KS3 Cambridge Maths: Fractions, Decimals and Percentages (p120 Q2) | 剑桥中学数学：分数、小数与百分数（p120 第2题）

📚 KS3 Cambridge Maths: Fractions, Decimals and Percentages (p120 Q2) | 剑桥中学数学：分数、小数与百分数（p120 第2题）

In this article we review a core KS3 Cambridge maths topic: fractions, decimals and percentages. This topic appears frequently in Checkpoint tests and in homework pages such as page 120, question 2. You will see how the three forms are linked, how to convert between them, and how to apply them to real problems.

本文复习剑桥初中数学的核心专题：分数、小数与百分数。该专题经常出现在 Checkpoint 测试以及类似第 120 页第 2 题的作业中。你将看到这三种形式之间的联系、如何互相转换，以及如何将它们应用于实际问题。

1. Understanding the Big Picture | 理解整体图景

Fractions, decimals and percentages are three different ways of describing the same idea: a part of a whole. A fraction uses a numerator and denominator, a decimal uses place value, and a percentage is always out of 100.

分数、小数和百分数是描述同一个概念的三种不同方式：整体的一部分。分数用分子和分母表示，小数使用位值，百分数则总是以 100 为基准。

For example, one half can be written as ½, 0.5 or 50%. The ability to move quickly between these forms is a key skill in the Cambridge KS3 curriculum.

例如，一半可以写成 ½、0.5 或 50%。在这些形式之间快速转换是剑桥 KS3 课程中的关键技能。

Before practising conversions, make sure you understand that the three representations have equal value even though they look different.

在练习转换之前，请确保你理解这三种表示虽然看起来不同，但数值相等。

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2. Equivalent Fractions | 等值分数

An equivalent fraction is created by multiplying or dividing both the numerator and denominator by the same non-zero number. This does not change the value of the fraction.

等值分数是通过将分子和分母同时乘以或除以同一个非零数而得到的分数。这样做不会改变分数的值。

For instance, 1/2 = 2/4 = 4/8 because both parts of the fraction have been scaled by the same factor.

例如，1/2 = 2/4 = 4/8，因为分数的分子和分母都按相同的倍数进行了缩放。

In a typical exercise such as page 120 question 2, you may be asked to write a fraction in its simplest form. To simplify, divide the numerator and denominator by their highest common factor.

在类似第 120 页第 2 题的典型练习中，你可能需要把分数化为最简形式。化简分数的方法是分子和分母同时除以它们的最大公因数。

For example, 12/16 simplifies to 3/4 because the highest common factor of 12 and 16 is 4.

例如，12/16 化简为 3/4，因为 12 和 16 的最大公因数是 4。

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3. Converting Fractions to Decimals | 分数转小数

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

将分数转换为小数的方法是分子除以分母。可以使用短除法，或者在允许的情况下使用计算器。

fraction → decimal: numerator ÷ denominator

A fraction like 3/8 becomes 0.375 because 3 ÷ 8 = 0.375.

像 3/8 这样的分数转换为 0.375，因为 3 ÷ 8 = 0.375。

Some fractions produce terminating decimals, such as 1/4 = 0.25, while others produce recurring decimals, such as 1/3 = 0.333… In KS3 you need to recognise both forms.

有些分数可以化为有限小数，例如 1/4 = 0.25；有些则化为循环小数，例如 1/3 = 0.333…… 在 KS3 中你需要识别这两种形式。

If you see a fraction like 7/20, multiply the denominator to 100 first: 7/20 = 35/100 = 0.35. This method is often quicker when the denominator is a factor of 100.

如果遇到 7/20 这样的分数，可以先把分母变成 100：7/20 = 35/100 = 0.35。当分母是 100 的因数时，这种方法通常更快。

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4. Converting Decimals to Percentages | 小数转百分数

To convert a decimal to a percentage, multiply the decimal by 100 and add the % symbol. This is equivalent to moving the decimal point two places to the right.

将小数转换为百分数的方法是小数乘以 100 并加上百分号。这相当于把小数点向右移动两位。

decimal → percentage: × 100%

For example, 0.35 becomes 35%, and 0.075 becomes 7.5%.

例如，0.35 变成 35%，0.075 变成 7.5%。

If the decimal is greater than 1, the percentage is greater than 100%. For instance, 1.25 = 125%. This is useful for increase problems.

如果小数大于 1，百分数就大于 100%。例如，1.25 = 125%。这在增长问题中很有用。

A common mistake is to write 0.5 as 0.50% instead of 50%. Remember that 0.5 is half of one, and half of 100 is 50.

一个常见错误是把 0.5 写成 0.50% 而不是 50%。请记住，0.5 是一的一半，而 100 的一半是 50。

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5. Converting Percentages to Fractions | 百分数转分数

To convert a percentage to a fraction, write the percentage over 100 and then simplify if possible.

将百分数转换为分数的方法是先把百分数写成以 100 为分母的分数，然后在可能的情况下进行化简。

percentage → fraction: percentage ÷ 100, then simplify

For example, 25% = 25/100 = 1/4, and 62.5% = 62.5/100 = 625/1000 = 5/8.

例如，25% = 25/100 = 1/4；62.5% = 62.5/100 = 625/1000 = 5/8。

If the percentage is a mixed number such as 33⅓%, write it as an improper fraction first: 33⅓% = (100/3)/100 = 100/300 = 1/3.

如果百分数是带分数，例如 33⅓%，先写成假分数：33⅓% = (100/3)/100 = 100/300 = 1/3。

KS3 questions often ask you to match fractions, decimals and percentages, so memorising common conversions such as 1/4 = 25% = 0.25 will save time.

KS3 题目经常要求匹配分数、小数和百分数，因此记住常见转换如 1/4 = 25% = 0.25 可以节省时间。

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6. Comparing and Ordering | 比较与排序

To compare fractions, decimals and percentages, convert all values into the same form. Decimals are usually the easiest for ordering.

要比较分数、小数和百分数，先将所有数值转换成同一种形式。小数通常最容易排序。

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