Question

bài 1)tính bằng cách thuận tiện A,6/4+6/28+6/70+6/130+6/208       B,0,7x430x2+1,4x570+200

Answer 1

a: \(\dfrac{6}{4}+\dfrac{6}{28}+\dfrac{6}{70}+\dfrac{6}{130}+\dfrac{6}{208}\)

 

\(=2\left(\dfrac{3}{1\text{x}4}+\dfrac{3}{4\text{x}7}+\dfrac{3}{7\text{x}10}+\dfrac{3}{10\text{x}13}+\dfrac{3}{13\text{x}16}\right)\)

\(=2\text{x}\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{16}\right)\)

\(=2\text{x}\left(1-\dfrac{1}{16}\right)=2\text{x}\dfrac{15}{16}=\dfrac{15}{8}\)

b: \(0,7\text{x}430\text{x}2+1,4\text{x}570+200\)

\(=1,4\text{x}430+1,4\text{x}570+200\)

\(=1,4\text{x}\left(430+570\right)+200\)

=1400+200

=1600

Answer 2

\(a,\dfrac{6}{4}+\dfrac{6}{28}+\dfrac{6}{70}+\dfrac{6}{130}+\dfrac{6}{208}\)

\(=\dfrac{6}{1.4}+\dfrac{6}{4.7}+\dfrac{6}{7.10}+\dfrac{6}{10.13}+\dfrac{6}{13.16}\)

\(=2.\left(\dfrac{1}{1.4}+\dfrac{1}{4.7}+\dfrac{1}{7.10}+\dfrac{1}{10.13}+\dfrac{1}{13.16}\right)\)

\(=2.\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{16}\right)\)

\(=2.\left(1-\dfrac{1}{16}\right)\)

\(=2.\dfrac{15}{16}=\dfrac{15}{8}=1,875\)

\(b,0,7\times430\times2+1,4\times570+200\)

\(=1,4\times430+1,4\times570+200\)
\(=1,4\times\left(430+570\right)+200\)

\(=1,4\times1000+200\)

\(=1400+200=1600\)