1/2x1/3+1/3x1/4+1/4x1/5+1/5x1/6+1/6x1/7+1/7x1/8+1/8x1/9

=7/18

5/6 x 1/7 - 1/7 x 1/6

= 1/7 x (5/6 - 1/6)

= 1/7 x 2/3

= 2/21

8/15 : 4/5 x 3/2

= 2/3 x 3/2

= 1

a: =1/7(5/6-1/6)=1/7x2/3=2/21

b: =8/15x5/4x3/2=1

`5/6xx1/7-1/7xx1/6`

`= 1/7 xx (5/6-1/6)`

`= 1/7 xx 2/3`

`= 2/21`

`8/15: 4/5 xx3/2`

`= 2/3 xx 3/2`

`= 1`

`1/3xx 1/2 + 1/2 xx 1/5`

`=1/2 xx (1/3 +1/5)`

`= 1/2 xx ( 5/15 +3/15)`

`= 1/2 xx 8/15`

`= 8/30`

`=4/15`

__

`1/3 xx 1/2 - 1/5 xx 1/2`

`= 1/2 xx (1/3 -1/5)`

`= 1/2 xx ( 5/15 -3/15)`

`=1/2 xx 2/15`

`= 2/30`

`=1/15`

a)

`1/3xx1/2+1/2xx1/5`

`=1/2xx(1/3+1/5)`

`=1/2xx(5/15+3/15)`

`=1/2xx8/15`

`=4/15`

b)

`1/3xx1/2-1/5xx1/2`

`=1/2xx(1/3-1/5)`

`=1/2xx(5/15-3/15)`

`=1/2xx2/15`

`=1/15`

a)

$1/3xx1/2+1/2xx1/5$

$=1/2xx(1/3+1/5)$

$=1/2xx(5/15+3/15)$

$=1/2xx8/15$

$=4/15$

b)

$1/3xx1/2-1/5xx1/2$

$=1/2xx(1/3-1/5)$

$=1/2xx(5/15-3/15)$

$=1/2xx2/15$

$=1/15$

\(\dfrac{1}{4}\) : 0,25 - \(\dfrac{1}{8}\) : 0,125 + \(\dfrac{1}{2}\) : 0,5 - 1

= 0,25 x 4 - 0,125 x 8 + 0,5 x 2 - 1

= 1 - 1 + 1 - 1

= 0 + 1 - 1

= 1 - 1

= 0

A = \(\dfrac{1}{4}\) : 0,25 - \(\dfrac{1}{8}\): 0,125 + \(\dfrac{1}{2}\): 0,5 - 1

A = \(\dfrac{1}{4}\) x 4 - \(\dfrac{1}{8}\) x 8 + \(\dfrac{1}{2}\) x 2 - 1

A = 1 - 1 + 1  - 1

A =  (1 - 1) + (1 - 1)

A = 0 

\(\dfrac{1}{10}+\dfrac{1}{2}:0,5-\dfrac{1}{4}:0,25+\dfrac{1}{8}:0,125\)

\(=\dfrac{1}{10}+\dfrac{1}{2}\times2-\dfrac{1}{4}\times4+\dfrac{1}{8}\times8\)

\(=\dfrac{1}{10}+1-1+1\)

\(=\dfrac{1}{10}+1=\dfrac{1}{10}+\dfrac{10}{10}=\dfrac{11}{10}\)

\(\dfrac{1}{10}+\dfrac{1}{2}\div0,5-\dfrac{1}{4}\div0,25+\dfrac{1}{8}\div0,125\)

= 0,1 + 0,5 x 2 - 0,25 x 4 + 0,125 x 8

= 0,1 + 1 - 1 + 1

= 1,1 - 1 +1

= 0,1 + 1

= 1,1

`#3107.101107`

\(\dfrac{1}{10}+\dfrac{1}{2}\cdot0,5-\dfrac{1}{4}\div0,25+\dfrac{1}{8}\div0,125\)

\(=\dfrac{1}{10}+\left(\dfrac{1}{2}\div0,5\right)-\left[\left(\dfrac{1}{2}\right)^2\div\left(0,5\right)^2\right]+\left(\dfrac{1}{2}\right)^3\div\left(0,5\right)^3\)

\(=\dfrac{1}{10}+\left(\dfrac{1}{2}\div0,5\right)-\left(\dfrac{1}{2}\div0,5\right)^2+\left(\dfrac{1}{2}\div0,5\right)^3\)

\(=\dfrac{1}{10}+1-1^2+1^3\)

\(=\dfrac{1}{10}+1\)

\(=\dfrac{11}{10}\)

1/2+1/4+1/8+1/16+1/32+1/64

=(1/2+1/4+1/8)+(1/16+1/32+1/64)

=(4/8+2/8+1/8)+(4/64+2/64+1/64)

=7/8+7/64

=56/64+7/64

=63/64

           B =        \(\dfrac{1}{2}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{8}\) +  \(\dfrac{1}{16}\)  + \(\dfrac{1}{32}\) + \(\dfrac{1}{64}\) 

    2 x B   = 1 + \(\dfrac{1}{2}\)+ \(\dfrac{1}{4}\)  +  \(\dfrac{1}{8}\) +  \(\dfrac{1}{16}\)+ \(\dfrac{1}{32}\)

2 x B - B = 1 - \(\dfrac{1}{64}\)

           B = \(\dfrac{63}{64}\)

đặt `A= 1/2 + 1/4 + 1/8 + 1/16+ 1/32 + 1/64`

`=> 2A = 2(1/2 + 1/4 + 1/8 + 1/16+ 1/32 + 1/64)`

`2A = 1+1/2 +1/4 +1/8+1/16 +1/32`

`=>A =2A -A =1+1/2 +1/4 +1/8+1/16 +1/32-1/2-1/4-1/8-1/16-1/32 -1/64`

`A = 1-1/64 = 64/64 -1/64 =63/64`