Question

assume that each circle shown below represents one unit. express the shaded amount as a single fraction and as a mixed number.

Explanation:

Step1: Analyze the circles

Each circle is divided into 10 equal parts. The first two circles are fully shaded (each represents 10/10 or 1 unit), and the third circle has 5 shaded parts out of 10.

Step2: Calculate the total shaded parts

For the first two circles: \( 2\times\frac{10}{10} = 2 \)
For the third circle: \( \frac{5}{10} \)
Total shaded as an improper fraction: \( 2+\frac{5}{10}=\frac{20 + 5}{10}=\frac{25}{10}=\frac{5}{2} \) (Wait, no, wait. Wait, looking at the image again: Wait, maybe I miscounted. Wait, the first two circles are fully shaded (each with 10 parts, all shaded), and the third circle: let's check the number of divisions. Wait, each circle is divided into 10 sectors? Wait, no, looking at the third circle (the top one), the shaded parts: let's count. Wait, maybe the first two circles are fully shaded (each is 1 whole, so 2 wholes), and the third circle has 5 shaded out of 10? Wait, no, maybe the first two circles are each divided into 10, fully shaded (so 10/10 each, so 2), and the third circle: let's see, the third circle (the upper one) has 5 shaded? Wait, no, maybe I made a mistake. Wait, let's re - examine.

Wait, the problem says "each circle represents one unit". Let's count the number of shaded parts:

First circle (bottom): all 10 parts shaded.

Second circle (middle): all 10 parts shaded.

Third circle (top): 5 parts shaded (since there are 10 parts, 5 shaded).

So total shaded parts: \( 10 + 10+5=25 \) parts, and each circle has 10 parts.

So as an improper fraction: \( \frac{25}{10}=\frac{5}{2}=2\frac{5}{10}=2\frac{1}{2} \)? Wait, no, wait \( 25\div10 = 2\frac{5}{10}=2\frac{1}{2} \), and the improper fraction is \( \frac{25}{10}=\frac{5}{2} \)? Wait, no, 10 + 10+5 = 25, denominator 10. So \( \frac{25}{10}=\frac{5}{2} \) (simplified) or \( 2\frac{5}{10}=2\frac{1}{2} \).

Wait, let's do it step by step:

1. Number of whole circles (fully shaded): 2 (each is 1, so 2×1 = 2)
2. Number of shaded parts in the non - whole circle: 5 (out of 10)
3. So as a mixed number: \( 2+\frac{5}{10}=2\frac{5}{10}=2\frac{1}{2} \)
4. As an improper fraction: \( 2\times10 + 5=25 \), so \( \frac{25}{10}=\frac{5}{2} \) (after simplifying by dividing numerator and denominator by 5)

Answer:

As an improper fraction: \(\frac{25}{10}=\frac{5}{2}\) (or \(\frac{25}{10}\) if not simplified), as a mixed number: \(2\frac{5}{10}=2\frac{1}{2}\)