Question

Tính nhanh:

\(\frac{1.5.6+2.10.12+4.20.24+9.45.54}{1.3.5+2.6.10+4.12.20+9.27.45}\)

Answer 1

\(\frac{1.5.6+2.10.12+4.20.24+9.45.54}{1.3.5+2.6.10+4.12.20+9.27.45}\)=\(\frac{1.5.6+\left(1.5.6\right)2+\left(1.5.6\right)4+\left(1.5.6\right)9}{1.3.5+\left(1.3.5\right)2+\left(1.3.5\right)4+\left(1.3.5\right)9}\)

=\(\frac{\left(1.5.6\right)\left(1+2+4+9\right)}{\left(1.3.5\right)+\left(1+2+4+9\right)}=\frac{1.5.6}{1.3.5}=\frac{6}{3}=2\)

Answer 2

\(\frac{1.5.6+2.10.12+4.20.24+9.45.54}{1.3.5+2.6.10+4.12.20+9.27.45}=\frac{1.5.6+\left(1.5.6\right)2+\left(1.5.6\right)4+\left(1.5.6\right)9}{1.3.5+\left(1.3.5\right)2+\left(1.3.5\right)4+\left(1.3.5\right)9}=\)

\(\frac{\left(1.5.6\right)\left(1+2+4+9\right)}{\left(1.3.5\right)\left(1+2+4+9\right)}=\frac{1.5.6}{1.3.5}=\frac{6}{3}=2\)

Answer 3

\(\frac{1.5.6+2.10.12+4.20.24+9.45.54}{1.3.5+2.6.10+4.12.20+9.27.45}\)

\(=\frac{1.5.6+\left(1.5.6\right)2+\left(1.5.6\right)4+\left(1.5.6\right)9}{1.3.5+\left(1.3.5\right)2+\left(1.3.5\right)4+\left(1.3.5\right)9}\)

\(=\frac{\left(1.5.6\right)\left(1+2+4+9\right)}{\left(1.3.5\right)\left(1+2+4+9\right)}\)

\(=\frac{1.5.6}{1.3.5}=\frac{6}{3}=2\)

Answer 4

$A=\frac{\mathrm{1.5.6}+\mathrm{2.10.12}+\mathrm{4.20.24}+\mathrm{9.45.54}}{\mathrm{1.3.5}+\mathrm{2.6.10}+\mathrm{4.12.20}+\mathrm{9.27.45}}$

$A=\frac{\mathrm{1.5.6.}\left({}^{}+{}^{}+{}^{}+{}^{}\right)}{\mathrm{1.3.5.}\left({}^{}+{}^{}+{}^{}+{}^{}\right)}=2$