\(x\) \(\times\) \(\dfrac{1}{4}\) = 6 : 1 : 2

\(x\) \(\times\) \(\dfrac{1}{4}\) = 6:2

\(x\) \(\times\) \(\dfrac{1}{4}\) =  3

\(x\)         = 3 : \(\dfrac{1}{4}\)

\(x\)        = 12

Mình nhầm đoạn 6:1/2.nhờ bạn giải lại hộ mình với

\(x\)\(\times\) \(\dfrac{1}{4}\) = 6 : \(\dfrac{1}{2}\)

\(x\) \(\times\) \(\dfrac{1}{4}\) = 6 \(\times\) \(\dfrac{2}{1}\)

\(x\) \(\times\) \(\dfrac{1}{4}\) = 12

\(x\)       =  12 : \(\dfrac{1}{4}\)

\(x\)      = 48

Tính nhanh:

                         A =         \(\dfrac{2}{3}\) + \(\dfrac{2}{9}\) + \(\dfrac{2}{27}\) + \(\dfrac{2}{81}\) + \(\dfrac{2}{243}\) + \(\dfrac{2}{729}\)

                  A \(\times\) 3 =  2  +  \(\dfrac{2}{3}\) + \(\dfrac{2}{9}\) + \(\dfrac{2}{27}\) + \(\dfrac{2}{81}\) + \(\dfrac{2}{243}\) 

            A \(\times\) 3 - A = 2 - \(\dfrac{2}{729}\)

           A \(\times\) ( 3 - 1) = 2 \(\times\) ( 1 - \(\dfrac{1}{729}\))

             A \(\times\) 2       = 2 \(\times\) \(\dfrac{728}{729}\)

            A = 2 \(\times\) \(\dfrac{728}{729}\) : 2

           A = \(\dfrac{728}{729}\)

c, tính:

 \(\dfrac{4}{5}\) + \(\dfrac{1}{2}\) - \(\dfrac{1}{6}\)

= \(\dfrac{4}{5}\) + \(\dfrac{1}{3}\)

= \(\dfrac{17}{15}\)

a ) 37 x 27 + 63 x 27 

= ( 37 + 63 ) x 27

= 100 x 27

= 2700

b ) 1 + 2 + 3 + 4 + ... + 97 + 98 + 99

= ( 99 - 1 ) : 1 + 1 

= 99 x ( 99 + 1 ) : 2 

= 4950

c ) 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10

= ( 1 + 9 ) + ( 2 + 8 ) + ( 3 + 7 ) + ( 4 + 6 ) + ( 5 + 10 )

= 10 + 10 + 10 + 10 + 15

= 55

37 x 27 x 63 x27

=(37+63)x27

=100 x 27

37 x 27 + 63 x 27

= ( 37 + 63 ) x 27

= 100 x 27

= 2700

1 + 2 + 3 + 4 + ... + 97 + 98 + 99

= ( 1 + 99 ) + ( 2 + 98 ) + .... + ( 51 + 49 ) + 50

= 100 + 100 + ... + 100 + 50   ( có 49 số 100 )

= 100 x 49 + 50

= 4900 + 50

= 4950

1 + 2 + 3 +4 + 5 + 6 +7 + 8 + 9 + 10

= ( 1 + 9 ) + ( 2 + 8 ) + ( 3 + 7 ) + ( 4 + 6 ) + 10 + 5

= 10 + 10 + 10 + 10 +10 + 5

= 10 x 5 + 5

= 55

a) 27.(15-12)-15.(27-12)

= 27.15-27.12-15.27-15.12

=405 - 324 - 405 - 180

= -504

a: =17+100

=117

2/3 x 4/5 + 4/5 x 8/3 = 4/5 x (2/3 + 8/3) = 4/5 x 10/3 = 8/3

27/32 x 16/9 -27/32 x7/9 + 27/32 

= 27/32 x (16/9 - 7/9 + 1 )

=27/32 x 2 

=27/16

\(\frac{2}{3}\) x   \(\frac{4}{5}\) +    \(\frac{4}{5}\) x     \(\frac{8}{3}\)

=\(\frac{4}{5}\) x    ( \(\frac{2}{3}\) +    \(\frac{8}{3}\) )

= \(\frac{4}{5}\) x    \(\frac{10}{3}\)

= \(\frac{40}{15}\) = \(\frac{8}{5}\)

A tính theo công thức tính tổng dãy số cách đều có khoảng cách là 3 (cấp số cộng có d=3)

\(3C=2x3x3+3x4x3+4x5x3+5x6x3+...x199x200x3+200x201x3\)

\(3C=2x3x\left(4-1\right)+3x4x\left(5-2\right)+4x5x\left(6-3\right)+...+200x201\left(202-199\right)\)

3C=--1x2x3+2x3x4-2x3x4+3x4x5-3x4x5+4x5x6-...-199x200x201+200x201x202

3C=200x201x202-1x2x3=> C=(200x201x202-1x2x3):3=200x67x202-2

Tính nhanh :

A = 2 + 5 + 8 + 11 +........+ 322 + 325 = ?????  

B = 1 x 3 + 5 x 7 + 9 x 11 + ..... + 301 x 303 = ????

C = 2 x 3 + 3 x 4 + 4 x 5 + 5 x 6 + ..... + 199 x 200 + 200 x 201 = ???????

a: \(=68\cdot72\cdot49\cdot\left[324-324\right]=0\)

b: \(=\left(1250-1250\right)\cdot\left(1+...+100\right)=0\)

\(a,\left(68\times72\times49\right)\times\left(27\times12-9\times36\right)=\left(68\times72\times49\right)\times0=0\\ b,\left(25\times50-125\times10\right)\times\left(1+2+...+100\right)=0\times\left(1+2+...+100\right)=0\)

a, ( 68 × 72 × 49 ) × ( 27 × 12 − 9 × 36 ) = ( 68 × 72 × 49 ) × 0 =

b, ( 25 × 50 − 125 × 10 ) × ( 1 + 2 + ... + 100 ) = 0 × ( 1 + 2 + ... + 100 ) = 0

P/s : mk làm từng phần một

\(\left(\frac{2}{3}\right)^x=\frac{8}{27}=\left(\frac{2}{3}\right)^3\)

=> x = 3

Vậy,........

2)

\(\left(\frac{5}{6}x+\frac{1}{2}\right)^2=\frac{9}{16}=\left(\frac{3}{4}\right)^2\)

\(\frac{5}{6}x+\frac{1}{2}=\frac{3}{4}\)

\(\frac{5}{6}x=\frac{1}{4}\)

\(x=\frac{3}{10}\)

3)

\(\left(\frac{2}{3}x+\frac{5}{6}\right)^3=\frac{-125}{27}=\left(\frac{-5}{3}\right)^3\)

\(\frac{2}{3}x+\frac{5}{6}=-\frac{5}{3}\)

\(\frac{2}{3}x=\frac{-5}{2}\)

\(x=\frac{-15}{4}\)