东北育才网校

{"root":{"nodeName":"document","nodeValue":null,"nodeType":"0","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"div","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"运用倒推法（还原法）解题的相应的“逆运算”是指：加法用减法还原，减法用加法还原，乘法用除法还原，除法用乘法还原，并且原来是加（减）几，还原时应为减（加）几，原来是乘（除）以几，还原时应为除（乘）以几。","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"　　对于一些比较复杂的还原问题，要学会列表，借助表格倒推，既能理清数量关系，又便于验算。","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"例1．某数加上6，乘以6，减去6，除以6，最后结果等于6，求某数。","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"　　解答：（6×6＋6）÷6－6=1","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"例2．一捆电线，第一次用去全长的一半多3米，第二次用去余下的一半少10米，第三次用去15米，最后还剩7米，这捆电线原有多少米？","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"　　解答：[（7+15－10）×2+3]=54（米）","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"例3．小明在计算一道加法计算时，把一个加数个位上的1看作7，把一个加数十位上的8看作3，这样所得的和是1955，原来两数相加的正确答案是多少？","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"　　解答：1995＋50－6=1999","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"例4．袋子里装着若干个乒乓球，小明每次拿出其中的一半再放回一个球，这样共拿了5次，袋子里还有5个球。袋中原有多少个乒乓球？","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"　　解答：","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"table","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":";text-align:center"}],"childNodes":[{"nodeName":"tbody","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"tr","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"操作次数","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"袋中球个数","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]}]},{"nodeName":"tr","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"初始","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"（50－1）×2=98","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]}]},{"nodeName":"tr","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"1","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"（26－1）×2=50","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]}]},{"nodeName":"tr","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"2","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"（14－1）×2=26","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]}]},{"nodeName":"tr","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"3","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"（8－1）×2=14","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]}]},{"nodeName":"tr","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"4","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"（5－1）×2=8","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]}]},{"nodeName":"tr","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"5","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"5","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]}]}]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"例5．甲、乙、丙三人各有小球若干个，甲先拿出自己的小球的一部分给乙和丙，使乙、丙每人的小球数增加一倍；然后乙也把自己的小球的一部分分给甲丙，使甲和丙每人的小球数增加一倍；最后丙也把自己小球的一部分分给甲和乙，使甲和乙每人的小球数增加一倍。这时甲乙丙都有48个小球。原来甲乙丙各有小球多少个？","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"解答：","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"table","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":";text-align:center"}],"childNodes":[{"nodeName":"tbody","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"tr","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"变动情况","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"甲","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"乙","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"丙","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]}]},{"nodeName":"tr","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"初始状态","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"12＋42+24=78","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"84÷2=42","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"48÷2=24","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]}]},{"nodeName":"tr","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"1","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"24÷2=12","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"24＋12＋48=84","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"96÷2=48","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]}]},{"nodeName":"tr","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"2","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"48÷2=24","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"48÷2=24","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"48＋24＋24=96","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]}]},{"nodeName":"tr","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"3","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"48","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"48","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"48","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]}]}]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"strong","nodeValue":null,"nodeType":"1","display":"inline","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"习题：","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"1.一位老人说，把我的年龄加上12，再用4除，再减去15后乘以10，恰好是100岁。这位老人现在有多少岁？","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"　　解答：（100÷10+15）×4－12=88(岁)","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"2.百货商店出售手机，上午售出总数的一半多20部，下午售出剩下的一半多15部，还剩下75部。商店原有手机多少部？","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"　　解答：[(75+15)×2+20]×2=400（部）","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"3.做一道减法算式，把减数的个位1看作3，把被减数十位上的2看作了5，这样结果等于200，差应该是多少？","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"　　解答：200+（3－1）－（50－20）=172","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"4.甲、乙、丙、丁四人共有画片80张，甲给乙13张，乙给丙18张，丙给丁16张，丁给甲2张后，四人画片张数相等。他们原来各有画片多少张？","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"　　解答：","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"blockquote","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"甲：80÷4+13－2=31（张）","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"乙：80÷4－13＋18=25（张）","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"丙：80÷4－18+16=18（张）","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"丁：80÷4－16+2=6（张）","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"5.有一篮鸡蛋，第一次取出全部的一半多2个，第二次取出余下的一半少2个，篮中还剩下12个。篮中原有鸡蛋多少个？","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"　　解答：[（12-2）×2+2]×2=44（个）","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"6.一筐梨，甲取一半又一个，乙取余下的一半又一个，丙再取余下的一半又一个，这时筐里只剩一个梨。这筐梨共值4.40元，每个梨值多少元？","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"　　解答：","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"（1+1）×2=4（个）（4+1）×2=10（个）（10+1）×2=22（个） 4.40÷22=0.20（元）","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"7．有26块砖，兄弟2人争着去挑，弟弟抢在前面，刚摆好砖，哥哥赶来了。哥哥看弟弟挑得太多，就拿来一半给自己。弟弟觉得自己能行，又从哥哥那里拿来一半。哥哥不让，弟弟只好给哥哥5块，这样哥哥比弟弟多挑2块。问最初弟弟准备挑多少块？","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"　　解答：我们得先算出最后哥哥、弟弟各挑多少块。","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"　　只要解一个“和差问题”就知道：哥哥挑“（26+2）÷2=14”块，弟弟挑“26-14=12”块。","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"　　下面根据题意列表还原：","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"img","nodeValue":null,"nodeType":"1","display":"inline","nodeAttrs":[{"attrName":"src","attrValue":"http://image13.360doc.com/DownloadImg/2010/08/1117/4559587_1.jpg"}],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"　　弟弟准备挑16 块。","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"8.甲乙两个汽车站共停了135辆汽车，如果从甲站开到乙站36辆，而从乙站开到甲站45辆，这时乙站停的车是甲站的1.5倍。原来甲乙两站各停多少辆？","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"　解答：甲：135÷（1.5+1）-45+36=45（辆）","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"blockquote","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"　乙：135-45=90（辆）","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"9.甲乙两桶油各有若干千克，如果从甲桶倒出和乙桶同样多的油放入乙桶，再从乙桶倒出和甲桶同样多的油放入甲桶，这是两桶油恰好都是16千克。两桶油原来各有多少千克？","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"解答：","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"table","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":";text-align:center"}],"childNodes":[{"nodeName":"tbody","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"tr","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"甲","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"乙","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]}]},{"nodeName":"tr","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"初始","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"8+12=20","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"24÷2=12","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]}]},{"nodeName":"tr","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"甲给乙后","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"16÷2=8","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"16+8=24","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]}]},{"nodeName":"tr","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"乙给甲后","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"16","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"16","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]}]}]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"10．甲、乙、丙各有棋子若干个。甲先给乙、丙一些棋子，使乙、丙每人的棋子数各增加一倍，然后乙也把自己的一些棋子给甲、丙，使甲、丙每人的棋子数各增加一倍，最后丙也按甲和乙的棋子数分别给甲、乙一些棋子，此时三人都各有16个棋子。开始时三人各有多少个棋子？","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"解答：","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"table","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":";text-align:center"}],"childNodes":[{"nodeName":"tbody","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"tr","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"甲","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"乙","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"丙","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]}]},{"nodeName":"tr","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"初始","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"4+14+8=26","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"28÷2=14","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"16÷2=8","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]}]},{"nodeName":"tr","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"第一次以后","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"8÷2=4","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"8+4+16=28","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"32÷2=16","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]}]},{"nodeName":"tr","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"第二次以后","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"16÷2=8","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"16÷2=8","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"16+8+8=32","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]}]},{"nodeName":"tr","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"第三次以后","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"16","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"16","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"16","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]}]}]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"11．甲、乙、丙、丁四人各有故事书若干本，甲将自己的故事书拿一部分给乙、丙、丁，使他们的书增加1倍，然后乙又拿出一部分故事书使得甲、丙、丁的书增加1倍，然后丙又拿出部分故事书使得甲、乙、丁的书增加1倍，最后丁也拿出部分故事书使得甲、乙、丙的书增加1倍。此时甲、乙、丙、丁手中都是32本书。问甲、乙、丙、丁四人原来各有多少本书？","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"解答：","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"　　我们还是采取倒推的办法，从最后一次丁分书出来考虑起。","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"　　由于丁拿出部分书分给甲、乙、丙后，甲、乙、丙的书各自增加了1倍，都为32本，说明在此之前，甲、乙、丙手中的书都为：","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"32÷2=16（本）","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"　　丁手中的书应为：","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"32+16×3=80（本）","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"　　同样可推出在丙拿出书之前，甲、乙、丁手中的书分别为：8本、8本、40本，","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"　　此时丙手中的书应为：","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"16+8+8+40=72（本）","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"　　继续下去，…，就可推出原来四人手中各有的书。","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"　　为方便起见，我们仍然列表加以说明。","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"table","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":";text-align:center"}],"childNodes":[{"nodeName":"tbody","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"tr","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"甲","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"乙","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"丙","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"丁","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]}]},{"nodeName":"tr","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"甲拿出书来之前各人手中的书","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"66","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"34","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"18","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"10","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]}]},{"nodeName":"tr","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"乙拿出书来之前各人手中的书","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"4","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"68","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"36","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"20","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]}]},{"nodeName":"tr","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"丙拿出书来之前各人手中的书","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"8","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"8","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"72","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"40","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]}]},{"nodeName":"tr","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"丁拿出书来之前各人手中的书","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"16","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"16","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"16","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"80","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]}]},{"nodeName":"tr","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"最后各人手中的书","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"32","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"32","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"32","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]},{"nodeName":"td","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"text","nodeValue":"32","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]}]}]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"由表可知，甲、乙、丙、丁最初各有书66本、34本、18本和10本。","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"12.魔方是一种益智的玩具。它是一个3×3×3的立方体。每个面的九个小块可以绕这个面的中心转动。没有打乱的魔方，每个面一种颜色，六个面分别涂有六种不同的颜色。某个魔方这六种颜色分别是：红、黄、蓝、绿、橙、白。下面是从三个不同的角度看到的这个魔方，请回答：与红色面相对的一面的颜色是­­­­­____色，与绿色面相对的一面的颜色是­­­­____色，与蓝色面相对的一面的颜色是­­­­­_____色。","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"img","nodeValue":null,"nodeType":"1","display":"inline","nodeAttrs":[{"attrName":"src","attrValue":"http://image13.360doc.com/DownloadImg/2010/08/1117/4559587_2.gif"}],"childNodes":[]},{"nodeName":"text","nodeValue":" ","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"　　现在我们取上面左图的情况：红面为前面，绿面为上面，蓝面为右面，与红面相对的面称作背面，与绿面相对的面称作下面，与蓝面相对的面称作左面。依次将左面、上面、右面、前面、下面按顺时针方向各转动90°，经过以上五步操作后，魔方背面最下一排的颜色从左至右分别是： ____色，____色，___色。注意，以上所说的“按顺时针方向”、“从左至右”都是指面对该面而言（上面我们改变的只是观察的位置,魔方的整体位置没变）。","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"解答：题目告诉我们，这个魔方六个面颜色分别是：红、黄、蓝、绿、橙、白。","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"　　从上图左边的魔方我们知道，绿面的邻面有红面和蓝面；从上图右边的魔方我们知道，绿面的邻面还有白面和橙面。这样，绿面的对面便是黄面。","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"　　从上图中间的魔方我们知道，橙面的邻面有黄面和蓝面；从上图右边的魔方我们知道，橙面的邻面还有白面和绿面。这样，橙面的对面便是红面。","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"　　从上图左边的魔方我们知道，蓝面的邻面有红面和绿面；从上图中间的魔方我们知道，蓝面的邻面还有黄面和橙面。这样，蓝面的对面便是白面。","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"　　第五次转动后，魔方各块的颜色我们无从知道，也无需知道，所以我们就仅只画一个没有颜色的魔方进行分析。我们知道，第五次转动的是最下面一层，而背面下层的三个小块是从右面下层的三个小块转过去的。题目让我们找的就是这三个小块的颜色，我们给这三个小块标上左、中、右。如下图（第四次转动之后的图）。","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"img","nodeValue":null,"nodeType":"1","display":"inline","nodeAttrs":[{"attrName":"src","attrValue":"http://image13.360doc.com/DownloadImg/2010/08/1117/4559587_3.gif"}],"childNodes":[]},{"nodeName":"text","nodeValue":" ","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"　　第四次转动是将前面顺时针转动90°得来的，现在我们只需将前面逆时针转动90°，就恢复到第三次转动后得情况。此时右面前侧的三块转到了上面，而带有 “左”字的一块是靠近右面的一块，而标有“中”、“右”的两个小块并没有动。再将右面逆时针转动90°，得到第二次转动后的情况，注意这次标字的三个小块的移动情况：标“左”字的小块转到了前面，标“中”字、“右”字的两块仍在右面，但逆时针转过90°。再将上面逆时针转动90°，得到第一次转动后的情况，注意此时标有“右”字的小块转到了背面，我们画了个箭头表示。最后，我们将左面逆时针转动90°，得到未转动时的魔方，注意此时标有“右”字的一块转到了魔方的下面上，应为下面上左后的一块。好了，我们知道了这三小块的原来位置，得出它们的颜色就轻而易举了。标“左”字的一块是从前面转过去的，前面为红面，它的颜色当然就是红色了。标“中”字的一块是从右面转过去的，当然就是蓝色了。标“右”字的一块是从下面转过去的，那就是黄色了。","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[{"attrName":"style","attrValue":"text-align: center;;"}],"childNodes":[{"nodeName":"img","nodeValue":null,"nodeType":"1","display":"inline","nodeAttrs":[{"attrName":"src","attrValue":"http://image13.360doc.com/DownloadImg/2010/08/1117/4559587_4.gif"}],"childNodes":[]}]},{"nodeName":"p","nodeValue":null,"nodeType":"1","display":"block","nodeAttrs":[],"childNodes":[{"nodeName":"text","nodeValue":"　　由此可得：与红色面相对的一面的颜色是­­­­­__黄__色，与绿色面相对的一面的颜色是­­­­__红__色，与蓝色面相对的一面的颜色是­­­­­__白___色。经过以上五步操作后，魔方背面最下一排的颜色从左至右分别是： __红__色，__蓝__色，_黄__色。","nodeType":"3","display":"inline","nodeAttrs":[],"childNodes":[]}]}]}]},"imageUrls":["https://image13.360doc.com/DownloadImg/2010/08/1117/4559587_1.jpg","https://image13.360doc.com/DownloadImg/2010/08/1117/4559587_2.gif","https://image13.360doc.com/DownloadImg/2010/08/1117/4559587_3.gif","https://image13.360doc.com/DownloadImg/2010/08/1117/4559587_4.gif"],"text":"运用倒推法（还原法）解题的相应的“逆运算”是指：加法用减法还原，减法用加法还原，乘法用除法还原，除法用乘法还原，并且原来是加（减）几，还原时应为减（加）几，原来是乘（除）以几，还原时应为除（乘）以几。　　对于一些比较复杂的还原问题，要学会列表，借助表格倒推，既能理清数量关系，又便于验算。例1．某数加上6，乘以6，减去6，除以6，最后结果等于6，求某数。　　解答：（6×6＋6）÷6－6=1例2．一捆电线，第一次用去全长的一半多3米，第二次用去余下的一半少10米，第三次用去15米，最后还剩7米，这捆电线原有多少米？　　解答：[（7+15－10）×2+3]=54（米）例3．小明在计算一道加法计算时，把一个加数个位上的1看作7，把一个加数十位上的8看作3，这样所得的和是1955，原来两数相加的正确答案是多少？　　解答：1995＋50－6=1999例4．袋子里装着若干个乒乓球，小明每次拿出其中的一半再放回一个球，这样共拿了5次，袋子里还有5个球。袋中原有多少个乒乓球？　　解答：操作次数袋中球个数初始（50－1）×2=981（26－1）×2=502（14－1）×2=263（8－1）×2=144（5－1）×2=855例5．甲、乙、丙三人各有小球若干个，甲先拿出自己的小球的一部分给乙和丙，使乙、丙每人的小球数增加一倍；然后乙也把自己的小球的一部分分给甲丙，使甲和丙每人的小球数增加一倍；最后丙也把自己小球的一部分分给甲和乙，使甲和乙每人的小球数增加一倍。这时甲乙丙都有48个小球。原来甲乙丙各有小球多少个？解答：变动情况甲乙丙初始状态12＋42+24=7884÷2=4248÷2=24124÷2=1224＋12＋48=8496÷2=48248÷2=2448÷2=2448＋24＋24=963484848习题：1.一位老人说，把我的年龄加上12，再用4除，再减去15后乘以10，恰好是100岁。这位老人现在有多少岁？　　解答：（100÷10+15）×4－12=88(岁)2.百货商店出售手机，上午售出总数的一半多20部，下午售出剩下的一半多15部，还剩下75部。商店原有手机多少部？　　解答：[(75+15)×2+20]×2=400（部）3.做一道减法算式，把减数的个位1看作3，把被减数十位上的2看作了5，这样结果等于200，差应该是多少？　　解答：200+（3－1）－（50－20）=1724.甲、乙、丙、丁四人共有画片80张，甲给乙13张，乙给丙18张，丙给丁16张，丁给甲2张后，四人画片张数相等。他们原来各有画片多少张？　　解答：甲：80÷4+13－2=31（张）乙：80÷4－13＋18=25（张）丙：80÷4－18+16=18（张）丁：80÷4－16+2=6（张）5.有一篮鸡蛋，第一次取出全部的一半多2个，第二次取出余下的一半少2个，篮中还剩下12个。篮中原有鸡蛋多少个？　　解答：[（12-2）×2+2]×2=44（个）6.一筐梨，甲取一半又一个，乙取余下的一半又一个，丙再取余下的一半又一个，这时筐里只剩一个梨。这筐梨共值4.40元，每个梨值多少元？　　解答：（1+1）×2=4（个）（4+1）×2=10（个）（10+1）×2=22（个） 4.40÷22=0.20（元）7．有26块砖，兄弟2人争着去挑，弟弟抢在前面，刚摆好砖，哥哥赶来了。哥哥看弟弟挑得太多，就拿来一半给自己。弟弟觉得自己能行，又从哥哥那里拿来一半。哥哥不让，弟弟只好给哥哥5块，这样哥哥比弟弟多挑2块。问最初弟弟准备挑多少块？　　解答：我们得先算出最后哥哥、弟弟各挑多少块。　　只要解一个“和差问题”就知道：哥哥挑“（26+2）÷2=14”块，弟弟挑“26-14=12”块。　　下面根据题意列表还原：　　弟弟准备挑16 块。8.甲乙两个汽车站共停了135辆汽车，如果从甲站开到乙站36辆，而从乙站开到甲站45辆，这时乙站停的车是甲站的1.5倍。原来甲乙两站各停多少辆？　解答：甲：135÷（1.5+1）-45+36=45（辆）　乙：135-45=90（辆）9.甲乙两桶油各有若干千克，如果从甲桶倒出和乙桶同样多的油放入乙桶，再从乙桶倒出和甲桶同样多的油放入甲桶，这是两桶油恰好都是16千克。两桶油原来各有多少千克？解答：甲乙初始8+12=2024÷2=12甲给乙后16÷2=816+8=24乙给甲后161610．甲、乙、丙各有棋子若干个。甲先给乙、丙一些棋子，使乙、丙每人的棋子数各增加一倍，然后乙也把自己的一些棋子给甲、丙，使甲、丙每人的棋子数各增加一倍，最后丙也按甲和乙的棋子数分别给甲、乙一些棋子，此时三人都各有16个棋子。开始时三人各有多少个棋子？解答：甲乙丙初始4+14+8=2628÷2=1416÷2=8第一次以后8÷2=48+4+16=2832÷2=16第二次以后16÷2=816÷2=816+8+8=32第三次以后16161611．甲、乙、丙、丁四人各有故事书若干本，甲将自己的故事书拿一部分给乙、丙、丁，使他们的书增加1倍，然后乙又拿出一部分故事书使得甲、丙、丁的书增加1倍，然后丙又拿出部分故事书使得甲、乙、丁的书增加1倍，最后丁也拿出部分故事书使得甲、乙、丙的书增加1倍。此时甲、乙、丙、丁手中都是32本书。问甲、乙、丙、丁四人原来各有多少本书？解答：　　我们还是采取倒推的办法，从最后一次丁分书出来考虑起。　　由于丁拿出部分书分给甲、乙、丙后，甲、乙、丙的书各自增加了1倍，都为32本，说明在此之前，甲、乙、丙手中的书都为：32÷2=16（本）　　丁手中的书应为：32+16×3=80（本）　　同样可推出在丙拿出书之前，甲、乙、丁手中的书分别为：8本、8本、40本，　　此时丙手中的书应为：16+8+8+40=72（本）　　继续下去，…，就可推出原来四人手中各有的书。　　为方便起见，我们仍然列表加以说明。甲乙丙丁甲拿出书来之前各人手中的书66341810乙拿出书来之前各人手中的书4683620丙拿出书来之前各人手中的书887240丁拿出书来之前各人手中的书16161680最后各人手中的书32323232由表可知，甲、乙、丙、丁最初各有书66本、34本、18本和10本。12.魔方是一种益智的玩具。它是一个3×3×3的立方体。每个面的九个小块可以绕这个面的中心转动。没有打乱的魔方，每个面一种颜色，六个面分别涂有六种不同的颜色。某个魔方这六种颜色分别是：红、黄、蓝、绿、橙、白。下面是从三个不同的角度看到的这个魔方，请回答：与红色面相对的一面的颜色是­­­­­____色，与绿色面相对的一面的颜色是­­­­____色，与蓝色面相对的一面的颜色是­­­­­_____色。 　　现在我们取上面左图的情况：红面为前面，绿面为上面，蓝面为右面，与红面相对的面称作背面，与绿面相对的面称作下面，与蓝面相对的面称作左面。依次将左面、上面、右面、前面、下面按顺时针方向各转动90°，经过以上五步操作后，魔方背面最下一排的颜色从左至右分别是： ____色，____色，___色。注意，以上所说的“按顺时针方向”、“从左至右”都是指面对该面而言（上面我们改变的只是观察的位置,魔方的整体位置没变）。解答：题目告诉我们，这个魔方六个面颜色分别是：红、黄、蓝、绿、橙、白。　　从上图左边的魔方我们知道，绿面的邻面有红面和蓝面；从上图右边的魔方我们知道，绿面的邻面还有白面和橙面。这样，绿面的对面便是黄面。　　从上图中间的魔方我们知道，橙面的邻面有黄面和蓝面；从上图右边的魔方我们知道，橙面的邻面还有白面和绿面。这样，橙面的对面便是红面。　　从上图左边的魔方我们知道，蓝面的邻面有红面和绿面；从上图中间的魔方我们知道，蓝面的邻面还有黄面和橙面。这样，蓝面的对面便是白面。　　第五次转动后，魔方各块的颜色我们无从知道，也无需知道，所以我们就仅只画一个没有颜色的魔方进行分析。我们知道，第五次转动的是最下面一层，而背面下层的三个小块是从右面下层的三个小块转过去的。题目让我们找的就是这三个小块的颜色，我们给这三个小块标上左、中、右。如下图（第四次转动之后的图）。 　　第四次转动是将前面顺时针转动90°得来的，现在我们只需将前面逆时针转动90°，就恢复到第三次转动后得情况。此时右面前侧的三块转到了上面，而带有 “左”字的一块是靠近右面的一块，而标有“中”、“右”的两个小块并没有动。再将右面逆时针转动90°，得到第二次转动后的情况，注意这次标字的三个小块的移动情况：标“左”字的小块转到了前面，标“中”字、“右”字的两块仍在右面，但逆时针转过90°。再将上面逆时针转动90°，得到第一次转动后的情况，注意此时标有“右”字的小块转到了背面，我们画了个箭头表示。最后，我们将左面逆时针转动90°，得到未转动时的魔方，注意此时标有“右”字的一块转到了魔方的下面上，应为下面上左后的一块。好了，我们知道了这三小块的原来位置，得出它们的颜色就轻而易举了。标“左”字的一块是从前面转过去的，前面为红面，它的颜色当然就是红色了。标“中”字的一块是从右面转过去的，当然就是蓝色了。标“右”字的一块是从下面转过去的，那就是黄色了。　　由此可得：与红色面相对的一面的颜色是­­­­­__黄__色，与绿色面相对的一面的颜色是­­­­__红__色，与蓝色面相对的一面的颜色是­­­­­__白___色。经过以上五步操作后，魔方背面最下一排的颜色从左至右分别是： __红__色，__蓝__色，_黄__色。"}