从0.1.2.3.4.5.6这7个数字中,任意取两个做除法,可得出不同的商的个数为
\u4ece0.1.2.3.4.5.6\u8fd97\u4e2a\u6570\u5b57\u4e2d,\u4efb\u610f\u53d6\u4e24\u4e2a\u505a\u9664\u6cd5,\u53ef\u5f97\u51fa\u4e0d\u540c\u7684\u5546\u7684\u4e2a\u6570\u4e3a_____.\u89e3\uff1a
\u88ab\u9664\u6570\u4e3a 0\u7684\u60c5\u51b5\uff0c\u53ea\u80fd\u5f97\u51fa\u4e00\u79cd\u5546 0
\u88ab\u9664\u6570\u4e3a 1\u7684\u60c5\u51b5\uff0c\u80fd\u5f97\u51fa1/2,1/3,1/4,1/5,1/6\uff0c\u4e94\u4e2a\u4e0d\u540c\u5546
\u88ab\u9664\u6570\u4e3a 2\u7684\u60c5\u51b5\uff0c\u80fd\u5f97\u51fa2/1,2/3,2/4,2/5,2/6\u4e94\u4e2a\u5546\uff0c
\u4f46\u662f 2/4=1/2, 2/6-1/3 \u4e0e\u4e0a\u8fb9\u91cd\u590d\u4f30\u65e0\u6548\uff0c\u6240\u4ee5\u53c8\u6709\u4e09\u79cd\u4e0d\u540c\u5546
\u88ab\u9664\u6570\u4e3a 3\u7684\u60c5\u51b5\uff0c\u80fd\u5f97\u51fa3/1,3/2,3/4,3/5,3/6 \u4e94\u4e2a\u5546
\u4f46\u662f 3/6=1/2 \u91cd\u590d \u4f30\u65e0\u6548 \u6240\u4ee5\u53c8\u6709\u56db\u79cd\u4e0d\u540c\u5546
\u88ab\u9664\u6570\u4e3a 4\u7684\u60c5\u51b5\uff0c\u80fd\u5f97\u51fa4/1,4/2,4/3,4/5,4/6 \u4e94\u4e2a\u5546
\u4f46\u662f 4/2=2/1,4/6=2/3\u91cd\u590d\u65e0\u6548 \u6240\u4ee5\u53c8\u6709 \u56db\u4e2a\u4e0d\u540c\u5546
\u88ab\u9664\u6570\u4e3a 5\u7684\u60c5\u51b5\uff0c\u80fd\u5f97\u51fa5/1,5/2,5/3,5/4,5/6 \u4e94\u4e2a\u4e0d\u540c\u5546
\u88ab\u9664\u6570\u4e3a 6\u7684\u60c5\u51b5\uff0c\u80fd\u5f97\u51fa6/1,6/2,6/3,6/4,6/5 \u4e94\u4e2a\u5546
\u4f46\u662f 6/2-3/1,6/3=2/1,6/4=3/2\u91cd\u590d\u65e0\u6548\uff0c\u53c8\u6709\u4e24\u4e2a\u4e0d\u540c\u5546
\u7efc\u5408\u5f97 \u5171\u67091+5+3+4+4+5+2=19\u79cd
\u8fd9\u6837\u53ef\u4ee5\u4e48
4/2=2
24/8=3
20/4=5
1和后面的数做除法,结果为2、3、4、5、6和他们的倒数。共10个,
2和后面的数做除法,结果有8个,
3有6个,
4有4个,
5有2个。
其中2和4、2和6、3和6、4和6组成的数可以约分,舍去。即少8个。
共有1+10+6+4+2-8=15个
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