Percentages | 百分比

📚 Percentages | 百分比

Percentages are one of the most useful and frequently tested topics in Grade 7 mathematics. They appear in everyday situations such as shopping discounts, bank interest and exam scores, and they form the foundation of many later IGCSE topics. This article covers everything you need to master percentages step by step.

百分比是7年级数学中最实用、最常考的主题之一。它出现在购物折扣、银行利息和考试成绩等日常情境中，也是日后许多IGCSE知识点的基础。本文将带你循序渐进地掌握百分比的全部要点。

1. What is a Percentage | 什么是百分比

A percentage is a special way of writing a fraction whose denominator is 100. The symbol % is read as ‘percent’, from the Latin phrase ‘per centum’, meaning ‘out of one hundred’. For example, 7% means 7 equal parts out of every 100 equal parts.

百分比是一种特殊的分数写法，其分母固定为100。符号%读作“百分之”，源自拉丁语“per centum”，意为“每一百中”。例如，7%表示每100等份中的7份。

Because a percentage is simply a fraction with denominator 100, it can be instantly converted into a decimal or a fraction. The number 100 is always the key reference point.

由于百分比本质上是分母为100的分数，因此可以立即转换为小数或普通分数。数字100始终是关键的参照基准。

1% = 1 ÷ 100 = 0.01, so n% = n ÷ 100

Visualising a 10 × 10 grid can help. Each small square represents 1% of the whole grid, each full row represents 10%, and the entire grid represents 100%. If you shade 35 small squares, you have shaded 35% of the grid.

借助10×10方格图可以直观理解。每个小方格代表整个方格的1%，每一整行代表10%，整个方格代表100%。若你涂满35个小方格，则涂色部分占方格的35%。

2. Converting Percentages, Fractions and Decimals | 百分比、分数与小数的互化

To convert a percentage into a fraction, write the number over 100 and simplify. For example, 60% = 60/100 = 3/5. To convert a decimal into a percentage, multiply by 100; to convert a percentage into a decimal, divide by 100.

将百分比化为分数时，把该数写在100上方并约分。例如，60% = 60/100 = 3/5。将小数化为百分比时乘以100；将百分比化为小数时除以100。

To convert a fraction into a percentage, first change the fraction into a decimal, then multiply by 100. For example, 3/8 = 0.375, so 3/8 = 37.5%.

将分数化为百分比时，先将分数化为小数，再乘以100。例如，3/8 = 0.375，因此3/8 = 37.5%。

The following table shows the common equivalents that you should memorise for quick mental calculation.

下表列出常见等价关系，建议熟记以便快速心算。

A useful shortcut is that the fraction and decimal forms always match: if you know that ¼ = 0.25, then you immediately know ¼ = 25%, because multiplying 0.25 by 100 gives 25.

一个小技巧是分数与小数形式总是对应：若你知道¼ = 0.25，则立刻可知¼ = 25%，因为0.25乘以100即为25。

3. Finding a Percentage of a Quantity | 求一个数的百分比

Finding ‘a percentage of a quantity’ is one of the most common calculation types in mathematics. The word ‘of’ translates directly to multiplication. For example, ‘15% of 80’ means 15% × 80.

“求一个数的百分比”是最常见的一种计算类型。数学中“的”字直接对应乘法。例如，“80的15%”即表示15% × 80。

Method 1: convert the percentage to a decimal and multiply. Method 2: convert the percentage to a fraction and multiply. Both methods give the same answer, so choose whichever you find more comfortable.

方法一：将百分比化为小数再相乘。方法二：将百分比化为分数再相乘。两种方法答案相同，选择你更习惯的一种即可。

p% of Q = (p ÷ 100) × Q

Worked example: Calculate 15% of 80. Using the decimal method, 0.15 × 80 = 12. Using the fraction method, 15% = 15/100 = 3/20, so 3/20 × 80 = 12. The answer is 12 either way.

实例：计算80的15%。用小数法：0.15 × 80 = 12。用分数法：15% = 15/100 =

Published by TutorHao | IGCSE Mathematics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）