2+5+9+10+1
10+58+2
Tính bằng cách thuận tiện
a. 42 + 24 + 58
c. 110 +3 4 - 10
b. 2 × 3 × 5
d. 25 × 8
a) 58.(-45)+(-58).24+(-69).42
b) 139-(-65+239)-(85+120)
c) 22.3-(110+8):32
d) 500-{5[409-(23.3-21)2+103]}:15
a)58(-45+-24)+-69.42
=58.(-69)+(-69).42
=-69.(58+42)
=-69.100
=-6900
a;
A= 58.(-45) + (-58).24 + (-69).42
A = -58.(45 + 24) - 69.42
A =-58.69 - 69.42
A = -69.(58 + 42)
A = -69.100
A = -6900
b; 139 - (-65 + 239) - (85 + 120)
B = 139 + 65 - 239 - 85 - 120
B = -(239 - 139) - (85 - 65) - 120
B = - 100 - 20 - 120
B = - 120 - 120
B = - 240
c;
C = 22.3 - (110 + 8) : 32
C = 4.3 - (1 + 8) : 32
C = 12 - 9:9
C = 12 - 1
C = 11
d;
D = 500 - { 5.[409 - (23.3 - 21)2 + 103 ]}: 15
D = 500 -{5.[409 - (8.3 - 21)2 + 1000]} : 15
D = 500 - {5.[409 - (24 - 21)2 + 1000]} : 15
D = 500 - {5.[409 - 32 + 1000]} : 15
D = 500 - {5.[409 - 9 + 1000]} : 15
D = 500 - {5.(400 + 1000]} : 15
D = 500 - 5.1400 : 15
D = 500 - \(\dfrac{1400}{3}\)
D = \(\dfrac{100}{3}\)
Bài 1: Tính hợp lý ( nếu có thể )
a) - 23 . 63 + 23 . 21 - 58. 23.
b) ( -124) - 3. [ (-2) mũ 3 + 2 . ( 5 - 15 )
Bài 2 : Tìm số nguyên x, biết :
a) 5x - 30 = 2x - 110.
b) I - 9 - x I - 5 = 12.
Bài 1: Tính hợp lý ( nếu có thể )
a) - 23 . 63 + 23 . 21 - 58. 23.
b) ( -124) - 3. [ (-2) mũ 3 + 2 . ( 5 - 15 )
Bài 2 : Tìm số nguyên x, biết :
a) 5x - 30 = 2x - 110.
b) I - 9 - x I - 5 = 12.
tinh :
10 . 58 .5 + 32 . 2 .25 + 50 .10
20 - 2 . [ x - 1 ] = 4
[ x + 1 mũ 2 ]= 9
10 . 58 . 5 + 32 . 2 . 25 + 50 . 10
= 50 . 58 + 50 . 32 + 50 . 10
= 50 . ( 58 + 32 + 10 )
= 50 . 100
= 5000
20 - 2 . ( x - 1 ) = 4
\(\Rightarrow\)2 . ( x - 1 ) = 16
\(\Rightarrow\)x - 1 = 16 : 2
\(\Rightarrow\)x - 1 = 8
\(\Rightarrow\)x = 9
( x + 1 )2 = 9 = 32 = ( -3 )2
\(\Rightarrow\orbr{\begin{cases}x+1=3\\x+1=-3\end{cases}\Rightarrow\orbr{\begin{cases}x=3-1\\x=3+1\end{cases}\Rightarrow}\orbr{\begin{cases}x=2\\x=4\end{cases}}}\)
a,=50.28+32.50+50.10=50.(28+32+10)=50.70=3500
b.2(x-1)=20-4
x-1=16/2
x=8+1=9
c,
Tính
A=1*2+3*4+...+57*58
B=1*2*3+2*3*4+...+8*9*10
C=1*3*5+3*5*7+5*7*9+...+7*9*11
So sánh:
a,
\(\frac{10^{109}+2}{10^{110}-5}\)với \(\frac{10^{110}+2}{10^{111}-5}\)
b,
\(\frac{9^{65}-1}{9^{64}+2}\)với \(\frac{9^{70}-1}{9^{69}+2}\)
c,
\(\frac{1+11+11^2+....+11^{10}}{1+11+11^2+...+11^{11}}\)với \(\frac{1+13+13^2+..+13^{10}}{1+13+13^2+...+13^{11}}\)
d,
\(1+2+2^2+...+2^{80}\)với \(2^{81}-2\)
e,
\(\frac{3}{4}+\frac{8}{9}+\frac{15}{16}+..+\frac{899}{900}\) với 29
d)
đặt A = 1 + 2 + 22 + ... + 280
2A = 2 + 22 + 23 + ... + 281
2A - A = ( 2 + 22 + 23 + ... + 281 ) - ( 1 + 2 + 22 + ... + 280 )
A = 281 - 1 > 281 - 2
e)
đặt \(A=\frac{3}{4}+\frac{8}{9}+\frac{15}{16}+...+\frac{899}{900}\)
\(A=\left(1-\frac{1}{4}\right)+\left(1-\frac{1}{9}\right)+\left(1-\frac{1}{16}\right)+...+\left(1-\frac{1}{900}\right)\)
\(A=\left(1+1+1+...+1\right)-\left(\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+...+\frac{1}{900}\right)\)
\(A=29-\left(\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+...+\frac{1}{900}\right)\)
đặt \(B=\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+...+\frac{1}{900}\)
\(B=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{30^2}\)
\(B< \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{29.30}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{29}-\frac{1}{30}\)
\(=1-\frac{1}{30}=\frac{29}{30}< 1\)
\(\Rightarrow A< 29\)
So sánh C và D biết
C=1+13+13^2+...+13^13/1+13+13^2+...+13^12
D=1+11+11^2+...+11^13/1+11+11^2+...+11^12
9*9
110*106
1+1
2+2
3+3
4+4
5+5
6+6
7+7
8+8
9+9
10+10
11+11+12
13+14+15
81 ; 11660 ; 2 ; 4 ; 6 ; 8 ; 10 ; 12 ; 14 ; 16 ; 18 ; 20 ; 34 ; 42 .
81
11660
2
4
6
8
10
12
14
16
18
20
34
42
81;11660;2;4;6;8;10;12;14;16;18;20;34;42
f) -20:2^2+(-5)^9:5^8
g)-100:5^2+-7.(-3)^2
h)-84:4+3^9:(-3)^7+(-5)^0
i)-29-[16+3.(51-49)]
j)-58.75+58.(-50)-58.(-25)
f: \(-20:2^2+\left(-5\right)^9:5^8\)
\(=-20:4-5^9:5^8\)
=-5-5
=-10
g: \(-100:5^2+\left(-7\right)\cdot\left(-3\right)^2\)
\(=-\dfrac{100}{25}-7\cdot9\)
=-4-63
=-67
h: \(-84:4+3^9:\left(-3\right)^7+\left(-5\right)^0\)
\(=-21-3^9:3^7+1\)
\(=-21-3^2+1\)
=-20-9
=-29
i: \(-29-\left[16+3\left(51-49\right)\right]\)
\(=-29-16-3\cdot2\)
=-45-6
=-51
j: \(-58\cdot75+58\cdot\left(-50\right)-58\left(-25\right)\)
\(=58\cdot\left(-75\right)+58\left(-50\right)+58\cdot25\)
\(=58\left(-75-50+25\right)\)
\(=-58\cdot100=-5800\)