Question

answer attempt 2 out of 2 one fraction: mixed number:

Explanation:

Step1: Analyze the circles

Each circle is divided into 10 equal parts. There are 3 full circles (each with 10 parts) and a fourth circle with 8 parts (since 2 parts are white, so \(10 - 2=8\) parts are purple).

Step2: Calculate the total number of parts as an improper fraction

For the improper fraction: The total number of purple parts is \(3\times10 + 8=30 + 8 = 38\). Since each circle has 10 parts, the improper fraction is \(\frac{38}{10}\) (we can also simplify it, but let's check the mixed number first).

Step3: Calculate the mixed number

The number of full circles is 3, and the remaining parts in the fourth circle is 8 out of 10. So the mixed number is \(3\frac{8}{10}\) (which can be simplified to \(3\frac{4}{5}\), but let's confirm with the improper fraction). Wait, maybe I miscounted. Wait, looking at the image: first three circles are fully shaded (10 parts each), fourth circle: how many shaded? Let's see, the fourth circle has some white parts. Let's count the shaded parts in the fourth circle. If the circle is divided into, say, 10 parts (since the first three are divided into 10, so likely the same). Let's say the fourth circle has 8 shaded (2 white). So total shaded: \(3\times10+8 = 38\), so improper fraction is \(\frac{38}{10}=\frac{19}{5}\) (simplified) or as a mixed number \(3\frac{8}{10}=3\frac{4}{5}\). Wait, maybe the circles are divided into 10? Wait, maybe the first three are 10 each, fourth is 8. So total is 38/10 or 19/5, and mixed number 3 8/10 or 3 4/5. But let's check again.

Wait, maybe the circles are divided into 10 equal sectors. First three circles: all 10 sectors shaded. Fourth circle: 8 sectors shaded (2 white). So total shaded sectors: \(3\times10 + 8=38\). So the improper fraction is \(\frac{38}{10}\) (or \(\frac{19}{5}\) when simplified), and the mixed number is \(3\frac{8}{10}\) (or \(3\frac{4}{5}\)).

But let's do it step by step.

Step1: Count full circles and partial

Number of full circles: 3. Each full circle is \(\frac{10}{10}\), so 3 full circles is \(3\times\frac{10}{10}=\frac{30}{10}\).

Step2: Count the partial circle

The fourth circle has 8 shaded parts out of 10, so \(\frac{8}{10}\).

Step3: Total improper fraction

Add the full circles and the partial: \(\frac{30}{10}+\frac{8}{10}=\frac{38}{10}=\frac{19}{5}\) (simplified).

Step4: Mixed number

The mixed number is the number of full circles plus the fraction of the partial circle. So \(3+\frac{8}{10}=3\frac{8}{10}=3\frac{4}{5}\) (simplified).

But maybe the problem expects the non - simplified version. Let's check the image again. If the fourth circle has 8 shaded (2 white) and each circle is divided into 10, then:

Improper fraction: \(\frac{3\times10 + 8}{10}=\frac{38}{10}\)

Mixed number: \(3\frac{8}{10}\)

Answer:

One Fraction: \(\frac{38}{10}\) (or \(\frac{19}{5}\))
Mixed Number: \(3\frac{8}{10}\) (or \(3\frac{4}{5}\))

(If we consider the circles are divided into 10, the above is correct. If there's a different division, but based on the first three circles, they seem to have 10 sectors each, so the fourth likely too.)