表达式与运算

考什么 · What it tests

需要先会 · Prerequisites

• 四则运算与运算顺序（先乘除后加减、括号优先） / Four operations and order of operations (multiply/divide before add/subtract, brackets first)
• 分数与小数互化 / Converting between fractions and decimals
• 乘方与开方的定义 / The definition of powers and roots

常见套路 · Common moves

1. 先看结构再动笔：别从左往右硬算，先找能约分、能配对、能提公因式的地方，往往整串塌缩成一个数——最通用的一招。

   Look at the structure before writing: don't grind left to right — first spot what cancels, pairs up, or shares a common factor, and the whole thing often collapses to a single number — the most general move.
2. 负号和括号一起管：去括号时若括号前是负号，里面每一项都要变号，这是最容易漏的一步。

   Handle signs and brackets together: when a minus sign sits before a bracket, every term inside flips sign — the step most often missed.
3. 指数别背混：$a^m \cdot a^n = a^{m+n}$（同底数相乘指数相加），$(a^m)^n = a^{mn}$；根号就是分数指数，$\sqrt{a}=a^{1/2}$。

   Keep exponent rules straight: $a^m \cdot a^n = a^{m+n}$ (same base, add exponents), $(a^m)^n = a^{mn}$; a root is a fractional exponent, $\sqrt{a}=a^{1/2}$.

易错点 · Common pitfalls

• 运算顺序错：看到 $2+3\times4$ 先算加法得 20，正确是先算乘法得 14——出题人必留 20 当陷阱选项。

  Wrong order: reading $2+3\times4$ as add-first gives 20, but multiply-first is correct and gives 14 — the writers always plant 20 as a trap choice.
• 负数平方漏括号：$-3^2 = -9$（只有 3 平方），$(-3)^2 = 9$，两者常被混为一谈。

  Missing brackets on a squared negative: $-3^2 = -9$ (only the 3 is squared) versus $(-3)^2 = 9$ — the two get confused constantly.