54 x 275 + 825 x 15 + 275 

=14850 + 825 x 15 + 275 

=14850 + 12375+275

=14850 + 12650

=27500

477x1998-1998x427

=1998x(477-427)

=1998x50

=99900

1985:2+15:2

=(1985+15):2

=2000:2

=1000

40x113x25-20x112x50

=(40x25)x113-(20x50)x112

=1000x113-1000-112

=1000x(113-112)

=1000x1

=1000

câu 1, ??????????????

câu 2, [477-427], +[1998-1998]=50+0=50

câu 3,[1985+15]:2=2000:2=1000

câu 4, ??????????

chú thích ? là ko có cách tính nhanh

54 x 275 + 825 x 15 + 275 

=14850 + 825 x 15 + 275 

=14850 + 12375+275

=14850 + 12650

=27500

477x1998-1998x427

=1998x(477-427)

=1998x50

=99900

1985:2+15:2

=(1985+15):2

=2000:2

=1000

40x113x25-20x112x50

=(40x25)x113-(20x50)x112

=1000x113-1000-112

=1000x(113-112)

=1000x1

=1000

Tham khảo

Bài 2: 

a: x+24=-15-4=-19

=>x=-19-24=-43

b: x+73=-127

=>x=-127-73=-200

c: |x-1|=|-10|+2=10+2=12

=>x-1=12 hoặc x-1=-12

=>x=13 hoặc x=-11

d: x+145=131-(-169)=131+169=300

=>x=155

e: x-96=443-(-15)=443+15=458

=>x=554

a) (15678 + 5938) x 4 = 21616 x 4    b) 9347 – 25636 : 4 = 9347 – 6409

   = 86464    = 2938

c) 21156 : 3 x 4 = 7052 x 4     d) 2450 : (825 – 820) = 2450 : 5

    = 28208    = 490

985

x + 102 = 825 + 143 

x + 102 = 968

x = 968 - 102 

x= 866

\(x+102=825+143\\ x+102=968\\ x=968-102=866\)

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

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

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

m) Đề bn xem ở trên

= \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\)

= \(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)

\(=\frac{1}{1}-\frac{1}{10}\)

\(=\frac{10}{10}-\frac{1}{10}=\frac{9}{10}\)

Vì ƯCLN(x;y) = 5

=> \(\hept{\begin{cases}x=5m\\y=5n\end{cases}\left(m;n\inℕ^∗\right);\left(m,n\right)=1}\)

Khi đó : xy = 825

<=> 5m.5n = 825

=> 25.mn = 825

=> mn = 33

Với m,n là số tự nhiên ta có : 33 = 11.3 = 1.33 

Lập bảng xét các trường hợp 

Vậy các cặp (x;y) thỏa mãn là : (5;165) ; (165;5) ; (55;15) ; (15;55) 

\(c,\)\(\left(x-1\right)+\left(x-2\right)+....+\left(x-100\right)=50\)

\(\left(x+x+...+x\right)-\left(1+2+...+100\right)=50\)

\(100x-5050=50\)

\(100x=50+5050\)

\(100x=5100\)

\(\Rightarrow x=\frac{5100}{100}=51\)

\(a,\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+....+\left(x+100\right)=5750\)

\(\left(x+x+x+...+x\right)+\left(1+2+3+...+100\right)=5750\)

\(100x+5050=5750\)

\(100x=5750-5050\)

\(100x=700\)

\(\Rightarrow x=7\)

\(b,x+\left(1+2+3+...+50\right)=2000\)

 \(x+\frac{\left[1+50\right]\cdot\left[\left(50-1\right)\div1+1\right]}{2}=2000\)

\(x+1275=2000\)

\(\Rightarrow x=2000-1275=725\)

c , ( x - 1 ) + ( x - 2 ) + ...... + ( x - 100 ) = 50

( x + x + ........ + ) - ( 1 + 2 + ..... + 100 ) = 50

100x - 5050 = 50

100x = 50 + 5050

100x = 5100

=> x = 5100/100 = 51