Question

each circle counts as one whole. write a mixed number giving the amount shaded. then, write this amount as an improper fraction. (a) mixed number: (b) improper fraction:

Explanation:

Step1: Analyze the shaded circles

There are 3 fully shaded circles (each is 1 whole) and 1 circle with 1 out of 3 parts shaded. So the whole number part of the mixed number is 3, and the fractional part is $\frac{1}{3}$.

Step2: Write the mixed number

Combining the whole number and the fractional part, the mixed number is $3\frac{1}{3}$.

Step3: Convert mixed number to improper fraction

To convert $3\frac{1}{3}$ to an improper fraction, use the formula: $a\frac{b}{c}=\frac{a\times c + b}{c}$. Here, $a = 3$, $b = 1$, $c = 3$. So $\frac{3\times3 + 1}{3}=\frac{9 + 1}{3}=\frac{10}{3}$. Wait, no, wait: wait, there are 3 full circles (each 3/3) and 1/3, so total shaded parts: 3 circles 3 parts + 1 part = 10 parts? Wait no, each circle is divided into 3 parts. First three circles are fully shaded (each has 3 shaded parts), fourth circle has 1 shaded part. So total shaded parts: 33 + 1 = 10? Wait no, wait the first three circles: each is 3/3, so 31 = 3 wholes, and the fourth circle has 1/3. So mixed number is $3\frac{1}{3}$. Then improper fraction: 33 + 1 = 10? Wait no, 3 (wholes) is 9/3, plus 1/3 is 10/3? Wait, no, wait: 3 wholes is 3, which is 9/3, plus 1/3 is 10/3? Wait, but let's check again. Each circle is divided into 3 equal parts. So first three circles: each has 3 shaded parts, so 3 circles 3 = 9 shaded parts. Fourth circle: 1 shaded part. Total shaded parts: 9 + 1 = 10. Total parts per circle: 3. So improper fraction is $\frac{10}{3}$? Wait, no, wait the mixed number: 3 wholes (3 circles) and 1/3 of the fourth circle, so $3\frac{1}{3}$. Then converting to improper fraction: (33 + 1)/3 = 10/3. Wait, but let's count the circles again. The first three circles are completely shaded (each is 1 whole), the fourth circle has 1 out of 3 parts shaded. So number of whole circles: 3, fractional part: 1/3. So mixed number is $3\frac{1}{3}$. Then improper fraction: 33 + 1 = 10, so $\frac{10}{3}$. Wait, but maybe I made a mistake. Wait, each circle is 3 parts. So 3 full circles: 33 = 9 parts. Plus 1 part: 10 parts. So improper fraction is 10/3. Mixed number is 3 1/3.

Wait, no, wait: 3 whole circles (each 3/3) is 9/3, plus 1/3 is 10/3. So mixed number is 3 1/3, improper fraction is 10/3. Wait, but let's check the number of circles. There are four circles: first three are fully shaded (each 3/3), fourth is 1/3. So total shaded: 3 + 1/3 = 3 1/3 (mixed number). Then improper fraction: (3*3 + 1)/3 = 10/3. Yes, that's correct.

Answer:

(a) Mixed number: $3\frac{1}{3}$
(b) Improper fraction: $\frac{10}{3}$