这部分需要会什么？
- 将百分数、小数和分数互换
- 识别百分比关系中的比较基准
- 根据部分量、整体量和比例中的两个求第三个
核心概念与公式
\(p\%=p/100\)。若 A 是 B 的 \(p\%\)，则 \(A=(p/100)B\)。B 是比较基准；要求 A 是 B 的百分之几，应计算 \(A/B\times100\%\)，前提是 \(B\ne0\)。
如果题目问“\(p\) 的值”且写作 \(p\%\)，最终通常填写百分数前的数，例如 25；如果问对应的小数比例，则为 0.25。应按题目的表达方式作答。
做题时怎样使用
- 圈出“谁的百分之几”，确定整体或比较对象
- 写出“部分量 = 比例 × 基准量”
- 求百分数时先求比值再乘 100，并检查答案的形式
容易混淆的地方
“A 是 B 的 120%”表示 \(A=1.2B\)；“A 比 B 多 120%”表示 \(A=2.2B\)。两句话不同。
用一个例题串起方法
知识点教学例题某班有 40 人，其中 14 人选择某门选修课。选择人数占全班的百分之几？
展开解题思路 ＋
以全班 40 人为基准，比例为 \(14/40=0.35\)，所以占 \(35\%\)。若题目要求 \(p\) 的值，则填写 35。
本知识点题库
先独立作答，再查看答案与解析。
百分比关系・求百分数进阶
\( \frac{7}{6} \) is p% of \( \frac{1}{30} \). What is p ?
原库参考解析
百分比关系・求百分数挑战
The composition of an animal is defined as the muscles, bones,and fat of the animal. A scientist studied the composition of one young swamp buffalo and determined the buffalo had 133 kilograms of muscle, which made up approximately 65.9% of its composition. Of the remaining composition of this buffalo, approximately 46.2% was bone, and the remainder was fat. Based on these approximations, to the nearest tenth, how many kilograms of this buffalo's composition was bone?
原库参考解析
百分比关系・求百分数进阶
The positive number a is 2,800% of the number c, and c is 20% of the number b. What is the value of a - b in terms of c ?
原库参考解析
百分比关系・求百分数进阶
For x > 0, the function f is defined as follows:
f(x ) equals 111% of x
Which of the following could describe this function?
原库参考解析
百分比关系・求百分数进阶
One minute after the start of an experiment, the volume of a mixture is 72% of its volume at the start of the experiment. Which expression best represents the volume of the mixture one minute after the start of the experiment, where v is its volume at the start of the experiment?
原库参考解析
百分比关系・求百分数挑战
The composition of an animal is defined as the muscles, bones, and fat of the animal. A scientist studied the composition of one young swamp buffalo and determined the buffalo had 120.2 kilograms of muscle, which made up approximately 68.3% of its composition. Of the remaining composition of this buffalo, approximately 53.9% was bone, and the remainder was fat. Based on these approximations, to the nearest tenth, how many kilograms of this buffalo's composition was bone?
原库参考解析
百分比关系・求百分数进阶
For x > 0, the function f is defined as follows:
f (x) equals 293% of x
Which of the following could describe this function?
原库参考解析
百分比关系・求百分数挑战
The mass of object A is 438% of the mass of object B, and the mass of object A is 0.073% of the mass of object C. If the mass of object C is p% of the mass of object B, what is the value of \( \frac{P}{1000} \) ?
原库参考解析
百分比关系・求百分数挑战
For the positive quantities h, j, and k, 44% of h is equivalent to 62% of j, and j is equivalent to 22% of k. What percentage of k is h? (Disregard the % sign when entering your answer. For example, if your answer is 39%, enter 39)
原库参考解析
百分比关系・求百分数进阶
A real estate company offers a series of three webinars. 4,000 people attended the first webinar. 65% of the people who attended the first webinar attended the second webinar, and 39% of the people who attended both the first and second webinar attended the third webinar. Of those who attended the first but did not attend the second webinar, 22% attended the third webinar. How many people attended both the first and third webinars but did not attend the second webinar?
原库参考解析
百分比关系・求百分数挑战
A square map has a side length of 30 inches, and 1 inch on the map represents an actual distance of 13 miles. A smaller version of the same map is printed as a square with the side length 85% shorter than the side length of the previous map. On the smaller map, which of the following is closest to the actual distance, in miles, represented by 1 inch?
原库参考解析
百分比关系・求百分数进阶
The table summarizes the number of objects in each group.
The number of objects in group C is p% of the number of objects in group A. What is the value of p?
原库参考解析
