Fractions, Decimals and Percentages | 分数、小数与百分数

📚 Fractions, Decimals and Percentages | 分数、小数与百分数

This revision guide covers fractions, decimals and percentages for the Cambridge KS3 Mathematics syllabus. You will learn how to convert between the three forms, carry out calculations and apply the ideas to exam-style questions.

本复习指南涵盖剑桥 KS3 数学课程中的分数、小数和百分数。你将学习这三者之间的互化、进行相关计算，并将这些知识应用到考试题型中。

1. Understanding Fractions | 理解分数

A fraction shows a part of a whole. The numerator is the top number and the denominator is the bottom number. In 3/4, 3 is the numerator and 4 is the denominator.

分数表示整体的一部分。分子是上面的数，分母是下面的数。在 3/4 中，3 是分子，4 是分母。

A proper fraction has a numerator smaller than its denominator, for example 2/5.

真分数的分子小于分母，例如 2/5。

An improper fraction has a numerator equal to or larger than its denominator, for example 7/4.

假分数的分子大于或等于分母，例如 7/4。

A mixed number combines a whole number with a proper fraction, for example 1 3/4.

带分数由一个整数和一个真分数组成，例如 1 3/4。

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

Equivalent fractions have the same value even though they look different. You can multiply or divide the numerator and denominator by the same non-zero number.

等值分数尽管形式不同，但数值相同。你可以将分子和分母同时乘以或除以同一个非零数。

1/2 = 2/4 = 3/6 = 6/12

To simplify a fraction, divide both the numerator and denominator by their highest common factor (HCF).

化简分数时，用分子和分母的最大公因数 (HCF) 同时除它们。

12/18 = (12 ÷ 6)/(18 ÷ 6) = 2/3

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

To change a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, then place the result over the original denominator.

将带分数化为假分数：整数乘以分母，加上分子，然后将结果写在原分母上。

2 3/5 = (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, the remainder is the new numerator, and the denominator stays the same.

将假分数化为带分数：用分子除以分母。商为整数部分，余数为新的分子，分母不变。

13/5 = 2 3/5 because 13 ÷ 5 = 2 remainder 3

4. Adding and Subtracting Fractions | 分数的加法与减法

Before adding or subtracting fractions, make sure the denominators are the same. Replace each fraction

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