solve this problem---**Question 21**
**Question Stem:**
In which model is the fraction of the whole shaded to represent the fraction 3/8?
**Options:**
* **Option A:**
* **Chart Type:** Circular diagram divided into equal sectors.
* **Main Elements:**
* A circle divided by lines into 8 equal sectors.
* 5 of these sectors are shaded (grey).
* 3 of these sectors are unshaded (white).
* **Represented Fraction:** 5/8 (5 shaded parts out of 8 total parts).
* **Option B:**
* **Chart Type:** Circular diagram divided into equal sectors.
* **Main Elements:**
* A circle divided by lines into 8 equal sectors.
* 4 of these sectors are shaded (grey).
* 4 of these sectors are unshaded (white).
* **Represented Fraction:** 4/8 (or 1/2) (4 shaded parts out of 8 total parts).
* **Option C:**
* **Chart Type:** Circular diagram divided into equal sectors.
* **Main Elements:**
* A circle divided by lines into 8 equal sectors.
* 3 of these sectors are shaded (grey).
* 5 of these sectors are unshaded (white).
* **Represented Fraction:** 3/8 (3 shaded parts out of 8 total parts).
* **Option D:**
* **Chart Type:** Circular diagram divided into equal sectors.
* **Main Elements:**
* A circle divided by lines into 8 equal sectors.
* 2 of these sectors are shaded (grey).
* 6 of these sectors are unshaded (white).
* **Represented Fraction:** 2/8 (or 1/4) (2 shaded parts out of 8 total parts).
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A fraction represents parts of a whole. The top number, called the numerator, shows how many parts we want. The bottom number, called the denominator, shows how many equal parts the whole is divided into. For example, one-half means 1 part out of 2 total parts. One-fourth means 1 part out of 4 total parts. The fraction three-eighths means 3 parts out of 8 total equal parts.
Circular diagrams are perfect for showing fractions. We divide a circle into equal sectors, and each sector represents one part of the whole. When we have 8 equal sectors, each sector represents one-eighth. By shading different numbers of sectors, we create different fractions. Two shaded sectors make two-eighths, four shaded sectors make four-eighths, and six shaded sectors make six-eighths.
Now let's focus on our target fraction three-eighths. To represent three-eighths correctly in a circular model, we need to divide the circle into 8 equal parts and shade exactly 3 of those sectors. This leaves 5 sectors unshaded. The key characteristics are: 8 total equal parts, 3 shaded parts, and 5 unshaded parts. This visual representation clearly shows what three-eighths looks like.
Now let's systematically examine each option to find which correctly represents three-eighths. Let's count the shaded sectors in each option. Option A has 5 shaded sectors out of 8, making it five-eighths. Option B has 4 shaded sectors out of 8, making it four-eighths. Option C has exactly 3 shaded sectors out of 8, making it three-eighths. Option D has 2 shaded sectors out of 8, making it two-eighths. Only Option C matches our target fraction of three-eighths.
The correct answer is Option C. Let's verify this by checking that it has exactly 3 shaded sectors out of 8 total sectors, which represents three-eighths. The other options are incorrect: Option A shows five-eighths with too many shaded sectors, Option B shows four-eighths with too many shaded sectors, and Option D shows two-eighths with too few shaded sectors. Remember the key principles: count the total equal parts for the denominator, count the shaded parts for the numerator, and match them to the target fraction.