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 amount of Hanna's bill for a food order was $50. Hanna gave a tip of 20% of the amount of the bill. What is the amount, in dollars, of the tip Hanna gave?
原库参考解析
百分比关系・求百分数进阶
The number of zebras in a population in 2018 was 1.27 times the number of zebras in this population in 2014. If the number of zebras in this population in 2014 is p% of the number of zebras in this population in 2018, what is the value of p, to the nearest whole number?
原库参考解析
百分比关系・求百分数挑战
The positive number a is 2,241% of the sum of the positive numbers b and c, and b is 83% of c. What percent of b is a?
原库参考解析
百分比关系・求百分数基础
What is 20% of 440?
原库参考解析
百分比关系・求百分数基础
There are 450 tiles in a box. Of these tiles, 6% are black. How many black tiles are in the box?
原库参考解析
百分比关系・求百分数挑战
In a sample, 80% of the items are faulty. There are 88 faulty items in the sample. How many total items are in the sample?
原库参考解析
百分比关系・求百分数挑战
The positive number a is 230% of the number b, and a is 60% 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
For \( x>0 \) , the function \( f \) is defined as follows:
\( f\left(x\right) \) equals 201% 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
According to a set of standards, a certain type of substance can contain a maximum of 0.001% phosphorus by mass. If a sample of this substance has a mass of 140 grams, what is the maximum mass, in grams, of phosphorus the sample can contain to meet these standards?
原库参考解析
百分比关系・求百分数挑战
37% of the items in a box are green. Of those, 37% are also rectangular. Of the green rectangular items, 42% are also metal. Which of the following is closest to the percentage of the items in the box that are not rectangular green metal items?
原库参考解析
百分比关系・求百分数挑战
Jennifer bought a box of Crunchy Grain cereal. The nutrition facts on the box state that a serving size of the cereal is \( \frac{3}{4} \) cup and provides 210 calories, 50 of which are calories from fat. In addition, each serving of the cereal provides 180 milligrams of potassium, which is 5% of the daily allowance for adults. If p percent of an adult’s daily allowance of potassium is provided by x servings of Crunchy Grain cereal per day, which of the following expresses p in terms of x ?
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百分比关系・求百分数挑战
A school district is forming a committee to discuss plans for the construction of a new high school. Of those invited to join the committee, 15% are parents of students, 45% are teachers from the current high school, 25% are school and district administrators, and the remaining 6 individuals are students. How many more teachers were invited to join the committee than school and district administrators?
原库参考解析
