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02:08:14",false,true,"\u003Ch2>先看一个负号怎么毁掉整题\u003C\u002Fh2>\n\u003Cpre>\u003Ccode>某市 2025 年商品房销售面积 480 万平方米，比上年下降 12%。\n问题一：比上年减少多少万平方米？\n问题二：2024 年销售面积是多少？\u003C\u002Fcode>\u003C\u002Fpre>\n\u003Cp>\u003Cstrong>两个问题都会算，但两个都会因为同一个原因错：方向。\u003C\u002Fstrong>\u003C\u002Fp>\n\u003Cpre>\u003Ccode>问题一：减少量 = 480 ÷ 0.88 × 0.12 ≈ 65.45 万㎡\n        （❌ 常见错解：480 × 12% = 57.6 万㎡）\n问题二：2024 年 = 480 ÷ 0.88 ≈ 545.45 万㎡\n        （❌ 常见错解：480 × 1.12 = 537.6 万㎡）\u003C\u002Fcode>\u003C\u002Fpre>\n\u003Cp>\u003Cstrong>两个错解的根因是同一个\u003C\u002Fstrong>：把\"下降 12%\"当成了\"在 480 的基础上加\u002F减 12%\"。\u003C\u002Fp>\n\u003Cp>\u003Cstrong>本篇只做一件事：把符号的方向管住。\u003C\u002Fstrong>\u003C\u002Fp>\n\u003Chr>\n\u003Ch2>增长量只有一个定义\u003C\u002Fh2>\n\u003Cpre>\u003Ccode>增长量 = 现期值 − 基期值\u003C\u002Fcode>\u003C\u002Fpre>\n\u003Cp>\u003Cstrong>就这一句，没有任何变体。\u003C\u002Fstrong> 注意两件事：\u003C\u002Fp>\n\u003Col>\u003Cli>\u003Cstrong>顺序\u003C\u002Fstrong>：一定是\"\u003Cstrong>现期 − 基期\u003C\u002Fstrong>\"，不是反过来\u003C\u002Fli>\u003Cli>\u003Cstrong>符号\u003C\u002Fstrong>：结果\u003Cstrong>可以为负\u003C\u002Fstrong>\u003C\u002Fli>\u003C\u002Fol>\n\u003Cpre>\u003Ccode>现期 > 基期  ⇒  增长量为正  ⇒  增长\n现期 < 基期  ⇒  增长量为负  ⇒  减少\u003C\u002Fcode>\u003C\u002Fpre>\n\u003Cp>\u003Cstrong>为什么强调\"顺序不能反\"？\u003C\u002Fstrong>\u003C\u002Fp>\n\u003Cpre>\u003Ccode>某指标 2024 年 500，2025 年 420\n正确：增长量 = 420 − 500 = −80\n错误：增长量 = 500 − 420 = +80\u003C\u002Fcode>\u003C\u002Fpre>\n\u003Cp>\u003Cstrong>同一组数据，反着减，结论从\"减少 80\"变成\"增长 80\"。\u003C\u002Fstrong>\u003C\u002Fp>\n\u003Cp>这在选择题里可能正好对应两个都存在的选项。\u003Cstrong>顺序是硬规则。\u003C\u002Fstrong>\u003C\u002Fp>\n\u003Chr>\n\u003Ch2>必背公式表：增长量的 7 条\u003C\u002Fh2>\n\u003Ctable>\u003Cthead>\u003Ctr>\u003Cth>#\u003C\u002Fth>\u003Cth>公式\u003C\u002Fth>\u003Cth>用途\u003C\u002Fth>\u003C\u002Ftr>\u003C\u002Fthead>\u003Ctbody>\u003Ctr>\u003Ctd>①\u003C\u002Ftd>\u003Ctd>\u003Cstrong>增长量 = 现期 − 基期\u003C\u002Fstrong>\u003C\u002Ftd>\u003Ctd>定义式（唯一）\u003C\u002Ftd>\u003C\u002Ftr>\u003Ctr>\u003Ctd>②\u003C\u002Ftd>\u003Ctd>增长量 = 基期 × r\u003C\u002Ftd>\u003Ctd>给了基期和增速\u003C\u002Ftd>\u003C\u002Ftr>\u003Ctr>\u003Ctd>③\u003C\u002Ftd>\u003Ctd>增长量 = 现期 × r ÷ (1+r)\u003C\u002Ftd>\u003Ctd>给了现期和增速（最常考）\u003C\u002Ftd>\u003C\u002Ftr>\u003Ctr>\u003Ctd>④\u003C\u002Ftd>\u003Ctd>\u003Cstrong>减少量 = 基期 − 现期 = 基期 × 降幅\u003C\u002Fstrong>\u003C\u002Ftd>\u003Ctd>下降场景\u003C\u002Ftd>\u003C\u002Ftr>\u003Ctr>\u003Ctd>⑤\u003C\u002Ftd>\u003Ctd>基期 = 现期 − 增长量\u003C\u002Ftd>\u003Ctd>反求基期（最省事）\u003C\u002Ftd>\u003C\u002Ftr>\u003Ctr>\u003Ctd>⑥\u003C\u002Ftd>\u003Ctd>\u003Cstrong>年均增长量 = (末期 − 初期) ÷ 年数\u003C\u002Fstrong>\u003C\u002Ftd>\u003Ctd>多年平均\u003C\u002Ftd>\u003C\u002Ftr>\u003Ctr>\u003Ctd>⑦\u003C\u002Ftd>\u003Ctd>累计增长量 = 末期 − 初期\u003C\u002Ftd>\u003Ctd>从序列开头算\u003C\u002Ftd>\u003C\u002Ftr>\u003C\u002Ftbody>\u003C\u002Ftable>\n\u003Cp>\u003Cstrong>①②③ 与《增长量：多出来的那部分怎么算》是同一组公式\u003C\u002Fstrong> —— 这里再列一遍，是为了把它和\"减少量\"并排看。\u003C\u002Fp>\n\u003Cp>\u003Cstrong>④ 与 ① 的符号关系\u003C\u002Fstrong>（这是本篇的核心）：\u003C\u002Fp>\n\u003Cpre>\u003Ccode>增长量 = 现期 − 基期\n减少量 = 基期 − 现期 = −(增长量)\n\n⇒ 两者是同一个数的两种说法，差一个负号\u003C\u002Fcode>\u003C\u002Fpre>\n\u003Cp>\u003Cstrong>⚠️ 所以题目说\"减少了 500 万吨\"时\u003C\u002Fstrong>：\u003C\u002Fp>\n\u003Cpre>\u003Ccode>减少量 = +500（正数写法）\n增长量 = −500（负数写法）\n两种写法都对，但**不能混着用**\u003C\u002Fcode>\u003C\u002Fpre>\n\u003Cp>\u003Cstrong>⑥ 的\"年数\"\u003C\u002Fstrong>：\u003C\u002Fp>\n\u003Cpre>\u003Ccode>年数 = 末期年份 − 初期年份（不是数年份个数）\n2018—2022 共 5 个年份 ⇒ 年数 = 4\u003C\u002Fcode>\u003C\u002Fpre>\n\u003Cp>\u003Cstrong>⑦ 与 ⑥ 的区别\u003C\u002Fstrong>（差的还是那个分母）：\u003C\u002Fp>\n\u003Cpre>\u003Ccode>累计增长量 = 五年一共多了多少（总增量）\n年均增长量 = 平均每年多了多少（总增量 ÷ 年数）\u003C\u002Fcode>\u003C\u002Fpre>\n\u003Cp>\u003Cstrong>⚠️ 三个常混的问法对照\u003C\u002Fstrong>：\u003C\u002Fp>\n\u003Ctable>\u003Cthead>\u003Ctr>\u003Cth>问法\u003C\u002Fth>\u003Cth>用哪条\u003C\u002Fth>\u003Cth>例（2018 年 800 → 2022 年 1200）\u003C\u002Fth>\u003C\u002Ftr>\u003C\u002Fthead>\u003Ctbody>\u003Ctr>\u003Ctd>2022 年比 2021 年增多少\u003C\u002Ftd>\u003Ctd>①③\u003C\u002Ftd>\u003Ctd>一步的差\u003C\u002Ftd>\u003C\u002Ftr>\u003Ctr>\u003Ctd>2022 年比 2018 年增多少\u003C\u002Ftd>\u003Ctd>⑦\u003C\u002Ftd>\u003Ctd>\u003Cstrong>400\u003C\u002Fstrong>\u003C\u002Ftd>\u003C\u002Ftr>\u003Ctr>\u003Ctd>2018—2022 年年均增多少\u003C\u002Ftd>\u003Ctd>⑥\u003C\u002Ftd>\u003Ctd>\u003Cstrong>100\u003C\u002Fstrong>\u003C\u002Ftd>\u003C\u002Ftr>\u003C\u002Ftbody>\u003C\u002Ftable>\n\u003Cp>\u003Cstrong>同一组数、三个答案，差在分母上。\u003C\u002Fstrong>\u003C\u002Fp>\n\u003Chr>\n\u003Ch2>减少量不是另一种量\u003C\u002Fh2>\n\u003Cp>\u003Cstrong>\"减少量\"不是一个新公式，它就是\"负的增长量\"取绝对值。\u003C\u002Fstrong>\u003C\u002Fp>\n\u003Cpre>\u003Ccode>增长量 = 现期 − 基期 = −80\n减少量 = ","none",{"id":112,"title":113},{"id":118,"title":119},1790222661587]