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
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
If 380% of n is 38, what is the value of n?
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 35 inches, and 1 inch on the map represents an actual distance of 17 miles. A smaller version of the same map is printed as a square with the side length 55% 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・求百分数挑战
For x > 0, the function \( f \) is defined as follows:
\( f\left(x\right) \) equals 300% 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
A researcher surveyed undergraduate students, graduate students, and postdoctoral students. The number of undergraduate students surveyed was 7,050% 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 3,384 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
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 123.8 kilograms of muscle, which made up approximately 67.4% of its composition. Of the remaining composition of this buffalo, approximately 58.7% was bone, and the remainder was fat. Based on these approximatious, to the nearest tenth, how many kilagrams of this buffalo's composition was fat?
原库参考解析
百分比关系・求百分数进阶
18 is 10% of what number?
原库参考解析
百分比关系・求百分数挑战
The mass of object A is 498% of the mass of object B, and the mass of object A is 0.830% 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
Julia purchased 400 feet of fencing. She used 90% of this fencing to surround a vegetable garden. How many feet of fencing did Julia use to surround the vegetable garden?
原库参考解析
百分比关系・求百分数挑战
The positive number a is 2,024% of the sum of the positive numbers b and c, and b is 88% of c. What percent of b is a?
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 , 35% of h is equivalent to 49% of j , and j is equivalent to 45% 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
5% of w is 741.41. What is the value of w?
原库参考解析
