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\(\frac{1996\cdot1995-996}{1000+1996\cdot1994}\)
\(=\frac{1996\cdot\left(1994+1\right)-996}{1000+1996\cdot1994}\)
\(=\frac{1996\cdot1994+1996-996}{1000+1996\cdot1994}\)
\(=\frac{1996\cdot1994+1000}{1000+1996\cdot1994}=1\)
Dạng toán: Tính nhanh ( vận dụng tính chất kết hợp phân phối giữa phép nhân và phép cộng)
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\(\frac{1996.1995-996}{1000+1996.1994}=\frac{1996.\left(1994+1\right)-996}{1000+1996.1994}=\frac{1996.1994+1996-996}{1000+1996.1994}\)
\(=\frac{1996.1994+1000}{1000+1996.1994}=1\)
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Ta có: \(1996\cdot1995-996-100-1996\cdot1994\)
\(=1996\left(1995-1994\right)-1996\)
\(=1996-1996=0\)
Ta có: \(1996\cdot1995-996-100-1996\cdot1994\)
\(=1996\left(1995-1994\right)-1996\)
\(=1996-1996=0\)
\(a,\frac{125\cdot81\cdot7}{49\cdot75\cdot27}=\frac{25\cdot5\cdot9\cdot9\cdot7}{7\cdot7\cdot15\cdot5\cdot3\cdot9}=\frac{25\cdot9}{7\cdot15\cdot3}=\frac{5\cdot5\cdot3\cdot3}{7\cdot3\cdot5\cdot3}=\frac{5}{7}\)
\(b,\frac{48\cdot25-48\cdot11-48}{16\cdot23-16\cdot10}=\frac{1200-528-48}{368-160}=\frac{624}{208}=3\)
\(c,\frac{15\cdot\left[4\cdot17+17\cdot5\right]}{18\cdot25\cdot34}=\frac{15\cdot\left[17\cdot\left(4+5\right)\right]}{15300}=\frac{15\cdot153}{15300}\)
\(=\frac{2295}{15300}=\frac{3}{20}\)
\(d,\frac{1996\cdot1995-996}{1000+1996\cdot1994}=\frac{3982020-996}{1000+3980024}=\frac{3981024}{3981024}=1\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{6.7}+\frac{1}{7.8}\)
\(=\frac{1}{1}-\frac{1}{8}\)
\(=\frac{7}{8}\)'
\(\frac{1996\times1995-996}{1000+1996\times1994}\)
\(=\frac{1996\times\left(1994+1\right)-996}{1996\times1994+1000}\)
\(=\frac{1996\times1994+1996\times1-996}{1996\times1994+1000}\)
\(=\frac{1996\times1994+1996-996}{1996\times1994+1000}\)
\(=\frac{1996\times1994+1000}{1996\times1994+1000}=1\)
\(\frac{1,65\times25+117\times1,65+1,65\times108}{150\times0,25+1,4\times150}\)
\(=\frac{\left(25+117+108\right)\times1,65}{150\times\left(0,25+1,4\right)}\)
\(=\frac{250\times1,65}{150\times1,65}\)
\(=\frac{\left(150+100\right)\times1,65}{150\times1,65}\)
\(=\frac{150\times1,65+100\times1,65}{150\times1,65}\)
\(=\frac{150\times1,65+165}{150\times1,65}=\frac{165}{1}=165\)