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 \( x>0 \) , 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
A researcher surveyed undergraduate students, graduate students, and postdoctoral students. The number of undergraduate students surveyed was 7,450% of the number of postdoctoral students surveyed and the number of graduate students surveyed was 24% of the number of undergraduate students surveyed. If there were 3,576 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・求百分数挑战
A square map has a side length of 55 inches, and 1 inch on the map represents an actual distance of 13 miles. A larger version of the same map is printed as a square with the side length 90% longer than the side length of the previous map. On the larger 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
On a plot of land, 52.0% of the square footage is farmland and the remaining square footage is pasture. There are buildings on exactly 21.5% of the square footage of the farmland, and there are buildings on exactly 14.0% of the square footage of the pasture. If there are buildings on exactly p% of the square footage of the plot of land, what is the value of p?
原库参考解析
百分比关系・求百分数挑战
If \( x>0 \) and x is 33% of y, which expression represents y in terms of x?
原库参考解析
百分比关系・求百分数挑战
The speeds of particles A, B, and C are a meters per second, b meters per second, and c meters per second, respectively. If the speed of particle A is 6,000% of the speed of particle C and the speed of particle C is 0.008% of the speed of particle B, which expression represents 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
Jasmin grows bean pods in her garden. This year, she harvested 330 bean pods and saved 10% of them to plant next year. How many of the harvested bean pods did Jasmin save to plant next year?
原库参考解析
百分比关系・求百分数挑战
Levi and Marissa each have stamp collections. The number of stamps in Levi's collection is 200% of the number of stamps in Marissa's collection. If there are 460 stamps in Marissa's collection, how many stamps are in Levi's collection?
原库参考解析
百分比关系・求百分数挑战
A real estate company offers a series of three webinars. 3,750 people attended the first webinar. 54% of the people who attended the first webinar attended the second webinar, and 36% 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
After 60% of the original number of objects in a group were removed from the group. 300 objects remained in the group, How many objects were removed from the group?
原库参考解析
百分比关系・求百分数进阶
If x > 0 and x is 24% of y, which expression represents y in terms of x?
原库参考解析
百分比关系・求百分数挑战
The speeds of particles A, B, and C are a meters per second, b meters per second, and c meters per second, respectively. If the speed of particle A is 6,600% of the speed of particle C and the speed of particle C is 0.004% of the speed of particle B, which expression represents the value of a + b in terms of c?
原库参考解析
