Circle with 4 of 8 equal parts shaded. Same-sized circle with 2 equal parts.
Understand the Problem
The question involves understanding the relationship between two circles, where one circle has 4 out of 8 equal parts shaded and the other has 2 equal parts. The focus is on the fractions representing the shaded parts.
Answer
Circle 1: $\frac{1}{2}$, Circle 2: $1$
Answer for screen readers
The shaded fraction for the first circle is $\frac{1}{2}$, and for the second circle, it is $1$.
Steps to Solve
- Identify the fractions for the shaded areas of each circle The first circle has 4 out of 8 parts shaded. We can represent this as a fraction:
$$ \text{Fraction for Circle 1} = \frac{4}{8} $$
The second circle has 2 equal parts shaded, which can be represented as:
$$ \text{Fraction for Circle 2} = \frac{2}{2} $$
- Simplify the fractions Now, let's simplify both fractions.
For Circle 1:
$$ \frac{4}{8} = \frac{1}{2} $$
For Circle 2:
$$ \frac{2}{2} = 1 $$
- Compare the fractions Next, we compare the two simplified fractions.
Circle 1's shaded area as a fraction:
$$ \frac{1}{2} $$
Circle 2's shaded area as a fraction:
$$ 1 $$
This means that Circle 2 has its entire area shaded, while Circle 1 has half of its area shaded.
- Express the comparison in words Lastly, we can express the relationship between the two circles: Circle 2 is completely shaded, while Circle 1 is only half shaded.
The shaded fraction for the first circle is $\frac{1}{2}$, and for the second circle, it is $1$.
More Information
Circle 1 is shaded by half, while Circle 2 is completely shaded. This illustrates the concept of fractions representing parts of a whole, using circles as visual aids.
Tips
- Forgetting to simplify the fractions after identifying them.
- Misinterpreting the parts shaded relative to the whole (e.g., not recognizing that Circle 2 represents a complete shaded area).
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