How to Find Percentages of Amounts | 如何求一个数的百分比

📚 How to Find Percentages of Amounts | 如何求一个数的百分比

Percentages appear everywhere in daily life – from shopping discounts to test scores and bank interest rates. Being able to calculate percentages of amounts is a fundamental skill in the Cambridge KS3 mathematics curriculum. This guide will walk you through different methods to find any percentage of a number, with and without a calculator, so you can tackle problems confidently.

百分比在日常生活中随处可见——从购物折扣到考试成绩和银行利率。能够计算一个数的百分比是剑桥KS3数学课程中的一项基本技能。本指南将带你学习使用不同的方法求任意数的百分比，无论有无计算器，都能让你自信地解决问题。

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1. What Are Percentages? | 什么是百分比？

A percentage is a fraction out of 100. The symbol for percentage is %. For example, 50% means 50 out of 100, which is the same as one-half. Understanding this definition is the key to all percentage calculations.

百分比是表示一个数是另一个数的百分之几的分数。百分比的符号是%。例如，50% 表示 100 份中的 50 份，相当于一半。理解这个定义是所有百分比计算的关键。

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2. Converting Percentages to Fractions | 将百分比转换为分数

To convert a percentage to a fraction, write the percentage number over 100 and simplify if possible. For example, 25% = 25/100 = 1/4. Similarly, 10% = 10/100 = 1/10. Always reduce the fraction to its simplest form to make further calculations easier.

要将百分比转换为分数，将百分数写在100上，然后约简。例如，25% = 25/100 = 1/4。类似地，10% = 10/100 = 1/10。记得将分数化为最简形式，以便进一步计算。

Here is a table of common percentage-fraction conversions:

以下是常见百分比与分数的转换表：

Percentage	Fraction	Simplified
50%	50/100	1/2
25%	25/100	1/4
20%	20/100	1/5
10%	10/100	1/10
75%	75/100	3/4
12%	12/100	3/25

You can use these simplified fractions to find percentages of amounts much more quickly.

你可以使用这些化简后的分数更快地求出一个数的百分比。

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3. Converting Percentages to Decimals | 将百分比转换为小数

To convert a percentage to a decimal, divide the percentage by 100. This is equivalent to moving the decimal point two places to the left. For instance, 75% = 75 ÷ 100 = 0.75; 8% = 8 ÷ 100 = 0.08; 120% = 120 ÷ 100 = 1.20. This decimal form is very useful for calculator methods.

要将百分比转换为小数，将百分数除以100。相当于将小数点向左移动两位。例如，75% = 75 ÷ 100 = 0.75；8% = 8 ÷ 100 = 0.08；120% = 120 ÷ 100 = 1.20。这种小数形式在使用计算器时非常有用。

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4. Key Building Blocks: 10%, 5% and 1% | 关键基石：10%、5% 和 1%

Many percentages can be found mentally by first working out 10%, 5% and 1% of the amount. These three values are incredibly simple to calculate and form the foundation of the ‘building block’ method.

许多百分比可以通过先计算出原数的10%、5%和1%来心算求得。这三个值计算起来非常简单，构成了“基石法”的基础。

To find 10% of an amount, divide by 10.

若要计算一个数的10%，将它除以10。

To find 5% of an amount, find 10% first and then halve it (because 5% is half of 10%). Alternatively, you can divide the original amount by 20.

若要计算5%，先求出10%再减半（因为5%是10%的一半）。或者直接把原数除以20。

To find 1% of an amount, divide by 100.

若要计算1%，将原数除以100。

Example with 240:

以240为例：

10% of 240 = 240 ÷ 10 = 24

240 的 10% = 240 ÷ 10 = 24

5% of 240 = 24 ÷ 2 = 12

240 的 5% = 24 ÷ 2 = 12

1% of 240 = 240 ÷ 100 = 2.4

240 的 1% = 240 ÷ 100 = 2.4

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5. Finding Any Percentage Using Building Blocks | 使用基石法求任意百分比

Once you know 10%, 5% and 1%, you can combine them to find almost any percentage without a calculator. Simply break the percentage down into a sum of these building blocks.

一旦你知道了10%、5%和1%，就可以将它们组合起来，无需计算器就能求出几乎任意百分比。只需将百分比拆解成这些基石之和。

Worked example: Find 23% of 240.

例题：求240的23%。

We can write 23% as 10% + 10% + 1% + 1% + 1%.

我们可以把23%写成 10% + 10% + 1% + 1% + 1%。

= 24 + 24 + 2.4 + 2.4 + 2.4 = 55.2

或者，23% = 20% + 3%，其中20% = 2 × 10% = 48，3% = 3 × 1% = 7.2，48 + 7.2 = 55.2。

Alternatively, 23% = 20% + 3%, where 20% = 2 × 10% = 48, and 3% = 3 × 1% = 7.2, giving 48 + 7.2 = 55.2.

This method is powerful for mental maths and helps you understand the composition of percentages.

这种方法在心算时十分强大，并且能帮助你理解百分比的构成。

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6. The Fraction Method for Percentages | 百分比分数法

Since a percentage is just a fraction with 100 as the denominator, you can find a percentage of an amount by multiplying by the simplified fraction. Multiply the amount by the numerator and then divide by the denominator.

既然百分比本质上是一个分母为100的分数，你可以通过乘以化简后的分数来求一个数的百分比。先用原数乘以分子，再除以分母。

Example 1: 40% of 60. Write 40% as 40/100 = 2/5. Then (2/5) × 60 = (2 × 60) ÷ 5 = 120 ÷ 5 = 24.

例1：60的40%。把40%写作40/100 = 2/5。然后 (2/5) × 60 = (2 × 60) ÷ 5 = 120 ÷ 5 = 24。

Example 2: 25% of 200. 25% = 1/4, so 1/4 × 200 = 50.

例2：

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