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
Of the 180 soccer players at a soccer camp, 72 are midfielders. What percentage of the soccer players at the camp are midfielders?
参考答案
百分比关系・求百分数进阶
The positive number a is 290% of the number b, and a is 90% of the number c. If c is p% of b, which of the following is closest to the value of p?
参考答案
百分比关系・求百分数挑战
A car dealership has only sedans, SUVs, and minivans for sale. On Monday, 20% of the vehicles for sale were sedans and 50% were SUVs. If there were 62 sedans for sale at the dealership on Monday, how many minivans were for sale?
参考答案
百分比关系・求百分数挑战
A car dealership has only sedans, SUVs, and minivans for sale. On Monday, 20% of the vehicles for sale were sedans and 50% were SUVs. If there were 65 SUVs for sale at the dealership on Monday, how many minivans were for sale?
参考答案
百分比关系・求百分数进阶
0.0048 is 0.8% of a, and 84 is 350% of b, where a and b are positive numbers. What percentage of a is b?
参考答案
百分比关系・求百分数进阶
Object A has a mass of k hectograms. The mass, in hectograms, of object B is 120% of the mass of object A. The positive difference between the mass of object B and the mass of object A is 68 hectograms. What is the value of k?
参考答案
百分比关系・求百分数进阶
Object A has a mass of k hectograms. The mass, in hectograms, of object B is 120% of the mass of object A. The positive difference between the mass of object B and the mass of object A is 76 hectograms. What is the value of k?
参考答案
百分比关系・求百分数进阶
There are 850 objects in a bag. Of these objects, 8% are cubes. How many cubes are in the bag?
参考答案
百分比关系・求百分数基础
32 is 10% of what number?
参考答案
百分比关系・求百分数挑战
360% of x is 18. What is the value of x?
参考答案
百分比关系・求百分数进阶
While the mass of an object is the same everywhere, the weight of an object is not the same on different planets. An object has a weight of 170.00 pounds on Earth and a weight of 186.32 pounds on Neptune. The object's weight on Jupiter is 252.8% of its weight on Earth. If the object's weight on Neptune is x% of its weight on Jupiter, which of the following is closest to the value of x?
原库参考解析
百分比关系・求百分数进阶
There are 550 objects in a bag. Of these objects, 4% are cubes. How many cubes are in the bag?
原库参考解析
