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
Jasmin grows bean pods in her garden. This year, she harvested 490 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・求百分数基础
The positive number a is 240% 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
A scientist analyzed a soil sample with a mass of 900 grams and determined that it contained 189 grams of water What is the percentage of water, by mass, in this soil sample?
原库参考解析
百分比关系・求百分数挑战
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・求百分数挑战
Of 400,000 objects in a group, 312,000 are new. What percentage of objects in that group are new?
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 490 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
According to a set of standards, pure biodiesel fuel can contain a maximum of 0.001% phosphorus by mass. If a sample of pure biodiesel fuel has a mass of 310 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
According to a set of standards, pure biodiesel fuel can contain a maximum of 0.001% phosphorus by mass.If a sample of pure biodiesel fuel has a mass of 310 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・求百分数进阶
A scientist analyzed a soil sample with a mass of 900 grams and determined that it contained 189 grams of water. What is the percentage of water, by mass, in this soil sample?
原库参考解析
百分比关系・求百分数挑战
If 310% of n is 62, what is the value of n?
原库参考解析
百分比关系・求百分数挑战
A barrel contains 32 liters of a chemical solution. 50% of this chemical solution, by volume, is water. How much of this chemical solution, in liters, is water?
原库参考解析
百分比关系・求百分数进阶
The positive number a is 2,800% of the number c, and c is 25% of the number b. If \( a-b=wc \) , where w is a constant, what is the value of w?
原库参考解析
