Ta có: \(A=\frac{5}{18x23}+\frac{1}{23x24}+\frac{7}{24x31}+\frac{2}{31x33}+\frac{4}{33x37}+\frac{1}{37x38}+\frac{7}{38x45}+\frac{9}{45x54}\)

\(\Rightarrow A=\frac{1}{18}-\frac{1}{23}+\frac{1}{23}-\frac{1}{24}+\frac{1}{24}-\frac{1}{31}+...+\frac{1}{38}-\frac{1}{45}+\frac{1}{45}-\frac{1}{54}\)

\(\Rightarrow A=\frac{1}{18}-\frac{1}{54}\)

\(\Rightarrow A=\frac{3}{54}-\frac{1}{54}=\frac{1}{27}\)

Vậy \(A=\frac{1}{27}\)

*Công thức: \(\frac{a}{b.c}=\frac{1}{b}-\frac{1}{c}\left(a+b=c\right)\)

Tớ mới chuẩn bị lớp 6 thôi, ko hiểu đâu.

Bài 1:

a) \(\frac{16}{15}.\frac{\left(-5\right)}{14}.\frac{54}{24}.\frac{56}{21}\)

\(=\frac{4.2.2}{5.3}.\frac{\left(-5\right)}{2.7}.\frac{3.3}{4}.\frac{8}{3}\)

\(=\frac{4.2.2.\left(-5\right).3.3.8}{5.3.2.7.4.3}\)

\(=\frac{-16}{7}\)

b) \(\frac{7}{3}.\frac{\left(-5\right)}{2}.\frac{15}{21}.\frac{4}{\left(-5\right)}\)

\(=\frac{7}{3}.\frac{\left(-5\right)}{2}.\frac{5}{7}.\frac{2.2}{\left(-5\right)}\)

\(=\frac{7.\left(-5\right).5.2.2}{3.2.7.\left(-5\right)}\)

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

Bài 2:

a) \(\frac{21}{24}.\frac{11}{9}.\frac{5}{7}=\frac{7}{8}.\frac{11}{9}.\frac{5}{7}=\frac{11.5}{8.9}=\frac{55}{72}\)

b) \(\frac{5}{23}.\frac{17}{26}+\frac{5}{23}.\frac{9}{26}\)

\(=\frac{5}{23}.\left(\frac{17}{26}+\frac{9}{26}\right)=\frac{5}{23}.1=\frac{5}{23}\)

c) \(\left(\frac{3}{29}-\frac{1}{5}\right).\frac{29}{3}=\frac{3}{29}.\frac{29}{3}-\frac{1}{5}.\frac{29}{3}\)

\(=1-1\frac{14}{15}=\frac{14}{15}\)

Bài 3:

a) x/5 = 2/5

=> x =2

b) -4/x = 20/14 = 10/7

=> -4/x = 10/7

=> x.10 = (-4).7

x.10 = - 28

x= -28 :10

x= -2,8

c) 4/7 = 12/x = 12/ 21

=> 12/x = 12/21

=> x = 21

d) 3/7 = x / 21 = 9/21

=> x/21 = 9/21

=> x= 9

(a x 27 + 116 x b): c

= (1368 x 27 + 116 x 54) : 108

= (36936 + 6264) : 108

= 43200 : 108

= 400

( a x 27 + 116 x b ) : c

= ( 1368 x 27 + 116 x 54 ) : 108

= ( 684 x 54 + 116 x 54 ) : 108

= [ ( 684 + 116 ) x 54 ] : 108

= ( 800 x 54 ) : 108

= 400 x 108 : 108

= 400

   23x55+45x23+250

=23x(55+45)+250

=23x100+250

=2300+250

=2550

1.

a, (x+50)*2=220

=> 2x+100=220

=> 2x = 120

=> x= 60

b, (2x-75)*12=144

=> 24x-900=144

=> 24x=1044

=>  x= 43,5

c, (47-3x)=5

=> 47-3x=5

=> 3x=42

=> x= 14

A. ( x + 50 ) x 2= 220

=> 2x + 100 = 220

=> 2x = 220 - 100

=> 2x = 120

=> x = 120 : 2

=> x = 60

B. ( 2x - 75 ) x 12 = 144

=> (2x - 75) x 12 = 144

=> 2x - 75 = 144 : 12

=> 2x - 75 = 12

=> 2x = 75 + 12 

=> 2x = 87

=> x = 87 : 2 = 43,5

C. 47 - 3x = 5

=> 3x = 47 - 5 = 42

=> x = 42 : 3

=> x = 14.

2)1 + 2 + 3 + 4 + 5 +..+ X = 2550

=> \(\frac{x.\left(x+1\right)}{2}\)=2550

=> x.(x+1) = 2550 x 2 = 5100. Mà không có 2 số liên tiếp nào nhân với nhau bằng 5100 nên x không thỏa mãn đề bài.

3)Đề sai nha bạn.

a)\(\left(x+50\right).2=220\)

\(\left(x+50\right)=220:2\)

\(x+50=110\)

\(x=110-50\)

\(x=60\)

b)\(\left(2x-75\right).12=144\)

\(\left(2x-75\right)=144:12\)

\(2x-75=12\)

\(2x=12+75\)

\(2x=87\)

\(x=87:2\)

\(x\notin N\)

c)\(\left(47-3x\right)=5\)

\(3x=47-5\)

\(3x=42\)

\(x=42:3\)

\(x=14\)

Câu 10:

\(a,y\times7+y\times3=70\\ \Rightarrow y\times\left(7+3\right)=70\\ \Rightarrow y\times10=70\\ \Rightarrow y=7\\ b,18:y+12:y=3\\ \Rightarrow\left(18+12\right):y=3\\ \Rightarrow30:y=3\\ \Rightarrow y=10\)

câu 11:

\(a,9\times365+2\times365-365=\left(9+2-1\right)\times365=10\times365=3650\\ b,108:9-18:9=\left(108-18\right):9=90:9=10\\ c,43\times95+4\times43+43=43\times\left(95+4+1\right)=43\times100=4300\)

1

a ) 

( 9407 - 7274 ) : y = 8058 : 34 

       2133         : y =    237 

                         y =     2133 : 237 

                        y =      9

b )

y x 128 - y x 17 - y x 11 = 576000

y x ( 128 - 17 - 11 )       = 576000

y x         100                  = 576000

y                                   = 576000 : 100

y                                  = 5760 

2

a )

( 125 x 36 ) : ( 5 x 9 ) =

    4500       :      45    =

         100

b )

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

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

          1            +            1          +            1           +          1             + 0,5 =

                                    4,

Chúc bạn học giỏi nhé !

bài 5:

tìm y:

y + 1 = 123

y = 123 - 1

y = 122

\(108\times5+108\times96-108=108\times\left(5+96-1\right)\)

                                                              \(=108\times100=10800\)

`108xx5+108xx96-108`

`=108xx(5+96-1)`

`=108xx100`

`=10800`