Problem Overview:
The task involves identifying equivalent fractions by analyzing pie charts. Equivalent fractions are fractions that represent the same portion of a whole, even though they have different numerators and denominators. The goal is to fill in the missing fractions based on the visual representations provided.
Solution Approach:
1.
Understand Each Pie Chart: Each pie chart shows a fraction of the circle shaded. The numerator represents the number of shaded parts, and the denominator represents the total number of equal parts in the circle.
2.
Identify Equivalent Fractions: Two fractions are equivalent if they represent the same shaded area. This can be verified by simplifying or expanding the fractions.
3.
Fill in the Missing Fractions: Use the given fractions and the visual representation to determine the missing fractions.
Step-by-Step Solution:
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First Row:
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Left Chart: The circle is divided into 3 equal parts, with 2 parts shaded. The fraction is \( \frac{2}{3} \).
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Right Chart: The circle is divided into 6 equal parts, with 4 parts shaded. The fraction is \( \frac{4}{6} \).
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Verification: Simplify \( \frac{4}{6} \) to \( \frac{2}{3} \). They are equivalent.
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Second Row:
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Left Chart: The circle is divided into 2 equal parts, with 1 part shaded. The fraction is \( \frac{1}{2} \).
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Right Chart: The circle is divided into 4 equal parts, with 2 parts shaded. The fraction is \( \frac{2}{4} \).
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Verification: Simplify \( \frac{2}{4} \) to \( \frac{1}{2} \). They are equivalent.
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Third Row:
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Left Chart: The circle is divided into 2 equal parts, with 1 part shaded. The fraction is \( \frac{1}{2} \).
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Right Chart: The circle is divided into 4 equal parts, with 2 parts shaded. The fraction is \( \frac{2}{4} \).
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Verification: Simplify \( \frac{2}{4} \) to \( \frac{1}{2} \). They are equivalent.
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Fourth Row:
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Left Chart: The circle is divided into 3 equal parts, with 1 part shaded. The fraction is \( \frac{1}{3} \).
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Right Chart: The circle is divided into 6 equal parts, with 2 parts shaded. The fraction is \( \frac{2}{6} \).
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Verification: Simplify \( \frac{2}{6} \) to \( \frac{1}{3} \). They are equivalent.
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Fifth Row:
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Left Chart: The circle is divided into 4 equal parts, with 3 parts shaded. The fraction is \( \frac{3}{4} \).
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Right Chart: The circle is divided into 8 equal parts, with 6 parts shaded. The fraction is \( \frac{6}{8} \).
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Verification: Simplify \( \frac{6}{8} \) to \( \frac{3}{4} \). They are equivalent.
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Sixth Row:
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Left Chart: The circle is divided into 4 equal parts, with 2 parts shaded. The fraction is \( \frac{2}{4} \).
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Right Chart: The circle is divided into 8 equal parts, with 4 parts shaded. The fraction is \( \frac{4}{8} \).
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Verification: Simplify \( \frac{4}{8} \) to \( \frac{2}{4} \), and further to \( \frac{1}{2} \). They are equivalent.
Final Answer:
\[
\boxed{
\begin{array}{cc}
\frac{2}{3} & \frac{4}{6} \\
\frac{1}{2} & \frac{2}{4} \\
\frac{1}{2} & \frac{2}{4} \\
\frac{1}{3} & \frac{2}{6} \\
\frac{3}{4} & \frac{6}{8} \\
\frac{2}{4} & \frac{4}{8} \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of 4th grade fraction worksheet.
