Teach me this question---**Question 21** **Question Stem:** In which model is the fraction of the whole shaded to represent the fraction 3/8? **Options:** * **Option A:** * **Chart/Diagram Description:** A circular geometric figure divided into 8 equal sectors. Three of these sectors are shaded grey, and five are left white. The shaded sectors are located at the top-left, bottom-left, and bottom-right positions relative to the circle's center. * **Fraction Represented:** 3/8 (3 shaded parts out of 8 total parts). * **Option B:** * **Chart/Diagram Description:** A circular geometric figure divided into 8 equal sectors. Five of these sectors are shaded grey, and three are left white. The shaded sectors occupy the entire right half of the circle and one sector in the bottom-left. * **Fraction Represented:** 5/8 (5 shaded parts out of 8 total parts). * **Option C:** * **Chart/Diagram Description:** A circular geometric figure divided into 8 equal sectors. Five of these sectors are shaded grey, and three are left white. The shaded sectors occupy the entire bottom half of the circle and one sector in the top-right. * **Fraction Represented:** 5/8 (5 shaded parts out of 8 total parts). * **Option D:** * **Chart/Diagram Description:** A circular geometric figure divided into 8 equal sectors. Three of these sectors are shaded grey, and five are left white. The shaded sectors are located at the top-right, bottom-right, and bottom-left positions relative to the circle's center. * **Fraction Represented:** 3/8 (3 shaded parts out of 8 total parts).

视频信息

答案文本 复制

视频字幕 复制

Fractions are a fundamental concept in mathematics that represent the relationship between parts and the whole. A fraction consists of two parts: the denominator shows how many equal parts the whole is divided into, and the numerator shows how many of those parts are selected or shaded. For example, in the circle shown, we have divided it into 8 equal sectors, and 3 of them are shaded, representing the fraction 3/8. Now let's examine the question. We need to find which model represents the fraction 3/8. Let's look at each option carefully. Option A shows a circle divided into 8 equal sectors with 3 sectors shaded, representing 3/8. Option B has 5 sectors shaded, representing 5/8. Option C also has 5 sectors shaded, representing 5/8. Option D shows 3 sectors shaded, representing 3/8. Both options A and D show 3 out of 8 parts shaded, so they both represent 3/8. The correct answer is that both Option A and Option D represent the fraction 3/8. This is because both circles are divided into 8 equal sectors, and exactly 3 sectors are shaded in each case. The key insight is that the position of the shaded sectors doesn't matter - what matters is the count. As long as 3 out of 8 parts are shaded, the fraction is 3/8. Options B and C are incorrect because they show 5 shaded sectors out of 8, which represents 5/8, not 3/8. Let's understand what the fraction 3/8 means. The denominator 8 tells us that the whole is divided into 8 equal parts. The numerator 3 tells us that we select or shade 3 of those parts. So 3/8 represents 3 out of 8 equal parts of the whole. In a circle model, this means we need to find circles where exactly 3 sectors out of 8 total sectors are shaded. The position of the shaded sectors doesn't matter, only the count matters. Now let's analyze all four options systematically. Option A shows a circle with 3 shaded sectors out of 8 total, which correctly represents 3/8. Option B has 5 shaded sectors, representing 5/8, so it's incorrect. Option C also has 5 shaded sectors, representing 5/8, so it's also incorrect. Option D shows 3 shaded sectors out of 8, which correctly represents 3/8. Therefore, both options A and D are correct answers to this question. Let's summarize the key learning points from this problem. First, the position of shaded sectors doesn't matter - only the count matters. Both options A and D are correct because they both show exactly 3 out of 8 parts shaded. Options B and C are incorrect because they show 5 out of 8 parts, which represents 5/8, not 3/8. Remember to always count carefully: the numerator tells us how many parts are shaded, and the denominator tells us the total number of equal parts. For the fraction 3/8, we need exactly 3 shaded sectors out of 8 total sectors. In conclusion, the final answer is that both Option A and Option D correctly represent the fraction 3/8. The key strategy for solving this type of problem is to count the shaded parts for the numerator and the total parts for the denominator, remembering that position doesn't matter. This problem tests your ability to identify fractions in visual models and understand that multiple arrangements can represent the same fraction. Both options show 3 shaded sectors out of 8 total sectors, which equals 3/8.