Fractions, Decimals and Percentages for Cambridge KS3 Mathematics | 剑桥KS3数学：分数、小数与百分比

📚 Fractions, Decimals and Percentages for Cambridge KS3 Mathematics | 剑桥KS3数学：分数、小数与百分比

Fractions, decimals and percentages are three different ways of representing parts of a whole. In the Cambridge KS3 Mathematics curriculum, learners are expected to move fluently between these forms, perform calculations with them, and apply them to real-life problems such as discounts, interest, and data comparison. This revision guide breaks the topic into core skills that frequently appear in Checkpoint tests and end-of-unit assessments.

分数、小数和百分比是表示整体的一部分的三种不同方式。在剑桥 KS3 数学课程中，学生需要在这三种形式之间灵活转换，运用它们进行计算，并将其应用于折扣、利率和数据比较等现实问题。本复习指南将该主题分解为 Checkpoint 考试和单元测验中经常出现的核心技能。

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 tells you how many equal parts the whole has been divided into, and the numerator tells you how many of those parts are being considered. For example, 3/4 means three out of four equal parts.

分数写作 a/b，其中 a 是分子，b 是分母。分母表示整体被分成多少个相等的部分，分子表示考虑其中的多少份。例如，3/4 表示四等份中的三份。

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

分数可以表示小于 1、等于 1 或大于 1 的值。真分数的分子比分母小，例如 2/5。假分数的分子大于或等于分母，例如 7/4。带分数由整数和真分数组合而成，例如 1 3/4。

2. Equivalent Fractions and Simplifying | 等值分数与化简

Equivalent fractions have the same value but different numerators and denominators. You can create equivalent fractions by multiplying or dividing both the numerator and denominator by the same non-zero whole number. For example, 1/2 = 2/4 = 3/6 = 50/100.

等值分数具有相同的值，但分子和分母不同。你可以将分子和分母同时乘以或除以同一个非零整数来得到等值分数。例如，1/2 = 2/4 = 3/6 = 50/100。

To simplify a fraction, divide the numerator and denominator by their highest common factor (HCF). For instance, 18/24 simplifies to 3/4 because the HCF of 18 and 24 is 6, and 18 ÷ 6 = 3, 24 ÷ 6 = 4. A fraction is in its simplest form when the numerator and denominator have no common factor other than 1.

化简分数时，用分子和分母的最大公因数（HCF）同时去除。例如，18/24 化简为 3/4，因为 18 和 24 的最大公因数是 6，且 18 ÷ 6 = 3，24 ÷ 6 = 4。当分子和分母除 1 以外没有其他公因数时，分数就是最简形式。

3. Mixed Numbers and Improper Fractions | 带分数与假分数

To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient becomes the whole number, the remainder becomes the numerator, and the denominator stays the same. For example, 17/5 = 3 2/5 because 17 ÷ 5 = 3 remainder 2.

将假分数转换为带分数时，用分子除以分母。商作为整数部分，余数作为分子，分母保持不变。例如，17/5 = 3 2/5，因为 17 ÷ 5 = 3 余 2。

To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and place the result over the original denominator. For example, 2 3/8 = (2 × 8 + 3)/8 = 19/8.

将带分数转换为假分数时，用整数部分乘以分母，再加上分子，将结果放在原分母之上。例如，2 3/8 = (

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