Mastering Fractions, Decimals and Percentages | 掌握分数、小数和百分比

📚 Mastering Fractions, Decimals and Percentages | 掌握分数、小数和百分比

In the Cambridge Lower Secondary Mathematics curriculum, fractions, decimals and percentages are not separate topics. They are three ways of representing the same idea: parts of a whole. This article will help KS3 students build fluency in converting between these forms and applying them to problems.

在剑桥初中数学课程中，分数、小数和百分比并不是彼此独立的主题。它们是表示同一个概念的三种方式：整体的一部分。本文将帮助 KS3 学生熟练地在这些形式之间转换，并将其应用于解决问题。

1. Understanding Fractions | 理解分数

A fraction is written as a/b, where a is the numerator and b is the denominator. The denominator cannot be zero, because you cannot divide a whole into zero equal parts.

分数写作 a/b，其中 a 是分子，b 是分母。分母不能为零，因为你不能把整体分成零等份。

For example, 3/8 means the whole is divided into 8 equal parts and we are interested in 3 of them. This is called a proper fraction because the numerator is smaller than the denominator.

例如，3/8 表示整体被分成 8 等份，我们取其中的 3 份。这叫做真分数，因为分子小于分母。

Improper fractions have a numerator greater than or equal to the denominator, such as 9/4. Mixed numbers combine a whole number and a proper fraction, such as 2 1/4.

假分数的分子大于或等于分母，例如 9/4。带分数由一个整数和一个真分数组成，例如 2 1/4。

9/4 = 2 1/4

A fraction can also describe part of a set. If there are 20 students and 12 are girls, then the fraction of girls is 12/20 = 3/5.

分数也可以描述一组对象中的一部分。如果有 20 名学生，其中 12 名是女生，那么女生的分数是 12/20 = 3/5。

2. Equivalent Fractions and Simplest Form | 等值分数与最简形式

Equivalent fractions represent the same amount even though they use different numerators and denominators. You can create an equivalent fraction by multiplying or dividing both the numerator and denominator by the same non-zero number.

等值分数表示相同的量，尽管它们的分子和分母不同。你可以通过将分子和分母同时乘以或除以同一个非零数来得到等值分数。

2/3 = 2×2 / 3×2 = 4/6 = 8/12

A fraction is in simplest form when the highest common factor (HCF) of the numerator and denominator is 1. To simplify 12/18, divide both terms by 6.

当分子和分母的最大公因数（HCF）为 1 时，分数就是最简形式。要化简 12/18，将分子和分母同时除以 6。

12/18 = 12÷6 / 18÷6 = 2/3

Always check whether a fraction can be simplified before giving a final answer in a test. You can also test equivalence by cross multiplying: 2/3 and 4/6 are equivalent because 2 × 6 = 3 × 4.

在考试中给出最终答案之前，一定要检查分数是否可以化简。你也可以通过交叉相乘来检验等值关系：2/3 和 4/6 是等值的，因为 2 × 6 = 3 × 4。

3. Converting Fractions to Decimals | 分数转换为小数

To convert a fraction to a decimal, divide the numerator by the denominator. You can use short division or a calculator.

要将分数转换为小数，用分子除以分母。你可以使用短除法或计算器。

3/4 = 3 ÷ 4 = 0.75

Some fractions give terminating decimals, such as 1/8 = 0.125. Others give recurring decimals, such as 1/3 = 0.333… which can be written as 0.3 with a dot above the 3.

有些分数会得到有限小数，例如 1/8 = 0.125。另一些会得到循环小数，例如 1/3 = 0.333…，可以写作 0.3 并在 3 上方加点。

Knowing common conversions by heart saves time: 1/2 = 0.5, 1/4 = 0.25, 1/5 = 0.2, 1/10 = 0.1.

熟记常见转换可以节省时间：1/2 = 0.5，1/4 = 0.25，1/5 = 0.2，1/10 = 0.1。

To compare a fraction and a decimal, convert both to the same form. For example, is 3/8 greater than 0.35? Since 3/8 = 0.375, the fraction is greater.

要比较一个分数和一个小数，先把它们都转换成同一种形式。例如，

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