📚 Adding and Subtracting Fractions | 分数的加法与减法
Understanding how to add and subtract fractions is a core number skill in the Cambridge Lower Secondary (KS3) Mathematics curriculum. This article explains equivalent fractions, common denominators, mixed numbers and the key steps needed to solve problems accurately.
掌握分数的加法与减法是剑桥初中（KS3）数学课程中的核心数感技能。本文将讲解等值分数、公分母、带分数以及准确解题的关键步骤。
1. What Are Fractions? | 什么是分数？
A fraction represents a part of a whole or a part of a set. The numerator is the top number and shows how many equal parts are selected. The denominator is the bottom number and shows how many equal parts make one whole.
分数表示一个整体或一组物体的一部分。分子是上面的数，表示选了多少个等份；分母是下面的数，表示整体被平均分成多少个等份。
There are three main types of fraction. A proper fraction has a numerator smaller than its denominator, such as 3/5. An improper fraction has a numerator equal to or greater than its denominator, such as 7/4. A mixed number combines a whole number and a proper fraction, such as 1 2/3.
分数有三种主要类型。真分数的分子小于分母，例如 3/5；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 2/3。
In word problems, fractions often describe lengths, amounts, shares or parts of a set. Before adding or subtracting, identify the unit whole. If the wholes are not the same, the fractions cannot be combined directly.
在应用题中，分数常用来描述长度、数量、份额或集合的一部分。在加减之前，要先确认单位整体。如果整体不同，就不能直接合并分数。
2. Equivalent Fractions and Simplest Form | 等值分数与最简形式
Equivalent fractions have the same value even though they look different. You can create an equivalent fraction by multiplying or dividing the numerator and denominator by the same non-zero whole number.
等值分数虽然形式不同，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整数来得到等值分数。
a/b = (a × k)/(b × k) and a/b = (a ÷ d)/(b ÷ d)
If you multiply the numerator and denominator of 1/2 by 3, you get 3/6. If you divide the numerator and denominator of 4/8 by 4, you get 1/2. Both operations produce equivalent fractions.
将 1/2 的分子和分母同时乘以 3，得到 3/6；将 4/8 的分子和分母同时除以 4，得到 1/2。这两种操作都能产生等值分数。
To simplify a fraction, divide the numerator and denominator by their highest common factor (HCF). The result is the simplest form. A fraction is in 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）同时除。所得结果就是最简形式。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。
| Fraction | HCF | Simplest form |
|---|---|---|
| 4/8 |
Published by TutorHao | KS3 Mathematics Revision Series | aleveler.com
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