5,5 + \(\dfrac{3}{4}\) - 5 + \(\dfrac{1}{4}\)

(5,5 - 5) + (\(\dfrac{3}{4}\) + \(\dfrac{1}{4}\))

= 0,5  + 1

= 1,5 

\(\dfrac{5}{2}\) x  \(\dfrac{2}{3}\) + \(\dfrac{1}{4}\) : \(\dfrac{3}{2}\)

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

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

= (\(\dfrac{10}{4}\) + \(\dfrac{1}{4}\)) x \(\dfrac{2}{3}\)

= \(\dfrac{11}{4}\) x \(\dfrac{2}{3}\)

= \(\dfrac{11}{6}\) 

Tính \(x\): 

  435  - [\(x\) + 16] = 425 : 17

  435 - [\(x\) + 16] = 25

          [\(x\) + 16] = 435 - 25

           \(x\) + 16 = 410

           \(x\)        = 410 - 16

          \(x\)         = 394

\(x\) x \(\dfrac{1}{4}\) - \(\dfrac{3}{4}\) = 6 : \(\dfrac{3}{4}\)

\(x\) \(\times\) \(\dfrac{1}{4}\) - \(\dfrac{3}{4}\) = 6 x \(\dfrac{4}{3}\)

\(x\) x \(\dfrac{1}{4}\) - \(\dfrac{3}{4}\)  = 8

\(x\) x \(\dfrac{1}{4}\)        = 8 + \(\dfrac{3}{4}\)

\(x\) x \(\dfrac{1}{4}\)        = \(\dfrac{32}{4}\) + \(\dfrac{3}{4}\)

\(x\) x \(\dfrac{1}{4}\)       = \(\dfrac{35}{4}\)

\(x\)              =  \(\dfrac{35}{4}\) : \(\dfrac{1}{4}\)

\(x\)              = \(\dfrac{35}{4}\) x 4

\(x\)             = 35

Bài 1

a) 3 2/5 - 1/2

= 17/5 - 1/2

= 34/10 - 5/10

= 29/10

b) 4/5 + 1/5 × 3/4

= 4/5 + 3/20

= 16/20 + 3/20

= 19/20

c) 3 1/2 × 1 1/7

= 7/2 × 8/7

= 4

d) 4 1/6 : 2 1/3

= 25/6 : 7/3

= 25/14

Bài 2

a) 3 × 1/2 + 1/4 × 1/3

= 3/2 + 1/12

= 18/12 + 1/12

= 19/12

b) 1 4/5 - 2/3 : 2 1/3

= 9/5 - 2/3 : 7/3

= 9/5 - 2/7

= 63/35 - 10/35

= 53/35

Bài 1

a) 3 2/5 - 1/2

= 17/5 - 1/2

= 34/10 - 5/10

= 29/10

b) 4/5 + 1/5 × 3/4

= 4/5 + 3/20

= 16/20 + 3/20

= 19/20

c) 3 1/2 × 1 1/7

= 7/2 × 8/7

= 4

d) 4 1/6 : 2 1/3

= 25/6 : 7/3

= 25/14

bủh

a)\(\dfrac{2}{3}.\dfrac{4}{5}+\dfrac{1}{3}.\dfrac{4}{5}=\left(\dfrac{2}{3}+\dfrac{1}{3}\right).\dfrac{4}{5}=1.\dfrac{4}{5}=\dfrac{4}{5}\)

b)\(\dfrac{2}{3}.\dfrac{4}{5}-\dfrac{1}{3}.\dfrac{4}{5}=\left(\dfrac{2}{3}-\dfrac{1}{3}\right).\dfrac{4}{5}=\dfrac{1}{3}.\dfrac{4}{5}=\dfrac{4}{15}\)

a) \(\dfrac{2}{3}\times\dfrac{4}{5}+\dfrac{1}{3}\times\dfrac{4}{5}=\dfrac{4}{5}\times\left(\dfrac{2}{3}+\dfrac{1}{3}\right)=\dfrac{4}{5}\times1=\dfrac{4}{5}\)

b) \(\dfrac{2}{3}\times\dfrac{4}{5}-\dfrac{1}{3}\times\dfrac{4}{5}=\dfrac{4}{5}\times\left(\dfrac{2}{3}-\dfrac{1}{3}\right)=\dfrac{4}{5}\times\dfrac{1}{3}=\dfrac{4}{15}\)

c) \(\dfrac{1}{2}:\dfrac{3}{4}+\dfrac{1}{6}:\dfrac{3}{4}=\dfrac{1}{2}\times\dfrac{4}{3}+\dfrac{1}{6}\times\dfrac{4}{3}=\dfrac{4}{3}\times\left(\dfrac{1}{2}+\dfrac{1}{6}\right)=\dfrac{4}{3}\times\dfrac{2}{3}=\dfrac{8}{9}\)

d) \(\dfrac{1}{2}:\dfrac{3}{4}-\dfrac{1}{6}:\dfrac{3}{4}=\dfrac{1}{2}\times\dfrac{4}{3}-\dfrac{1}{6}\times\dfrac{4}{3}=\dfrac{4}{3}\left(\dfrac{1}{2}-\dfrac{1}{6}\right)=\dfrac{4}{3}\times\dfrac{1}{3}=\dfrac{4}{9}\)

c)\(\dfrac{1}{2}:\dfrac{3}{4}+\dfrac{1}{6}:\dfrac{3}{4}=\dfrac{1}{2}.\dfrac{4}{3}+\dfrac{1}{6}.\dfrac{4}{3}=\left(\dfrac{1}{2}+\dfrac{1}{6}\right).\dfrac{4}{3}=\dfrac{2}{3}.\dfrac{4}{3}=\dfrac{8}{9}\)

d)\(\dfrac{1}{2}:\dfrac{3}{4}-\dfrac{1}{6}:\dfrac{3}{4}=\dfrac{1}{2}.\dfrac{4}{3}-\dfrac{1}{6}.\dfrac{4}{3}=\left(\dfrac{1}{2}-\dfrac{1}{6}\right).\dfrac{4}{3}=\dfrac{1}{3}.\dfrac{4}{3}=\dfrac{4}{9}\)

Sửa đề: Các dấu bằng ở yêu cầu là dấu cộng.

1. Có: \(x+y=3\)

\(\Leftrightarrow\left(x+y\right)^2=3^2\)

\(\Leftrightarrow x^2+2xy+y^2=9\)

\(\Leftrightarrow x^2+y^2=9-2\cdot1=7\) (do \(xy=1\))

\(------\)

Lại có: \(x+y=3\)

\(\Leftrightarrow\left(x+y\right)^3=3^3\)

\(\Leftrightarrow x^3+y^3+3xy\left(x+y\right)=27\)

\(\Leftrightarrow x^3+y^3+3\cdot1\cdot3=27\) (do x + y = 3; xy = 1)

\(\Leftrightarrow x^3+y^3=18\)

Ta có: \(x^2+y^2=7\)

\(\Leftrightarrow\left(x^2+y^2\right)^2=7^2\)

\(\Leftrightarrow x^4+y^4+2\cdot\left(xy\right)^2=49\)

\(\Leftrightarrow x^4+y^4=49-2\cdot1=47\) (do xy = 1)

2 câu c,d làm tương tự  

5:

a: \(3^{2n}=\left(3^2\right)^n=9^n\)

\(\left(2^{3n}\right)=\left(2^3\right)^n=8^n\)

=>\(3^{2n}>2^{3n}\)

b: \(199^{20}=\left(199^4\right)^5=1568239201^5\)

\(2003^{15}=\left(2003^3\right)^5=8036054027^5\)

mà \(1568239201< 8036054027\)

nên \(199^{20}< 2003^{15}\)

4: \(100< 5^{2x-1}< 5^6\)

mà \(25< 100< 125\)

nên \(125< 5^{2x-1}< 5^6\)

=>3<2x-1<6

=>4<2x<7

=>2<x<7/2

mà x nguyên

nên x=3

2^2022 mà bạn chuche ơi

A = 2⁵.(-5)² - 8² - 7

= 32.25 - 64 - 7

= 729

= 27²

B = 2³.(-4)² + (-3)².3² - 40

= 8.16 + 9.9 - 40

= 169

= 13²

C = (1/4 - 1/2 - 1)³ . (2 - 2/5)³

= (-5/4)³ . (8/5)³

= (-5/4 . 8/5)³

= (-2)³

D = (-1/4)² : (1/2 - 1/3)

= 1/16 : 1/6

= 3/8

E = 4 . (1/4)² + 25 . [(3/4)³ : (5/4)³] : (3/2)³

= 1/4 + 25 . (3/4 . 5/4)³ : (3/2)³

= 1/4 + 25 . (15/16)³ : 27/8

= 1/4 + 25 . 3375/4096 : 27/8

= 1/4 + 84375/4096 : 27/8

= 1/4 + 3125/512

= 3253/512

F = 2³ + 3.(1/2)⁰ - 1 + [(-2)² : 1/2] - 8

= 8 + 3.1 - 1 + (4 : 1/2) - 8

= 8 + 3 - 1 + 8 - 8

= 10

Cách 1:
Xét số bị trừ, ta có:
(2/3 + 3/4 + 4/5 + ... + 2016/2017) x (1/2 + 2/3 + 3/4 + ... + 2015/2016)
= (2/3 + 3/4 + 4/5 + ... + 2015/2016 + 2016/2017) x (1/2 + 2/3 + 3/4 + ... + 2015/2016)
= (2/3 + 3/4 + 4/5 + ... + 2015/2016) x (1/2 + 2/3 + 3/4 + ... + 2015/2016) + 2016/2017 x (1/2 + 2/3 + 3/4 + ... + 2015/2016)
Xét số trừ, ta có: 
(1/2 + 2/3 + 3/4 + ... + 2016/2017) x (2/3 + 3/4 + 4/5 + ... + 2015/2016)
= (1/2 + 2/3 + 3/4 + ... + 2015/2016 + 2016/2017) x (2/3 + 3/4 + 4/5 + ... + 2015/2016)
= (1/2 + 2/3 + 3/4 + ... + 2015/2016) x (2/3 + 3/4 + 4/5 + ... + 2015/2016) + 2016/2017 x (2/3 +3/4 + 4/5 + ... + 2015/2016) =
Ta thấy số bị trừ và số trừ có số hạng giống nhau là:
(2/3 +3/4 + 4/5 + ... + 2015/2016) x (1/2 + 2/3 + 3/4 + ... + 2015/2016)
Nên phép trừ trên có thể viết lại:
2016/2017 x (1/2 + 2/3 + 3/4 + ... + 2015/2016) - 2016/2017 x (2/3 + 3/4 + 4/5 + ... + 2015/2016)
= 2016/2017 x [(1/2 + 2/3 + 3/4 + ... + 2015/2016) - (2/3 +3/4 + 4/5 + ... + 2015/2016)]
= 2016/2017 x 1/2
= 1008/2017

Cách 2:

Là 1008/2017 đó nha

Tính: (2/3 + 3/4 + 4/5 + ... + 2016/2017) x (1/2 + 2/3 + 3/4 + ... + 2015/2016) – (1/2 + 2/3 + 3/4 + ... + 2016/2017) x (2/3 + 3/4 + 4/5 + ... + 2015/2016).

a) 1/2x1/3 +1/3x1/4

cách 1: 1/2 x1/3+ 1/3 x1/4

=1/6 + 1/12 

= 1/4

cách 2: 1/2 x1/3+ 1/3 x1/4

= 1/3x (1/2+1/4)

= 1/3x3/4

= 1/4

b) (3/4+ 1/2)x2

cách 1: (3/4+1/2)x2

= 5/4x2

= 5/4

cách 2: (3/4+1/2)x2

=3/4 x2 + 1/2x2

=3/2+2/2

= 5/4

a. \(\frac{1}{2}\times\frac{1}{3}+\frac{1}{3}\times\frac{1}{4}\) 

Cách 1 = \(\frac{1}{3}\times\left(\frac{1}{2}+\frac{1}{4}\right)\)                                 Cách 2 =\(\frac{1}{6}+\frac{1}{12}\)

            = \(\frac{1}{3}\times\frac{3}{4}\)                                                                 =\(\frac{1}{4}\)

            =\(\frac{1}{4}\)

b. \(\left(\frac{3}{4}+\frac{1}{2}\right)\times2\)                        

Cách 1    =\(\frac{5}{4}\times2\)                                              Cách 2           =\(\frac{3}{4}\times2+\frac{1}{2}\times2\)

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

                                                                                                          =\(\frac{5}{2}\)

c. \(\frac{1}{2}\times\frac{1}{3}-\frac{1}{3}\times\frac{1}{4}\)

C1           =\(\frac{1}{3}\times\left(\frac{1}{2}-\frac{1}{4}\right)\)                                 C2              =\(\frac{1}{6}-\frac{1}{12}\)

                =\(\frac{1}{3}\times\frac{1}{4}\)                                                                      =\(\frac{1}{12}\)

                =\(\frac{1}{12}\)

d. \(\left(\frac{4}{3}-\frac{1}{2}\right)\times\frac{2}{3}\)

C1           =\(\frac{5}{6}\times\frac{2}{3}\)                                        C2              =\(\frac{4}{3}\times\frac{2}{3}-\frac{1}{2}\times\frac{2}{3}\)

                =\(\frac{5}{9}\)                                                                       =\(\frac{8}{9}-\frac{2}{6}\)

                                                                                                   =\(\frac{5}{9}\)

a: =91/105+60/105-101/105

=50/105=10/21

c: \(\dfrac{3}{4}\cdot\dfrac{5}{2}\cdot\dfrac{7}{6}=\dfrac{3}{6}\cdot\dfrac{7}{2}\cdot\dfrac{5}{4}=\dfrac{1}{2}\cdot\dfrac{7}{2}\cdot\dfrac{5}{4}=\dfrac{35}{16}\)

d: =2-2/9

=18/9-2/9

=16/9

e: =24/36-9/36+8/36

=23/36

g: =5/2+1/2

=3

a) Cách 1 : (3/4 + 1/2) x 5/7

               = 5/4 x 5/7

                = 25/28

Cách 2 : (3/4 + 1/2) x 5/7

           = 3/4 x 5/7 + 1/2 x 5/7

            = 15/28 + 5/14

            = 25/28

b) Cách 1 : 5/7 x 13/21 + 2/7 x 13/21

= 65/147 + 26/147

= 13/21

Cách 2 : 5/7 x 13/21 + 2/7 x 13/21

= (5/7 + 2/7) x 13/21

= 1 x 13/21

= 13/21

câu c tự làm

8 /15 :2/3+7/15:2/3 =                                              tính bằng 2 cách nhé các bạn

Cách 1:6/8+4/8+5/7=10/8*5/7=50/56=25/28

Cách 2 :3/4*5/7+1/2*
5/7=15/28+10/28=25/28

Cái này thầy tôi đã chữa yên tâm