What fraction of this circle is shaded blue or green? Give your answer in its simplest form.
Understand the Problem
The question is asking what fraction of a circle is shaded either blue or green, requiring the user to analyze the fractions provided for each color and find the combined total for blue and green.
Answer
The fraction of the circle that is shaded blue or green is $\frac{7}{12}$.
Answer for screen readers
The fraction of the circle that is shaded blue or green is $\frac{7}{12}$.
Steps to Solve
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Identify the fractions for blue and green The fraction of the circle that is blue is given as $\frac{1}{6}$ and for green, it is $\frac{5}{12}$.
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Find a common denominator To add the two fractions, we need a common denominator. The denominators here are 6 and 12. The least common denominator (LCD) is 12.
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Convert the fractions to have the common denominator
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For blue: $$ \frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12} $$
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For green: $$ \frac{5}{12}$$ The green fraction remains as $\frac{5}{12}$.
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Add the fractions Now that both fractions have the same denominator, we can add them: $$ \frac{2}{12} + \frac{5}{12} = \frac{2 + 5}{12} = \frac{7}{12} $$
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Simplify if necessary In this case, $\frac{7}{12}$ is already in its simplest form.
The fraction of the circle that is shaded blue or green is $\frac{7}{12}$.
More Information
The combined shaded area of blue and green represents a significant portion of the circle, amounting to approximately 58.3% of the total area.
Tips
- Forgetting to find a common denominator: Always check if your fractions share a common denominator before adding.
- Not simplifying the final fraction: Ensure your answer is in its simplest form unless specified otherwise.
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