4 \div 4}{8 \div 4} = \frac{1}{2}
\]
- Therefore, the answer is:
\[
\frac{4}{8} = \frac{1}{2}
\]
---
- Visual Representation:
- Left: A circle divided into 8 equal parts, with 4 parts shaded.
- Right: A circle divided into 3 equal parts, with 2 parts shaded.
- Both have yellow bars below them.
- Fraction Interpretation:
- Left: \( \frac{4}{8} \)
- Right: \( \frac{2}{3} \)
- Solution:
- The fractions \( \frac{4}{8} \) and \( \frac{2}{3} \) are not equivalent. Simplifying \( \frac{4}{8} \):
\[
\frac{4 \div 4}{8 \div 4} = \frac{1}{2}
\]
So, \( \frac{4}{8} = \frac{1}{2} \), but \( \frac{1}{2} \neq \frac{2}{3} \).
Assuming the right side should be \( \frac{2}{4} \) instead of \( \frac{2}{3} \):
\[
\frac{4}{8} = \frac{2}{4}
\]
---
- Visual Representation:
- Left: A circle divided into 6 equal parts, with 3 parts shaded.
- Right: A circle divided into 2 equal parts, with 1 part shaded.
- Both have yellow bars below them.
- Fraction Interpretation:
- Left: \( \frac{3}{6} \)
- Right: \( \frac{1}{2} \)
- Solution:
- The fractions \( \frac{3}{6} \) and \( \frac{1}{2} \) are equivalent because \( \frac{3}{6} \) can be simplified:
\[
\frac{3 \div 3}{6 \div 3} = \frac{1}{2}
\]
- Therefore, the answer is:
\[
\frac{3}{6} = \frac{1}{2}
\]
---
- Visual Representation:
- Left: A circle divided into 8 equal parts, with 4 parts shaded.
- Right: A circle divided into 3 equal parts, with 2 parts shaded.
- Both have yellow bars below them.
- Fraction Interpretation:
- Left: \( \frac{4}{8} \)
- Right: \( \frac{2}{3} \)
- Solution:
- The fractions \( \frac{4}{8} \) and \( \frac{2}{3} \) are not equivalent. Simplifying \( \frac{4}{8} \):
\[
\frac{4 \div 4}{8 \div 4} = \frac{1}{2}
\]
So, \( \frac{4}{8} = \frac{1}{2} \), but \( \frac{1}{2} \neq \frac{2}{3} \).
Assuming the right side should be \( \frac{2}{4} \) instead of \( \frac{2}{3} \):
\[
\frac{4}{8} = \frac{2}{4}
\]
---
- Visual Representation:
- Left: A circle divided into 8 equal parts, with 2 parts shaded.
- Right: A circle divided into 4 equal parts, with 1 part shaded.
- Both have yellow bars below them.
- Fraction Interpretation:
- Left: \( \frac{2}{8} \)
- Right: \( \frac{1}{4} \)
- Solution:
- The fractions \( \frac{2}{8} \) and \( \frac{1}{4} \) are equivalent because \( \frac{2}{8} \) can be simplified:
\[
\frac{2 \div 2}{8 \div 2} = \frac{1}{4}
\]
- Therefore, the answer is:
\[
\frac{2}{8} = \frac{1}{4}
\]
---
\[
\boxed{
\begin{aligned}
1 \text{ a. } & \frac{2}{8} = \frac{1}{4} \\
1 \text{ b. } & \frac{3}{6} = \frac{1}{2} \\
2 \text{ a. } & \frac{4}{8} = \frac{2}{4} \\
2 \text{ b. } & \frac{4}{8} = \frac{2}{4} \\
3 \text{ a. } & \frac{2}{4} = \frac{1}{2} \\
3 \text{ b. } & \frac{4}{8} = \frac{1}{2} \\
4 \text{ a. } & \frac{3}{6} = \frac{1}{2} \\
4 \text{ b. } & \frac{3}{6} = \frac{1}{2} \\
5 \text{ a. } & \frac{4}{8} = \frac{2}{4} \\
5 \text{ b. } & \frac{2}{8} = \frac{1}{4}
\end{aligned}
}
\]
---
1 a.
- Visual Representation:
- Left: A circle divided into 8 equal parts, with 2 parts shaded.
- Right: A circle divided into 4 equal parts, with 1 part shaded.
- Both have yellow bars below them.
- Fraction Interpretation:
- Left: \( \frac{2}{8} \)
- Right: \( \frac{1}{4} \)
- Solution:
- The fractions \( \frac{2}{8} \) and \( \frac{1}{4} \) are equivalent because \( \frac{2}{8} \) can be simplified by dividing both the numerator and denominator by 2:
\[
\frac{2 \div 2}{8 \div 2} = \frac{1}{4}
\]
- Therefore, the answer is:
\[
\frac{2}{8} = \frac{1}{4}
\]
---
1 b.
- Visual Representation:
- Left: A circle divided into 6 equal parts, with 3 parts shaded.
- Right: A circle divided into 2 equal parts, with 1 part shaded.
- Both have yellow bars below them.
- Fraction Interpretation:
- Left: \( \frac{3}{6} \)
- Right: \( \frac{1}{2} \)
- Solution:
- The fractions \( \frac{3}{6} \) and \( \frac{1}{2} \) are equivalent because \( \frac{3}{6} \) can be simplified by dividing both the numerator and denominator by 3:
\[
\frac{3 \div 3}{6 \div 3} = \frac{1}{2}
\]
- Therefore, the answer is:
\[
\frac{3}{6} = \frac{1}{2}
\]
---
2 a.
- Visual Representation:
- Left: A circle divided into 8 equal parts, with 4 parts shaded.
- Right: A circle divided into 3 equal parts, with 2 parts shaded.
- Both have yellow bars below them.
- Fraction Interpretation:
- Left: \( \frac{4}{8} \)
- Right: \( \frac{2}{3} \)
- Solution:
- The fractions \( \frac{4}{8} \) and \( \frac{2}{3} \) are not equivalent. However, if we simplify \( \frac{4}{8} \):
\[
\frac{4 \div 4}{8 \div 4} = \frac{1}{2}
\]
So, \( \frac{4}{8} = \frac{1}{2} \), but \( \frac{1}{2} \neq \frac{2}{3} \).
It seems there might be a misunderstanding in the question. If the right side were \( \frac{2}{4} \) instead of \( \frac{2}{3} \), then it would be equivalent. Assuming the correct interpretation:
\[
\frac{4}{8} = \frac{2}{4}
\]
---
2 b.
- Visual Representation:
- Left: A circle divided into 8 equal parts, with 4 parts shaded.
- Right: A circle divided into 4 equal parts, with 2 parts shaded.
- Both have yellow bars below them.
- Fraction Interpretation:
- Left: \( \frac{4}{8} \)
- Right: \( \frac{2}{4} \)
- Solution:
- The fractions \( \frac{4}{8} \) and \( \frac{2}{4} \) are equivalent because both can be simplified:
\[
\frac{4 \div 4}{8 \div 4} = \frac{1}{2} \quad \text{and} \quad \frac{2 \div 2}{4 \div 2} = \frac{1}{2}
\]
- Therefore, the answer is:
\[
\frac{4}{8} = \frac{2}{4}
\]
---
3 a.
- Visual Representation:
- Left: A circle divided into 4 equal parts, with 2 parts shaded.
- Right: A circle divided into 2 equal parts, with 1 part shaded.
- Both have yellow bars below them.
- Fraction Interpretation:
- Left: \( \frac{2}{4} \)
- Right: \( \frac{1}{2} \)
- Solution:
- The fractions \( \frac{2}{4} \) and \( \frac{1}{2} \) are equivalent because \( \frac{2}{4} \) can be simplified:
\[
\frac{2 \div 2}{4 \div 2} = \frac{1}{2}
\]
- Therefore, the answer is:
\[
\frac{2}{4} = \frac{1}{2}
\]
---
3 b.
- Visual Representation:
- Left: A circle divided into 8 equal parts, with 4 parts shaded.
- Right: A circle divided into 2 equal parts, with 1 part shaded.
- Both have yellow bars below them.
- Fraction Interpretation:
- Left: \( \frac{4}{8} \)
- Right: \( \frac{1}{2} \)
- Solution:
- The fractions \( \frac{4}{8} \) and \( \frac{1}{2} \) are equivalent because \( \frac{4}{8} \) can be simplified:
\[
\frac{4 \div 4}{8 \div 4} = \frac{1}{2}
\]
- Therefore, the answer is:
\[
\frac{4}{8} = \frac{1}{2}
\]
---
4 a.
- Visual Representation:
- Left: A circle divided into 8 equal parts, with 4 parts shaded.
- Right: A circle divided into 3 equal parts, with 2 parts shaded.
- Both have yellow bars below them.
- Fraction Interpretation:
- Left: \( \frac{4}{8} \)
- Right: \( \frac{2}{3} \)
- Solution:
- The fractions \( \frac{4}{8} \) and \( \frac{2}{3} \) are not equivalent. Simplifying \( \frac{4}{8} \):
\[
\frac{4 \div 4}{8 \div 4} = \frac{1}{2}
\]
So, \( \frac{4}{8} = \frac{1}{2} \), but \( \frac{1}{2} \neq \frac{2}{3} \).
Assuming the right side should be \( \frac{2}{4} \) instead of \( \frac{2}{3} \):
\[
\frac{4}{8} = \frac{2}{4}
\]
---
4 b.
- Visual Representation:
- Left: A circle divided into 6 equal parts, with 3 parts shaded.
- Right: A circle divided into 2 equal parts, with 1 part shaded.
- Both have yellow bars below them.
- Fraction Interpretation:
- Left: \( \frac{3}{6} \)
- Right: \( \frac{1}{2} \)
- Solution:
- The fractions \( \frac{3}{6} \) and \( \frac{1}{2} \) are equivalent because \( \frac{3}{6} \) can be simplified:
\[
\frac{3 \div 3}{6 \div 3} = \frac{1}{2}
\]
- Therefore, the answer is:
\[
\frac{3}{6} = \frac{1}{2}
\]
---
5 a.
- Visual Representation:
- Left: A circle divided into 8 equal parts, with 4 parts shaded.
- Right: A circle divided into 3 equal parts, with 2 parts shaded.
- Both have yellow bars below them.
- Fraction Interpretation:
- Left: \( \frac{4}{8} \)
- Right: \( \frac{2}{3} \)
- Solution:
- The fractions \( \frac{4}{8} \) and \( \frac{2}{3} \) are not equivalent. Simplifying \( \frac{4}{8} \):
\[
\frac{4 \div 4}{8 \div 4} = \frac{1}{2}
\]
So, \( \frac{4}{8} = \frac{1}{2} \), but \( \frac{1}{2} \neq \frac{2}{3} \).
Assuming the right side should be \( \frac{2}{4} \) instead of \( \frac{2}{3} \):
\[
\frac{4}{8} = \frac{2}{4}
\]
---
5 b.
- Visual Representation:
- Left: A circle divided into 8 equal parts, with 2 parts shaded.
- Right: A circle divided into 4 equal parts, with 1 part shaded.
- Both have yellow bars below them.
- Fraction Interpretation:
- Left: \( \frac{2}{8} \)
- Right: \( \frac{1}{4} \)
- Solution:
- The fractions \( \frac{2}{8} \) and \( \frac{1}{4} \) are equivalent because \( \frac{2}{8} \) can be simplified:
\[
\frac{2 \div 2}{8 \div 2} = \frac{1}{4}
\]
- Therefore, the answer is:
\[
\frac{2}{8} = \frac{1}{4}
\]
---
Final Answers:
\[
\boxed{
\begin{aligned}
1 \text{ a. } & \frac{2}{8} = \frac{1}{4} \\
1 \text{ b. } & \frac{3}{6} = \frac{1}{2} \\
2 \text{ a. } & \frac{4}{8} = \frac{2}{4} \\
2 \text{ b. } & \frac{4}{8} = \frac{2}{4} \\
3 \text{ a. } & \frac{2}{4} = \frac{1}{2} \\
3 \text{ b. } & \frac{4}{8} = \frac{1}{2} \\
4 \text{ a. } & \frac{3}{6} = \frac{1}{2} \\
4 \text{ b. } & \frac{3}{6} = \frac{1}{2} \\
5 \text{ a. } & \frac{4}{8} = \frac{2}{4} \\
5 \text{ b. } & \frac{2}{8} = \frac{1}{4}
\end{aligned}
}
\]
Parent Tip: Review the logic above to help your child master the concept of 2nd grade fractions worksheet maker.
