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
A car dealership has only sedans, SUVs, and minivans for sale. On Monday, 30% of the vehicles for sale were sedans and 50% were SUVs. If there were 57 sedans for sale at the dealership on Monday, how many minivans were for sale?
原库参考解析
百分比关系・求百分数挑战
0.1242 is 0.09% of the number b. The number b is 25% of the number c. What is the value of c ?
原库参考解析
百分比关系・求百分数进阶
Of the 300,000 people in a region, 174,000 people voted in an election. If p% is the percentage of people in that region voted in that election, what is the value of p?
原库参考解析
百分比关系・求百分数挑战
0.1323 is 0.09% of the number b . The number b is 75% of the number c. What is the value of c?
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
百分比关系・求百分数进阶
During a study, scientists researched neutrinos (subatomic particles) that strike the earth's surface. The energy, E, of the neutrinos is measured in units of \( 10^{12} \) electron volts (TeV). The table shows the results of the scientists' research.
What percentage of these neutrinos had an energy of 90 TeV or less?
原库参考解析
百分比关系・求百分数进阶
For the positive quantities m, q, and r, m is 20% of \( m+q+r \), q is 30% of \( q+r \), and the value of r is 1,526. What is the value of m?
原库参考解析
百分比关系・求百分数进阶
What is 20% of 230?
原库参考解析
百分比关系・求百分数进阶
If x is a positive integer, the expression \( 0.36x \) represents what percent of x?
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. 3,750 people attended the first webinar. 72% of the people who attended the first webinar attended the second webinar, and 40% 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, 32% attended the third webinar. How many people attended both the first and third webinars but did not attend the second webinar?
参考答案
百分比关系・求百分数进阶
A jar has 610 marbles, and 20% of these marbles are orange. How many marbles in the jar are orange?
参考答案
百分比关系・求百分数挑战
The mass of object A is 481% of the mass of object B, and the mass of object A is 0.740% 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 p?
参考答案
