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
For the positive quantities h, j, and k, 15% of h is equivalent to 20% of j, and j is equivalent to 60% 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・求百分数挑战
A researcher surveyed undergraduate students, graduate students, and postdoctoral students. The number of undergraduate students surveyed was 6,950% of the number of postdoctoral students surveyed and the number of graduate students surveyed was 32% of the number of undergraduate students surveyed. If there were 4,448 graduate students surveyed, what was the sum of the number of undergraduate students and postdoctoral students surveyed?
原库参考解析
百分比关系・求百分数进阶
A jar has 330 buttons, and 20% of these buttons are green. How many buttons in the jar are green?
原库参考解析
百分比关系・求百分数挑战
Stefan purchased 500 feet of fencing. He used 80% of this fencing to surround a vegetable garden. How many feet of fencing did Stefan use to surround the vegetable garden?
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, 42% of h is equivalent to 84% of j, and j is equivalent to 64% 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
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?
原库参考解析
百分比关系・求百分数挑战
Object Z has a mass of 170 grams. The mass of object X is 4,400% of the mass of object Z. The mass of object Z is 20% of the mass of object Y. The sum, in grams, of the mass of object X and the mass of object Y is equal to the product, in grams, of w and the mass of object Z, where w is a constant. What is the value of w?
原库参考解析
百分比关系・求百分数基础
There are a total of 340 seats in a school auditorium. During an assembly, students occupied 50% of the seats in the auditorium. How many seats did the students occupy during this assembly?
原库参考解析
百分比关系・求百分数挑战
The mass of object A is 444% 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?
原库参考解析
百分比关系・求百分数进阶
A certain university's research farm is 1,000 acres, of which 71 acres contain rice. What percentage of the acres of this research farm contain rice?
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百分比关系・求百分数进阶
A real estate company offers a series of three webinars. 3,125 people attended the first webinar. 56% of the people who attended the first webinar attended the second webinar, and 26% of the people who attended the first and second webinars attended the third webinar. How many people attended all three webinars?
原库参考解析
百分比关系・求百分数挑战
Which expression represents 1% of \( 31x \) ,where \( x>0 \) ?
原库参考解析
