Mastering Algebra Basics: Expressions, Equations and Formulae | 掌握代数基础：表达式、方程和公式

📚 Mastering Algebra Basics: Expressions, Equations and Formulae | 掌握代数基础：表达式、方程和公式

Algebra is a cornerstone of mathematics that unlocks the ability to solve a huge range of problems. In the Cambridge Lower Secondary programme, you will build skills in using letters for unknowns, simplifying expressions, solving equations and applying formulae. This article covers the essential techniques with clear examples and step-by-step explanations.

代数是数学的基石，它为你解决大量问题提供了可能。在剑桥初中课程中，你将逐步掌握用字母表示未知数、化简表达式、解方程和应用公式等技能。本文将通过清晰的示例和分步解释，涵盖这些核心技巧。

1. What is Algebra? | 什么是代数？

Algebra is the part of mathematics where we use letters or symbols to stand for numbers that we do not know yet, or numbers that can vary. This allows us to write general rules and solve puzzles involving unknown values.

代数是数学中运用字母或符号代表未知或可变数字的部分。这使得我们可以书写通用规则，并解决涉及未知数值的谜题。

For instance, if you know that after buying a £3 pen you have £7 left, you can express the original amount you had as x and write the equation x – 3 = 7.

例如，如果你知道买了3英镑的钢笔后还剩7英镑，你就可以把你原来有的金额表示为 x，并写出方程 x – 3 = 7。

Algebra also helps us to describe patterns, such as the number of matchsticks in a sequence of squares. The nth term might be 3n + 1.

代数还能帮助我们描述规律，例如一系列正方形中的火柴棍数量。第 n 项可能是 3n + 1。

2. Using Letters to Represent Numbers | 用字母表示数

Letters in algebra are called variables or unknowns. You often see statements like ‘Let p be the price of a book’ or ‘The sum of two numbers is a + b‘. Remember that 3a means 3 multiplied by a.

代数中的字母被称为变量或未知数。你经常会看到这样的表述：“设 p 为一本书的价格”或“两数之和为 a + b”。请记住，3a 表示 3 乘以 a。

When a number and a letter are placed next to each other, the multiplication sign is omitted. So 5 x y is written simply as 5y.

当数字和字母紧挨着书写时，乘号省略。因此 5 x y 就直接写成 5y。

We also use fractions in algebra, for example x/2 means x / 2, but to keep it clear you can write it as 1/2x or use the division sign.

代数中也会用到分数，例如 x/2 表示 x / 2。为了清晰，你也可以写成 1/2x 或使用除号。

3. Algebraic Terminology: Terms, Coefficients, Constants | 代数术语：项、系数、常数

An expression is made up of terms. In 4x^2 + 3x – 7, there are three terms: 4x^2, 3x and -7.

一个表达式由若干项组成。在 4x^2 + 3x – 7 中，有三项：4x^2

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