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

The first circle is fully shaded (4/4), so that's 1 whole. The second circle has 1 out of 4 parts shaded. So the mixed number is the sum of the whole and the fraction: \(1 + \frac{1}{4} = 1\frac{1}{4}\)? Wait, no, wait. Wait, the first circle is divided into 4 parts, all shaded, so that's 4/4 = 1. The second circle: 1 part shaded out of 4. Wait, no, wait the first circle: looking at the diagram, first circle has all 4 quadrants shaded? Wait, the first circle is divided into 4 equal parts, all shaded. The second circle: 1 part shaded (top left quadrant). Wait, no, maybe I miscounted. Wait, the first circle: 4 parts, all shaded (so 4/4 = 1). The second circle: 1 part shaded (so 1/4). Wait, but wait, maybe the first circle is 4/4 (1 whole), the second circle: 1/4? No, wait, no—wait the first circle: let's check again. The first circle: 4 quadrants, all shaded. So that's 4/4 = 1. The second circle: 1 quadrant shaded (top left). So total shaded is 1 (from first circle) + 1/4 (from second circle) = \(1\frac{1}{4}\)? Wait, no, wait, no—wait the first circle: 4 parts, all shaded (so 4/4 = 1). The second circle: 1 part shaded (1/4). So mixed number is \(1\frac{1}{4}\)? Wait, but wait, maybe I made a mistake. Wait, no, the first circle: 4 sections, all shaded (so 4/4 = 1). The second circle: 1 section shaded (1/4). So total shaded is \(1 + \frac{1}{4} = 1\frac{1}{4}\). Then, to convert to improper fraction: multiply the whole number (1) by the denominator (4) and add the numerator (1): \(1 \times 4 + 1 = 5\), so improper fraction is \(\frac{5}{4}\)? Wait, no, wait: 1 whole is 4/4, plus 1/4 is 5/4? Wait, no, 4/4 + 1/4 = 5/4. So mixed number is \(1\frac{1}{4}\), improper fraction is \(\frac{5}{4}\)? Wait, but wait, maybe the first circle is 4/4 (1), the second circle: 1/4. So total is 1 + 1/4 = 5/4. Wait, but let's confirm. Each circle is a whole (4/4). First circle: 4/4 (1). Second circle: 1/4. So total shaded: 4/4 + 1/4 = 5/4. So mixed number is \(1\frac{1}{4}\), improper fraction is \(\frac{5}{4}\).

Step2: Write the mixed number

From the analysis, the mixed number is \(1\frac{1}{4}\).

Step3: Convert to improper fraction

To convert \(1\frac{1}{4}\) to an improper fraction: multiply the whole number (1) by the denominator (4) to get 4, then add the numerator (1) to get 5. The denominator remains 4. So the improper fraction is \(\frac{5}{4}\).

Answer:

(a) Mixed number: \(1\frac{1}{4}\)
(b) Improper fraction: \(\frac{5}{4}\)