Mastering Fractions, Decimals and Percentages | 掌握分数、小数与百分比

📚 Mastering Fractions, Decimals and Percentages | 掌握分数、小数与百分比

In IGCSE Mathematics, fractions, decimals and percentages are not three separate topics. They are three different ways of describing the same proportion. You will see them in number calculations, estimation, probability, ratio and percentage problems. This revision guide covers the conversions, arithmetic rules and percentage techniques that examiners expect you to use accurately and quickly.

在 IGCSE 数学中，分数、小数和百分比并不是三个独立的主题。它们是描述同一个比例的三种不同方式。你会看到它们出现在数值计算、估算、概率、比和百分比问题中。本复习指南涵盖转换方法、运算规则和百分比技巧，这些正是考官希望你准确、快速掌握的内容。

1. The Core Idea: Three Forms of One Quantity | 核心概念：同一个量的三种形式

Every percentage, decimal and fraction is just a number expressed in a different notation. One half can be written as 1/2, 0.5 or 50%, but all three refer to exactly the same amount. The key skill is not memorising three isolated topics; it is seeing how they switch between forms.

每个百分比、小数和分数都只是同一个数用不同记号表示。二分之一可以写成 1/2、0.5 或 50%，但三者表示的数量完全相同。关键技能不是把三个主题割裂记忆，而是理解它们如何相互转换。

Use this equivalence as a mental anchor: 1/2 = 0.5 = 50%. Once you can convert any one form into the other two, percentage and fraction questions become much simpler. In many IGCSE problems, changing a percentage into a decimal makes multiplication easier, while changing a decimal into a fraction helps you simplify exact answers.

请把这个等式当作心理锚点：1/2 = 0.5 = 50%。一旦你能把任意一种形式转换成另外两种，百分比和分数问题就会简单得多。在许多 IGCSE 题目中，把百分比转换为小数会让乘法更简单，而把小数转换为分数有助于化简精确答案。

2. Converting Fractions to Decimals and Percentages | 将分数转换为小数和百分比

To convert a fraction to a decimal, divide the numerator by the denominator. For example, 3/8 means 3 ÷ 8, which gives 0.375. To convert that decimal to a percentage, multiply by 100 and add the percent sign: 0.375 × 100% = 37.5%.

要把分数转换为小数，用分子除以分母。例如 3/8 表示 3 ÷ 8，得到 0.375。要把该小数转换为百分比，乘以 100 并加上百分号：0.375 × 100% = 37.5%。

decimal = numerator ÷ denominator

percentage = (numerator ÷ denominator) × 100%

If the fraction is mixed, such as 1 3/4, convert the fractional part to 0.75 and then add the whole number: 1 + 0.75 = 1.75, which is 175%. A quick check is that a proper fraction gives a

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

更多咨询请联系16621398022（同微信）