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
The positive number a is 2,136% of the sum of the positive numbers b and c, and b is 89% 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 \( x>0 \), the function \( f \) is defined as follows:
\( f\left(x\right) \) equals 293% 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 real estate company offers a series of three webinars. 1,250 people attended the first webinar. 46% of the people who attended the first webinar attended the second webinar, and 32% 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
A square map has a side length of 45 inches, and 1 inch on the map represents an actual distance of 13 miles. A smaller version of the same map is printed as a square with the side length 70% 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・求百分数进阶
The positive number a is 2,047% of the sum of the positive numbers b and c, and b is 89% 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
A square map has a side length of 55 inches, and 1 inch on the map represents an actual distance of 13 miles. A smaller version of the same map is printed as a square with the side length 70% 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
The positive number a is 2,184% of the sum of the positive numbers b and c, and b is 84% 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
In a collection of items, 10% are red, 25% are green, 35% are blue, and 30% are yellow. If there are 40 green items. How many blue items are in the collection?
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 30 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 65% 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・求百分数进阶
Jasmnin grows bean pods in her garden. This year, she harvested 480 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
In a collection of items, 10% are red, 25% are green, 35% are blue, and 30% are yellow. If there are 40 green items, how many blue items are in the collection?
原库参考解析
