⚖️ 正反比例：同涨同落还是一涨一落⚖️ Direct & Inverse Proportion: together or opposite?
分糖时你多我就少——那是一种「一涨一落」。生活里还有「一起涨」的关系。这一片把两种「一起变」的规律一次讲清：什么时候同涨同落，什么时候一涨一落。When sharing candies, the more you get the less I get — one up, one down. But other quantities rise together. This leaf sorts out both patterns: when things move together, and when they move oppositely.
第 1 步：正比例——一起涨，一起落Step 1: Direct proportion — rising together
先看糖果铺里最平常的买卖：买几包糖，付几份钱。Start with the shop's plainest deal: buy packs of candy, pay for them.
每包 5 元不变：买 2 包付 10 元，买 3 包付 15 元——包数翻倍，价钱跟着翻倍。两个量同涨同落，叫正比例（direct proportion）。判断诀窍：两个量的比值（价钱 ÷ 包数 = 5）始终不变。At 5 yuan a pack: 2 packs cost 10, 3 packs cost 15 — double the packs, double the price. When two quantities rise and fall together, that's direct proportion. The test: their ratio (price ÷ packs = 5) never changes.
那有没有「你涨我就落」的关系？糖果铺门口的跷跷板就是。But is there a “you rise, I fall” pattern? The seesaw outside the shop says yes.
第 2 步：反比例——你涨我就落Step 2: Inverse proportion — one up, one down
从糖果铺到糖厂 360 公里。速度 60 千米/时要开 6 小时；速度翻倍到 120 千米/时，时间减半成 3 小时。速度涨、时间落，像跷跷板一头升一头降——这叫反比例（inverse proportion）。判断诀窍：两个量的乘积（速度 × 时间 = 360）始终不变。From the candy shop to the factory it's 360 km. At 60 km/h the trip takes 6 hours; double the speed to 120 km/h and the time halves to 3. Speed up, time down — like a seesaw, one end up and one end down. That's inverse proportion. The test: the product (speed × time = 360) never changes.
只看两个数字容易迷糊，怎么一眼看出是哪一种？Two lone numbers can be confusing — how do you see the pattern at a glance?
第 3 步：一张表看穿两种比例Step 3: One table reveals it all
同一段 360 公里路程：速度 60→120 翻倍，时间 6→3 减半；速度 120→180，时间 3→2。速度列往上走，时间列往下走——一眼是反比例。表格里看方向、算乘积，规律藏不住。On the same 360 km trip: speed 60→120 doubles while time 6→3 halves; speed 120→180, time 3→2. One column climbs, the other slides down — inverse at a glance. In a table, watch the direction and compute the product; the pattern can't hide.
🎮 跷跷板与齿轮（30 秒）🎮 Seesaw & gears (30 seconds)
跷跷板和齿轮，各藏一种规律。先判断正反，再拖动滑块亲手验证。A seesaw and a pair of gears each hide one pattern. Judge first, then drag to verify.
一句话记住它：两个量同涨同落、比值不变 → 正比例；一个涨一个落、乘积不变 → 反比例。Remember it in one line: rise and fall together with a fixed ratio → direct proportion; one up, one down with a fixed product → inverse proportion.
正比例：倍数相同（买 3 包付 3 倍钱），比值不变Direct: same multiplier (3 packs, 3× the price), constant ratio反比例：你翻倍我减半（速度翻倍、时间减半），乘积不变Inverse: double one, halve the other (double speed, half time), constant product判断先看方向，再算比值或乘积；表格是最快的检验场Check direction first, then ratio or product — a table is the fastest testing ground
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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