Tính một cách nhanh nhất
1/1*2+1/2*3+1/3*4
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1/2 + 1/3 + 1/4 + 1/5 + 4/5 + 3/4 + 2/3 + 1/2
= (1/2 + 1/2) + (1/3 + 2/3) + (1/4 + 3/4) + (1/5 + 4/5)
= 1 + 1 + 1 + 1
= 4
2/
a)\(\dfrac{1}{5}+\dfrac{4}{5}+\dfrac{4}{11}+\dfrac{7}{11}\)
= \(\dfrac{5}{5}+\dfrac{11}{11}\)
= \(1+1\)
= \(2\)
b) \(\left(\dfrac{1}{8}+\dfrac{3}{8}\right)+\left(\dfrac{4}{12}+\dfrac{5}{12}\right)\)
= \(\dfrac{4}{8}+\dfrac{8}{12}\)
= \(\dfrac{12}{24}+\dfrac{16}{24}\)
= \(\dfrac{28}{24}\)
= \(\dfrac{7}{6}\)
1+2+3+4+5+6+7+8+9 = ( 1+9) + ( 2+8) + (3+7) + (4+6) +5
= 10 + 10 + 10 + 10 + 5
= 45
\(=\dfrac{4}{3}\cdot\dfrac{9}{8}\cdot\dfrac{16}{15}\cdot\dfrac{25}{24}\cdot\dfrac{36}{35}=\dfrac{12}{7}\)
= 4/3*9/8*16/15*25/24*36/35
=2*2/1*3 * 3*3/2*4 *4*4/3*5 *5*5/4*6 * 6*6/5*7
= (2*3*4*5*6 / 1*2*3*4*5) * ( 2*3*4*5*6 / 3*4*5*6*7)
=6/1* 2/7
= 12/7
\(=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot\dfrac{6}{5}\cdot\dfrac{5}{6}=\dfrac{1}{2}\cdot\dfrac{2}{3}=\dfrac{1}{3}\)
\(\dfrac{1}{2}\times\dfrac{2}{3}:\dfrac{5}{6}\times\dfrac{5}{6}\)
\(=\dfrac{1}{2}\times\left(\dfrac{2}{3}:\dfrac{5}{6}\times\dfrac{5}{6}\right)\)
\(=\dfrac{1}{2}\times\dfrac{2}{3}\)
\(=\dfrac{1}{3}\)
Đặt \(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}\)
\(\Rightarrow A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}\)
\(\Rightarrow A=1-\frac{1}{4}\)
\(\Rightarrow A=\frac{3}{4}\)
\(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}\)
\(=\frac{1}{1}-\frac{1}{4}\)
\(=\frac{3}{4}\)
\(x\)bằng dấu nhân