当前位置:首页>学习笔记>陪娃学奥数|《奥数精讲与测试》学习笔记②:糖水法比较大小 口算奥数题

陪娃学奥数|《奥数精讲与测试》学习笔记②:糖水法比较大小 口算奥数题

  • 2026-03-24 17:50:36
陪娃学奥数|《奥数精讲与测试》学习笔记②:糖水法比较大小 口算奥数题
此篇是奥数精讲与测试》(2007年版 熊斌教授主编)学习笔记的第1篇。(具体版本应该是属于比较老的版本,但是不失经典。现在版本已经进行了几轮更新,好像最新版本是第3版了。如涉及侵权请联系我删除)
分数的大小比较

比较两个分数的大小, 有两种基本方法. 第一种是: 如果两个分数分母相同, 分子大的分数较大; 第二种是: 如果两个分数分子相同, 分母小的分数较大; 或者统一分母, 或者统一分子, 再进行比较.(比较分子或分母)

有时候可另辟蹊径, 例如相减比较, 如果差大, 那么减数就小; 相除比较, 若商是真分数, 则被除数小于除数, 若商是假分数, 则被除数大于除数; 交叉相乘比较,分数 (a)/(b) 和 (c)/(d)(b,d都大于0) ,如果 ad>bc ,那么 (a)/(b)>(c)/(d) ; 倒数比较,倒数大的分数小于倒数小的分数; 化为小数或循环小数比较, 等等.(作差作差倒数叉乘等)

在解题中必须认真分析, 要学会多角度、多侧面思考问题, 灵活动用解题方法, 不断开拓解题思路, 提高解题能力.

(以上摘自《奥数精讲与测试》一书,除手写解法和部分思路分析外,后面题目和解答也均选自本书)
🧮 典型例题:(同分子
🧮 典型例题:较难,初高中可尝试
B组习题精选
🧮 典型练习(这一题我先用字母表示数,再使用交叉相乘得到结果)
🧮 典型练习(这一题我使用的“糖水法”比较大小)
我们可以认为这里有2份糖水,A糖水:222g(含糖11g),B糖水:2222g(含糖111g),他们的浓度不一样。
混合后糖水浓度应介于二者之间,因此(11+111)/(222+2222)是中间数;
10倍的A糖水为C糖水:2220g(含糖110g),这份糖水加入2g浓度为50%的糖水即可变成B糖水;
由于混合后糖水浓度介于混合前2种糖水之间,
因此易得结果为:
🧮 典型练习:(初中生必会的基础题)
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  1. CONNECT:[ UseTime:0.000681s ] mysql:host=127.0.0.1;port=3306;dbname=no_67808;charset=utf8mb4
  2. SHOW FULL COLUMNS FROM `fenlei` [ RunTime:0.000873s ]
  3. SELECT * FROM `fenlei` WHERE `fid` = 0 [ RunTime:0.000269s ]
  4. SELECT * FROM `fenlei` WHERE `fid` = 63 [ RunTime:0.000390s ]
  5. SHOW FULL COLUMNS FROM `set` [ RunTime:0.000527s ]
  6. SELECT * FROM `set` [ RunTime:0.002516s ]
  7. SHOW FULL COLUMNS FROM `article` [ RunTime:0.000546s ]
  8. SELECT * FROM `article` WHERE `id` = 477204 LIMIT 1 [ RunTime:0.000432s ]
  9. UPDATE `article` SET `lasttime` = 1774398814 WHERE `id` = 477204 [ RunTime:0.007772s ]
  10. SELECT * FROM `fenlei` WHERE `id` = 65 LIMIT 1 [ RunTime:0.000841s ]
  11. SELECT * FROM `article` WHERE `id` < 477204 ORDER BY `id` DESC LIMIT 1 [ RunTime:0.004725s ]
  12. SELECT * FROM `article` WHERE `id` > 477204 ORDER BY `id` ASC LIMIT 1 [ RunTime:0.000401s ]
  13. SELECT * FROM `article` WHERE `id` < 477204 ORDER BY `id` DESC LIMIT 10 [ RunTime:0.002217s ]
  14. SELECT * FROM `article` WHERE `id` < 477204 ORDER BY `id` DESC LIMIT 10,10 [ RunTime:0.000864s ]
  15. SELECT * FROM `article` WHERE `id` < 477204 ORDER BY `id` DESC LIMIT 20,10 [ RunTime:0.003524s ]
0.202367s