Mình mới làm được phần (b) thôi bạn Natsu Dragneel , phần (a) khó quá !

\(b,\frac{167x198+98}{198x168-100}\)

\(=\frac{167x198+98}{198x\left(167+1\right)-100}\)

\(=\frac{167x198+98}{198x167+198x1-100}\)

\(=\frac{167x198+98}{198x167+98}=1\)

\(17.8+51.4=34.4+51.4=4\left(51+34\right)=4.84=336\) \(2.2.3.5.19=\left(2.5\right).\left(3.19\right).2=10.2.57=570.2=1140\) \(54.275+825.15+275=54.275+45.275+275=275\left(54+45+1\right)=100.275=27500\) \(\frac{167.198+98}{198.168-100}=\frac{167.198+98}{198.167+198-100}=\frac{167.198+98}{167.198+98}=1\)

\(\frac{1}{n}-\frac{1}{n+k}=\frac{k}{n\left(n+k\right)}\Rightarrow\frac{1}{1.2}+\frac{1}{2.3}+.....+\frac{1}{2019.2020}=1-\frac{1}{2}+\frac{1}{2}-....-\frac{1}{2020}=1-\frac{1}{2020}=\frac{2019}{2020}\)

a) 17 x 8 + 51 x 4

= 17 x 4 x 2 + 17 x 3 x 4

= 17 x 4 x ( 2 + 3 )

= 14 x 4 x 5

= 14 x 20

= 280

b) 2 x 2 x 3 x 5 x 19

= ( 2 x 5 ) x ( 3 x 19 ) x 2

= 10 x 57 x 2

= 570 x 2

= 1140

c) 54 x 275 + 825 x 15 + 275

= 54 x 275 + 275 x 3 x 15 + 275 x 1

= 54 x 275 + 275 x 45 + 275 x 1

= 275 x ( 54 + 45 + 1 )

= 275 x 100

= 27500

d) 100 - 99 + 98 - 97 + 96 - 95 + 94 - 93 + ... + 4 - 3 + 2

= (100 - 99) + (98 - 97) + (96 - 95) + (94 - 93) + ... + (4 - 3) + 2

= (1 + 1 + ... + 1) + 2

( 49 số 1 )

= 49 + 2

= 51

k) 1,5 + 2,5 + 3,5 + 4,5 + 5,5 + 6,5 + 7,5 + 8,5

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

= 10 + 10 + 10 + 10

= 40

chỉ có 1 37/12 thôi viết nhầm

=10,231

Bài 1 :

Ta có : 120 = 6 x 20

           120 = 3 x 2 x 4 x 5

Vậy số đó là : 3245

Bài 2 :

A =\(\left(\frac{28}{31}:\frac{8}{9}\right):\left(\frac{7}{31}:\frac{2}{9}\right)\)

A = \(\left(\frac{28}{31}X\frac{9}{8}\right):\left(\frac{7}{31}X\frac{9}{2}\right)\) 

A = \(\left(\frac{28X9}{31X8}\right):\left(\frac{7X9}{31X2}\right)\)

A =\(\frac{28X9}{31X8}X\frac{31X2}{7X9}\)

A = \(\frac{28X9X31X2}{31X8X7X9}\)

A = \(\frac{28X2}{8X7}\)

A = \(\frac{7X4X2}{4X2X7}\)

A = 1

Bài 1: số đó là: 456

Bài 2: 

A = \(\left(\frac{28}{31}:\frac{8}{9}\right):\left(\frac{7}{31}:\frac{2}{9}\right)\)

   \(=\left(\frac{28}{31}.\frac{9}{8}\right):\left(\frac{7}{31}.\frac{9}{2}\right)\)

    \(=\frac{63}{62}:\frac{63}{62}=1\)

VẬy: A = 1

Chú ý: Dấu \(.\)là dấu nhân.

\(\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}+...+\frac{1}{2005\times2006}\)                                                                                           =\(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{2005}-\frac{1}{2006}\)                                                                 =\(\frac{1}{3}-\frac{1}{2006}=\frac{2003}{6018}\)

\(=\dfrac{2005^2-10}{2005^2-2005+2005-10}\)

\(=\dfrac{2005^2-10}{2005^2-10}=1\)

=1/3-1/4+1/4-1/5+...+1/2005-1/2006

=1/3-1/2006

=2006/6018-3/6018

=2003/6018

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