tính nhanh
6.5 +1.2 +3.5 -5.2 +6.5-4.8
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a)
\(\frac{1\cdot2+2\cdot4+3\cdot6+4\cdot8+5\cdot10}{3\cdot4+6\cdot8+9\cdot12+12\cdot16+15\cdot20}\)
\(=\frac{1\cdot2\cdot\left(1+2\cdot2+3\cdot3+4\cdot4+5\cdot5\right)}{3\cdot4\cdot\left(1+2\cdot2+3\cdot3+4\cdot4+5\cdot5\right)}\)
\(=\frac{1\cdot2}{3\cdot4}=\frac{1}{6}\)
b) \(\frac{12\cdot13+24\cdot26+36\cdot39}{24\cdot26+48\cdot52+72\cdot78}\)
\(=\frac{12\cdot13\cdot\left(1+2\cdot2+3\cdot3\right)}{24\cdot26\cdot\left(1+2\cdot2+3\cdot3\right)}\)
\(=\frac{12\cdot13}{24\cdot26}=\frac{1}{4}\)
\(\frac{2\cdot3+4\cdot6+14\cdot21}{3\cdot5+6\cdot10+21\cdot35}=\frac{2\cdot3\cdot\left(1+2\cdot2+7\cdot7\right)}{3\cdot5\cdot\left(1+2\cdot2+7\cdot7\right)}=\frac{2\cdot3}{3\cdot5}=\frac{2}{5}\)
\(\dfrac{1.2+2.4+3.6+4.8+5.10}{3.4+6.8+9.12+12.16+15.20}\)
\(=\dfrac{1.2+2.4+3.6+4.8+5.10}{3.4+3.4.2.2+3.4.3.3+3.4.2.8+3.4.5.5}\)
\(=\dfrac{1.2.\left(4+3^2+2.8+5^2\right)}{3.4.\left(4+3^2+2.8+5^2\right)}\)
\(=\dfrac{1}{6}\)
\(\dfrac{1.2+2.4+3.6+4.8+5.10}{3.4+6.8+9.12+12.16+15.20}\)
\(=\dfrac{1.2+1.2.2^2+1.2.3^2+1.2.4^2+1.2.5^2}{3.4+3.4.2^2+3.4.3^2+3.4.4^2+3.4.5^2}\)
\(=\dfrac{1.2\left(1+2^2+3^2+4^2+5^2\right)}{3.4\left(1+2^2+3^2+4^2+5^2\right)}\\ =\dfrac{2}{12}=\dfrac{1}{6}\)
Câu 1 : \(0,36\times630+0,6\times36\times6+3,6\)
\(=0,36\times10\times63+0,6\times6\times36+3,6\)
\(=3,6\times63+3,6\times36+3,6\)
\(=3,6\times\left(63+36+1\right)\)
\(=3,6\times100\)
\(=360\)
Câu 2 :\(3,5\times20,2+6,5\times27,9+3,5\times2,2-6,5\times5,5\)
\(=3,5\times\left(20,2+2,2\right)+6,5\times\left(27,9-5,5\right)\)
\(=3,5\times22,4+6,5\times22,4\)
\(=22,4\times\left(3,5+6,5\right)\)
\(=22,4\times10\)
\(=224\)
\(6.5+1.2+3.5-5.2+6.5-4.8\)
\(=30+2+15-10+30-32\)
\(=\left(30+2\right)+\left(15-10+30\right)-32\)
\(=32+35-32\)
\(=\left(32-32\right)+35\)
\(=0+35\)
\(=35\)