Question

[Le Thuy]

2/5: 3/7 nhan 3/7 : 2/5 + 1999

{1- 1/2} nhan { 1 - 1/3} nhan { 1 - 1/4 } nhan { 1 - 1/5}

Answer 1

[Nguyễn Gia Huy]

\(\frac{2}{5}:\frac{3}{7}x\frac{3}{7}:\frac{2}{5}+1999=\)\(\frac{2}{5}x\frac{7}{3}x\frac{3}{7}x\frac{5}{2}+1999=\)\(\left(\frac{2x7x3x5}{5x3x7x2}\right)+1999=\)\(1+1999=2000\)

\(\left(1-\frac{1}{2}\right)x\left(1-\frac{1}{3}\right)x\left(1-\frac{1}{4}\right)x\left(1-\frac{1}{5}\right)\)\(=\left(\frac{2}{2}-\frac{1}{2}\right)\)\(x\left(\frac{3}{3}-\frac{1}{3}\right)\)\(x\left(\frac{4}{4}-\frac{1}{4}\right)\)\(x\left(\frac{5}{5}-\frac{1}{5}\right)\)\(=\frac{1}{2}x\frac{2}{3}x\frac{3}{4}x\frac{4}{5}=\)\(\frac{1x2x3x4}{2x3x4x5}=\frac{1x\left(2x3x4\right)}{\left(2x3x4\right)x5}=\frac{1}{5}\)\(.\)

Answer 2

[Đinh Quang Đại]

2/5:3/7 nhân 3/7:2/5+1999

=2/5 nhân 7/3 nhân 3/7nhân 5/2+1999

=14/15 nhân 15/14+1999

=1+1999

=2000

(1-1/2) nhân (1-1/3) nhân (1-1/4) nhân (1-1/5)

=1/2 nhân 2/3 nhân 3/4 nhân 4/5

=24/120

=1/5