Cambridge KS3 Maths: Fractions, Decimals and Percentages | 剑桥 KS3 数学：分数、小数和百分比

📚 Cambridge KS3 Maths: Fractions, Decimals and Percentages | 剑桥 KS3 数学：分数、小数和百分比

Working confidently with fractions, decimals and percentages is a core skill in the Cambridge KS3 Mathematics curriculum. This topic often appears on pages such as 123 of the learner's book, where you are asked to convert, compare and calculate with all three forms. This revision guide explains the key ideas step by step and gives you clear examples.

在剑桥 KS3 数学课程中，熟练处理分数、小数和百分比是一项核心技能。这类内容经常出现在教材第 123 页等位置，要求同学们在三种形式之间进行转换、比较和计算。本复习指南将逐步讲解关键概念，并给出清晰的示例。

1. Understanding Fractions | 理解分数

A fraction is written as a numerator over a denominator, for example 3/4. The denominator tells you how many equal parts make one whole, and the numerator tells you how many of those parts are being considered.

分数写作分子在上、分母在下的形式，例如 3/4。分母表示一个整体被平均分成多少份，分子表示我们选取了多少份。

A proper fraction has a numerator smaller than its denominator, such as 2/5. An improper fraction has a numerator equal to or greater than its denominator, such as 7/4, and a mixed number combines a whole number with a proper fraction, such as 1 3/4.

真分数的分子小于分母，例如 2/5。假分数的分子大于或等于分母，例如 7/4。带分数由一个整数和一个真分数组成，例如 1 3/4。

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

Equivalent fractions represent the same quantity even though they look different. 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，尽管形式不同。将分子和分母同时乘以或除以同一个非零数，就可以得到等值分数。

To write a fraction in its simplest form, divide the numerator and denominator by their highest common factor (HCF). For example, 12/16 becomes 3/4 because the HCF of 12 and 16 is 4.

要把分数化为最简形式，用分子和分母的最大公因数 (HCF) 同时去除它们。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 Between Improper Fractions and Mixed Numbers | 假分数与带分数互转

the result over the original denominator. For example, 2 3/5 becomes (2 × 5 + 3)/5 = 13/5.

将带分数化为假分数时，用整数乘以分母，加上分子，再把结果放在原分母上。例如，2 3/5 变为 (2 × 5 + 3)/5 = 13/5。

To change an improper fraction to a mixed number, divide the numerator by the denominator. The quotient is the whole number part, the remainder is the new numerator, and the denominator stays the same.

将假分数化为带分数时，用分子除以分母。商是整数部分，余数是新的分子，分母保持不变。

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4. Understanding Decimals | 理解小数

Decimals are another way of writing fractions whose denominators are powers of 10. The first decimal place is tenths, the second is hundredths, and the third is thousandths.

小数是分母为 10 的幂的分数的另一种写法。小数点后第一位是十分位，第二位是百分位，第三位是千分位。

For example, 0.3 means 3/10, 0.25 means 25/100, and 0.375 means 375/1000. This place-value link makes converting between decimals and fractions easier.

例如，0.3 表示 3/10，0.25 表示 25/100，0.375 表示 375/1000。这种位值联系使小数与分数的转换更加容易。

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5. Converting Fractions to Decimals | 分数转小数

rator by the denominator. You can use short division or a calculator: 3/8 = 3 ÷ 8 = 0.375.

要将分数转换为小数，用分子除以分母。可以使用短除法或计算器：3/8 = 3 ÷ 8 = 0.375。

repeats forever. A recurring decimal can be written with a dot above the repeating digit.

有些分数会得到有限小数，例如 1/4 = 0.25。另一些则得到循环小数，例如 1/3 = 0.333...，其中 3 无限重复。循环小数可以在重复数字上方加点表示。

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6. Converting Decimals to Fractions | 小数转分数

To convert a terminating decimal to a fraction, write the decimal as a fraction with denominator 10, 100, 1000 and so on, depending on the number of decimal places. Then simplify if possible.

将有限小数转换为分数时，根据小数位数，将小数写成分母为 10、100、1000 等的分数，然后尽可能化简。

braic method: let x = 0.444..., then 10x = 4.444..., subtracting gives 9x = 4, so x = 4/9.

例如，0.45 = 45/100 = 9/20。对于 0.444... 这样的循环小数，转换时使用一种特殊的代数方法：设 x = 0.444...，则 10x = 4.444...，相减得 9x = 4，所以 x = 4/9。

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7. Understanding Percentages | 理解百分比

A percentage is a fraction with denominator 100. The symbol % means 'out of 100', so 35% = 35/100 = 0.35.

百分比是分母为 100 的分数。百分号 % 表示 "每一百"，因此 35% = 35/100 = 0.35。

s to a common scale of 100. For example, a test score of 17 out of 20 is 17/20 = 0.85 = 85%.

百分比便于比较数量，因为它把不同的总量都换算成以 100 为统一标准。例如，20 分中获得 17 分就是 17/20 = 0.85 = 85%。

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8. Converting Between Fractions, Decimals and Percentages | 分数、小数和百分比互转

To convert a percentage to a decimal, divide by 100. To convert a decimal to a percentage, multiply by 100. To convert a percentage to a fraction, write it over 100 and simplify.

将百分比化为小数，除以 100；将小数化为百分比，乘以 100；将百分比化为分数，写成百分号下的数除以 100 再化简。

The table below shows common conversions that are worth memorising for Cambridge KS3 assessments.

下表列出了一些值得在剑桥 KS3

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