{"id":2628,"date":"2017-04-28T10:19:11","date_gmt":"2017-04-28T02:19:11","guid":{"rendered":"http:\/\/www.systemsci.org\/jinshanw\/?p=2628"},"modified":"2017-07-05T19:20:21","modified_gmt":"2017-07-05T11:20:21","slug":"%e5%88%86%e6%95%b0%e9%99%a4%e6%b3%95%e7%9a%84%e6%95%99%e5%ad%a6","status":"publish","type":"post","link":"https:\/\/www.systemsci.org\/jinshanw\/2017\/04\/28\/%e5%88%86%e6%95%b0%e9%99%a4%e6%b3%95%e7%9a%84%e6%95%99%e5%ad%a6\/","title":{"rendered":"\u5206\u6570\u9664\u6cd5\u7684\u6559\u5b66"},"content":{"rendered":"<p>\u5206\u6570\u9664\u6cd5\u7684\u8ba1\u7b97\u6b65\u9aa4\u662f\u6bd4\u8f83\u5bb9\u6613\u5b66\u4f1a\u7684\uff0c\u4f8b\u5982<br \/>\n\\begin{align}<br \/>\n\\frac{3}{4} \\div \\frac{3}{8} = \\frac{3}{4} \\times \\frac{8}{3} = \\frac{3\\times 8}{4\\times 3} = 2 ,<br \/>\n\\end{align}<br \/>\n\u4e5f\u5c31\u662f\u628a\u540e\u9762\u7684\u5f53\u505a\u9664\u6570\u7684\u5206\u6570\u5206\u5b50\u5206\u6bcd\u5012\u8fc7\u6765\uff0c\u7136\u540e\u6309\u7167\u4e58\u6cd5\u8ba1\u7b97\uff0c\u8ba1\u7b97\u7684\u8fc7\u7a0b\u4e2d\u9700\u8981\u6ce8\u610f\u5206\u5b50\u5206\u6bcd\u6d88\u6389\u76f8\u540c\u7684\u56e0\u5b50\uff08\u5206\u5b50\u5206\u6bcd\u540c\u9664\u4ee5\u67d0\u4e2a\u6570\uff09\u7684\u6280\u5de7\u3002<\/p>\n<p>\u4f46\u662f\uff0c\u8fd9\u6837\u7684\u6559\u5b66\uff0c\u5bf9\u4e8e\u4e3a\u4ec0\u4e48\u5206\u6570\u76f8\u9664\u8981\u8fd9\u6837\u8ba1\u7b97\u662f\u4e0d\u660e\u767d\u7684\u3002\u5f53\u7136\uff0c\u6559\u6750\u4e5f\u6ce8\u610f\u5230\u4e86\u8fd9\u4e2a\u95ee\u9898\u3002\u56e0\u6b64\uff0c\u5927\u591a\u6570\u6559\u6750\u662f\u4ece\u4e24\u4e2a\u65b9\u9762\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u7684\uff1a\u5206\u6570\u9664\u6cd5\u7684\u610f\u4e49\u548c\u95ee\u9898\u80cc\u666f\uff0c\u5206\u6570\u9664\u6cd5\u7684\u8ba1\u7b97\u3002\u8fd9\u4e2a\u601d\u8def\u6ca1\u6709\u4e1d\u6beb\u95ee\u9898\uff0c\u6211\u4eec\u4e5f\u4ece\u8fd9\u8fde\u4e2a\u65b9\u9762\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u3002<\/p>\n<ol>\n<li>\u6211\u4eec\u5148\u6765\u770b\u8ba1\u7b97\u7684\u95ee\u9898\u3002\u6211\u5199\u4e0b\u6765\u6bcf\u4e00\u4e2a\u6b65\u9aa4\u548c\u8fd9\u4e2a\u6b65\u9aa4\u7684\u7406\u7531\uff0c<br \/>\n\\begin{align}<br \/>\n\\frac{3}{4} \\div \\frac{3}{8}<br \/>\n= (3\\div 4) \\div (3\\div 8) \uff08\u5206\u6570\u7ebf\u53ef\u4ee5\u770b\u505a\u9664\u6cd5\uff0c\u5206\u6570\u7684\u610f\u4e49\uff09 \\\\<br \/>\n= (3\\div 4) \\div 3 \\times 8 \uff08\u9664\u6cd5\u53bb\u62ec\u53f7\uff09\\\\<br \/>\n=  3\\div 4 \\div 3 \\times 8 \uff08\u518d\u53bb\u62ec\u53f7\uff0c\u7ed3\u5408\u5f8b\uff09 \\\\<br \/>\n= 3 \\div 3 \\times 8 \\div 4\uff08\u4e58\u9664\u6cd5\u4ea4\u6362\u5f8b\uff0c\u5148\u9664\u6389\u5bb9\u6613\u9664\u7684\uff09\\\\<br \/>\n= 1 \\times 8 \\div 4  \uff08\u8ba1\u7b97\u9664\u6cd5\u7684\u7ed3\u679c\uff09\\\\<br \/>\n= 1  \\times 2 \uff08\u4e58\u9664\u6cd5\u7ed3\u5408\u5f8b\uff09 \\\\<br \/>\n= 2 \uff08\u8ba1\u7b97\u4e58\u6cd5\u7684\u7ed3\u679c\uff09<br \/>\n\\end{align}<br \/>\n\u6216\u8005\u66f4\u4e00\u822c\u5730\uff0c<br \/>\n\\begin{align}<br \/>\n\\frac{3}{4} \\div \\frac{3}{8}<br \/>\n= (3\\div 4) \\div (3\\div 8) \uff08\u5206\u6570\u7ebf\u53ef\u4ee5\u770b\u505a\u9664\u6cd5\uff0c\u5206\u6570\u7684\u610f\u4e49\uff09\\\\<br \/>\n= (3\\div 4) \\div 3 \\times 8 \uff08\u9664\u6cd5\u53bb\u62ec\u53f7\uff09\\\\<br \/>\n= 3\\div 4 \\div 3 \\times 8 \uff08\u518d\u53bb\u62ec\u53f7\uff09\\\\<br \/>\n= 3 \\div 4 \\times 8 \\div 3\uff08\u4e58\u9664\u6cd5\u4ea4\u6362\u5f8b\uff0c\u5148\u9664\u6389\u5bb9\u6613\u9664\u7684\uff09\\\\<br \/>\n= (3\\div 4) \\times (8 \\div 3) \uff08\u4e58\u6cd5\u52a0\u62ec\u53f7\uff0c\u7ed3\u5408\u5f8b\uff09\\\\<br \/>\n=\\frac{3}{4}\\times \\frac{8}{3}\uff08\u9664\u6cd5\u53ef\u4ee5\u770b\u505a\u5206\u6570\u7ebf\uff0c\u5206\u6570\u7684\u610f\u4e49\uff09\\\\<br \/>\n= \\frac{3\\times 8}{4\\times 3}\uff08\u5206\u6570\u4e58\u6cd5\u8ba1\u7b97\uff09\\\\<br \/>\n= 2\uff08\u540c\u9664\u4ee5\u67d0\u4e2a\u6570\uff09\\\\<br \/>\n\\end{align}<br \/>\n\u53ef\u4ee5\u770b\u5230\uff0c\u8fd9\u6837\u7684\u8ba1\u7b97\u7684\u9053\u7406\u8981\u60f3\u5f97\u660e\u767d\u7684\u8bdd\uff0c\u9700\u8981\u5b66\u751f\u4e4b\u524d\u5c31\u660e\u767d\u201c\u5206\u6570\u7ebf\u53ef\u4ee5\u770b\u505a\u9664\u6cd5\u201d\u3001\u201c\u6574\u6570\u4e58\u9664\u6cd5\u7684\u7ed3\u5408\u5f8b\u201d\u3001\u201c\u6574\u6570\u4e58\u9664\u6cd5\u7684\u4ea4\u6362\u5f8b\u201d\u3001\u201c\u6574\u6570\u4e58\u9664\u6cd5\u7684\u9000\u62ec\u53f7\u201d\u3002\u5176\u4e2d\uff0c<strong>\u201c\u5206\u6570\u7ebf\u53ef\u4ee5\u770b\u505a\u9664\u6cd5\u201d\u548c\u201c\u9664\u6cd5\u53bb\u62ec\u53f7\u201d<\/strong>\u6700\u6700\u91cd\u8981\uff0c\u5e76\u4e14\u201c\u9664\u6cd5\u53bb\u62ec\u53f7\u201d\u53ef\u80fd\u9700\u8981\u590d\u4e60\u6216\u8005\u989d\u5916\u8865\u5145\u4e00\u4e0b\u3002\u4e0d\u8fc7\uff0c\u539f\u5219\u4e0a\uff0c\u8fd9\u4e2a\u5e94\u8be5\u662f\u5728\u5b66\u4e60\u6574\u6570\u9664\u6cd5\u7684\u65f6\u5019\u5c31\u5df2\u7ecf\u901a\u8fc7\u7406\u89e3\u578b\u5b66\u4e60\u89e3\u51b3\u7684\u4e8b\u60c5\u3002<\/p>\n<p>\u5728\u8fd9\u91cc\uff0c\u6211\u60f3\u5f3a\u8c03\u7684\u4e8b\u60c5\u662f\u201c\u6bcf\u4e00\u4e2a\u601d\u8003\u7684\u6b65\u9aa4\uff0c\u90fd\u9700\u8981\u7ed9\u51fa\u6765\u660e\u786e\u7684\u7406\u7531\u201d\u3002\u5b66\u6570\u5b66\uff0c\u8981\u5b66\u4f1a\u8fd9\u4e2a\u3002\u5f53\u7136\uff0c\u8fd9\u4ec5\u4ec5\u662f\u5f62\u5f0f\u4e0a\u5b66\u4f1a\u5982\u4f55\u8ba1\u7b97\uff0c\u5c3d\u7ba1\u5df2\u7ecf\u6bd4\u524d\u9762\u6559\u7eaf\u7cb9\u8ba1\u7b97\u65b9\u5f0f\u7684\u8981\u597d\uff0c\u4f46\u662f\u8fd8\u662f\u4e0d\u591f\u7684\u3002<\/p>\n<li>\u6211\u4eec\u5728\u6765\u770b\uff0c\u5206\u6570\u9664\u6cd5\u7684\u610f\u4e49\u600e\u4e48\u6559\u3002\n<ol>\n<li>\u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u6784\u9020\u4e00\u4e2a\u610f\u4e49\u573a\u666f\uff0c\u800c\u4e14\u548c\u4e4b\u524d\u5df2\u7ecf\u5b66\u4e60\u8fc7\u7684\u4e1c\u897f\u6bd4\u8f83\u63a5\u8fd1\u7684\u610f\u4e49\u573a\u666f\u3002\u4f8b\u5982\uff0c\u6211\u4eec\u8003\u8651\u5148\u4ece\u4e00\u4e2a\u5207\u6210\\(4\\)\u5757\u53d6\u8d70\u5176\u4e2d\\(1\\)\u5757\uff0c\u5269\u4e0b\u7684\u86cb\u7cd5\u5982\u679c\u518d\u6709\\(3\\)\u4e2a\u4eba\u5e73\u5747\u5206\u4f1a\u5f97\u5230\u591a\u5c11\u86cb\u7cd5\uff0c\u8fd9\u6837\u7684\u95ee\u9898\u3002\u4ece\u90a3\u91cc\u9762\uff0c\u6211\u4eec\u53ef\u4ee5\u590d\u4e60\u4e00\u4e0b\u5206\u6570\u9664\u4ee5\u6574\u6570\uff0c\\(\\left(1-\\frac{1}{4}\\right)\\div 3 = \\frac{3}{4}\\div 3 = \\frac{1}{4}\\)\u3002\n<li>\u63a5\u7740\uff0c\u6211\u4eec\u53ef\u4ee5\u518d\u94fa\u57ab\u4e00\u4e2a\u7c7b\u4f3c\u4e8e\u5206\u6570\u9664\u4ee5\u4ec0\u4e48\u4ec0\u4e48\u5206\u4e4b\u4e00\u7684\u4f8b\u5b50\u3002\u4f8b\u5982\uff0c\u6211\u4eec\u8003\u8651\u5148\u4ece\u4e00\u4e2a\u5207\u6210\\(4\\)\u5757\u53d6\u8d70\u5176\u4e2d\\(1\\)\u5757\uff0c\u5269\u4e0b\u7684\u86cb\u7cd5\u7ed9\u5b69\u5b50\u4eec\u5403\uff0c\u53ef\u4ee5\u5582\u9971\u51e0\u4e2a\u5c0f\u5b69\uff1f\u5982\u679c\u6211\u4eec\u5047\u8bbe8\u4e2a\u5b69\u5b50\u5403\u4e00\u4e2a\u86cb\u7cd5\u5c31\u53ef\u4ee5\u5403\u9971\u7684\u8bdd\u3002\u4e8e\u662f\uff0c\u4ece\u5047\u8bbe\u6211\u4eec\u5148\u77e5\u9053\uff0c\u6bcf\u4e2a\u5c0f\u5b69\u7684\u809a\u5b50\u80fd\u591f\u88c5\u8fd9\u4e48\u591a\u86cb\u7cd5<br \/>\n\\begin{align}<br \/>\n1 \\div 8 =\\frac{1}{8}.<br \/>\n\\end{align}<br \/>\n\u76ee\u524d\u5269\u4e0b\u7684\u86cb\u7cd5\u5462\uff0c\u6709<br \/>\n\\begin{align}<br \/>\n1-\\frac{1}{4} = \\frac{3}{4}<br \/>\n\\end{align}<br \/>\n\u5757\u3002<br \/>\n\u90a3\u4e48\u5206\u5462\uff1f\u5f88\u7b80\u5355\uff0c\u52a8\u624b\u5207\u4e00\u4e0b\uff0c\u5c31\u77e5\u9053\u4e86\uff0c\u53ef\u4ee5\u5206\u6210\\(6\\)\u4e2a\\(\\frac{1}{8}\\)\u7684\u5927\u5c0f\uff0c\u4e5f\u5c31\u662f\u7ed9\\(6\\)\u4e2a\u5b69\u5b50\u5403\u9971\u3002\u4ece\u9664\u6cd5\u7684\u610f\u4e49\u4e5f\u77e5\u9053\u4e86\uff0c\u8fd9\u4e2a\\(6\\)\u76f8\u5f53\u4e8e\u662f\u4e0b\u9762\u7684\u9664\u6cd5\u7684\u7b54\u6848\uff08\u4e00\u4e2a\u603b\u91cf\u7ed9\u6bcf\u4e00\u4e2a\u4eba\u5206\uff0c\u5df2\u77e5\u6bcf\u4e00\u4e2a\u4eba\u9700\u8981\u591a\u5c11\uff0c\u80fd\u591f\u5206\u51e0\u4e2a\u4eba\u7684\u95ee\u9898\uff0c\u662f\u9664\u6cd5\u3002\u81f3\u4e8e\u8fd9\u4e2a\u4e3a\u4ec0\u4e48\uff0c\u5b66\u4e60\u9664\u6cd5\u7684\u65f6\u5019\u5e94\u8be5\u5df2\u7ecf\u89e3\u51b3\u4e86\u7684\uff1a\u9664\u6cd5\u6765\u81ea\u4e8e\u51cf\u6cd5\u7684\u7b80\u4fbf\u8fd0\u7b97\uff0c\u5c31\u597d\u50cf\u4e58\u6cd5\u662f\u52a0\u6cd5\u7684\u7b80\u4fbf\u8fd0\u7b97\u3002\uff09\uff0c<br \/>\n\\begin{align}<br \/>\n6= \\frac{3}{4} \\div \\left(\\frac{1}{8}\\right).<br \/>\n\\end{align}<\/p>\n<li>\u8fd9\u4e2a\u65f6\u5019\uff0c\u770b\u5177\u4f53\u60c5\u51b5\uff0c\u53ef\u4ee5\u628a\u8ba1\u7b97\u8fc7\u7a0b\u548c\u610f\u4e49\u5148\u5c1d\u8bd5\u8054\u7cfb\u4e00\u4e0b\uff0c\u4e5f\u5c31\u662f\uff0c\u5982\u679c\u7528\u524d\u9762\u5b66\u5230\u7684\u8ba1\u7b97\u8fc7\u7a0b\uff0c\u6765\u9a8c\u8bc1\u4e00\u4e0b\u7684\u8bdd\uff0c\u8fd9\u4e2a\u6765\u81ea\u4e8e\u201c\u52a8\u624b\u5207\u5206\u201d\u7684\u7b49\u5f0f\u5bf9\u4e0d\u5bf9\u3002\n<li>\u8fd9\u4e2a\u65f6\u5019\uff0c\u518d\u628a\u573a\u666f\u8fdb\u4e00\u6b65\u53d8\u5f97\u590d\u6742\u4e00\u70b9\uff0c\u5047\u8bbe\u5b69\u5b50\u4eec\u6210\u4e86\u201c\u9ad8\u4e2d\u7684\u5927\u809a\u738b\u201d\uff0c\u6bcf\u4e2a\u4eba\u9700\u8981\u5403\u4e09\u7247\u90a3\u6837\u7684\u5c0f\u7247\u86cb\u7cd5\u624d\u80fd\u9971\uff0c\u95ee\u8fd9\u4e2a\u65f6\u5019\u53ef\u4ee5\u5582\u9971\u51e0\u4e2a\u4eba\uff1f\u4e8e\u662f\uff0c\u63d0\u793a\u4e00\u4e0b\u5b66\u751f\u4eec\uff0c\u5c31\u6709\u53ef\u80fd\u53ef\u4ee5\u6ce8\u610f\u5230\uff0c\u662f\u628a\u73b0\u5728\u7684\u4e09\u4e2a\u5b69\u5b50\u5f53\u505a\u4e00\u4e2a\u3002\u90a3\u4e48\uff0c\u5c31\u6709\u4e86\u5982\u4e0b\u7684\u8ba1\u7b97<br \/>\n\\begin{align}<br \/>\n2= 6 \\div 3.<br \/>\n\\end{align}<br \/>\n\u6ce8\u610f\uff0c\u8fd9\u91cc\u6211\u4eec\u7528\u4e86\u9664\u6cd5\u3002\u90a3\u4e48\uff0c\u6574\u4f53\u6765\u770b\uff0c\u8fd9\u4e2a\u5f97\u6570\u53ef\u4ee5\u770b\u505a\u4ec0\u4e48\u95ee\u9898\u7684\u7b54\u6848\u5462\uff1f<br \/>\n\\begin{align}<br \/>\n2= \\frac{3}{4} \\div \\left(\\frac{3}{8}\\right),<br \/>\n\\end{align}<br \/>\n\u56e0\u4e3a\u5927\u809a\u738b\u7684\u996d\u91cf\u662f\\(\\frac{3}{8}\\)\u3002<\/p>\n<li>\u603b\u7ed3\uff0c\u6211\u4eec\u770b\u5230\u4e86\u5173\u952e\u7684\u51e0\u6b65\uff1a\u7b2c\u4e00\uff0c\u5f53\u5206\u6570\u9664\u4ee5\u6574\u6570\u7684\u65f6\u5019\uff0c\u5c31\u628a\u6574\u6570\u653e\u5728\u6700\u540e\u7684\u5206\u6bcd\u4e0a\u5c31\u53ef\u4ee5\uff1b\u7b2c\u4e8c\uff0c\u5f53\u5206\u6570\u9664\u4ee5\u5206\u6570\uff0c\u4f46\u662f\u90a3\u4e2a\u5206\u6570\u662f\u4ec0\u4e48\u4ec0\u4e48\u5206\u4e4b\u4e00\u7684\u4e4b\u540e\uff0c\u76f8\u5f53\u4e8e\u628a\u90a3\u4e2a\u4ec0\u4e48\u4ec0\u4e48\u4e58\u5728\u5206\u5b50\u4e0a\uff1b\u7b2c\u4e09\uff0c\u5f53\u5206\u6570\u9664\u4ee5\u4e00\u822c\u7684\u5206\u6570\u7684\u65f6\u5019\uff0c\u76f8\u5f53\u4e8e\u5728\u8ba1\u7b97\u5b8c\u4e86\u524d\u4e00\u6b65\u4ec0\u4e48\u4ec0\u4e48\u5206\u4e4b\u4e00\u4e4b\u540e\uff0c\u518d\u6765\u8ba1\u7b97\u4e00\u4e2a\u9664\u6cd5\u3002\u5728\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u90fd\u662f\u7528\u601d\u8003\u6216\u8005\u52a8\u624b\u5207\u5206\u6765\u5f97\u5230\u7b54\u6848\u7684\uff0c\u800c\u4e0d\u662f\u524d\u9762\u6559\u8fc7\u7684\u8ba1\u7b97\u8fc7\u7a0b\u3002\n    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