📝 代数式：用字母替未知数📝 Algebraic Expressions: Letters for Unknown Numbers
上一片里，数轴上每个数都有名字了。可生活里，有些数我们还不知道——比如“购物车里会买几支笔”。这一片请字母来帮忙，把这些“还不知道的数”带进算式。Last leaf, every number on the line got a name. But in real life some numbers are still unknown — how many pens will this shopper buy? This leaf invites letters in, to bring those unknowns into our math.
第 1 步：把生活句子翻译成式子Step 1: Translating life into expressions
收银小票上就藏着一个“还不知道”的数——数学用一个字母来替它。The receipt hides a number we don’t know yet — math replaces it with a letter.
收银小票写着“单价 3 元，买 n 个”，总价就是 3 × n。数学给它一个更短的写法：3n——数字写在字母前面，乘号可以省略。把“每人分 2 个，共 m 人”翻译过来，就是 2m。句子里的“每……”，翻译出来通常就是乘法。The receipt says “3 yuan each, n items”, so the total is 3 × n. Math writes it shorter: 3n — number first, and the × sign can be dropped. “2 each, m people” translates to 2m. In a sentence, every “each” usually turns into a multiplication.
那这个字母 n，到底装着什么？看看这只挂锁盒子。So what exactly does that letter n hold? Look at this locked box.
第 2 步：x 是“还不知道的那个数”Step 2: x is “the number we don’t know yet”
盒子里的数我们一时不知道，就先给它起个名字：x。“x 个”不等于某个具体的数，它是一个“等知道了再填”的空位——像收银员先留一栏空白，等顾客决定了买几支，再填上真数。We don’t know the number yet, so we give it a name: x. “x items” is not one fixed number — it is a slot that waits to be filled, like a cashier leaving a blank until the shopper decides.
式子真正好用，是因为把数代进去，它立刻能算。An expression earns its keep when you put numbers in and it computes.
第 3 步：3n 会算账Step 3: 3n does the bookkeeping
n 换成 4，3n 就是 12 元；n 换成 10，就是 30 元。式子像一台小机器：喂进一个 n，吐出一个总价。生活里所有“每份多少、一共多少份”，都能写成这样一台机器——字母就是数学里最好用的“待填空格”。Put in n = 4 and 3n gives 12 yuan; n = 10 gives 30. An expression is a little machine: feed it an n, it returns a total. Any “so much each, that many in all” can become such a machine — that’s why letters are math’s favorite blank to fill.
🎮 句子配式子（30 秒）🎮 Match sentences to expressions (30 seconds)
道理讲完了。左边 4 句生活话，右边 4 个代数式——一张一张配起来，4 对全中撒花。Theory done. Four everyday sentences on the left, four expressions on the right — pair them up, get all 4 and we celebrate.
一句话记住它：代数式 = 把“还不知道的数”写成字母，再把生活里的关系写成算式。Remember it in one line: an algebraic expression writes unknown numbers as letters, and life’s relationships as math.
字母代表数：x 是“等确定了再填”的空位Letters stand for numbers: x is a slot waiting for a value乘号可以省略：3 × n 写成 3nThe × sign can be dropped: 3 × n becomes 3n把数代进去就能算：n = 4 → 3n = 12Put numbers in and it computes: n = 4 → 3n = 12
内容参考 OpenStax 等公开教材，多来源核对 · AI 生成、人工审核 · 发现错误欢迎指正，帮这片叶子长得更好。Based on OpenStax and other open textbooks, cross-checked across sources · AI-generated, human-reviewed · Spotted a mistake? Tell us — help this leaf grow.
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