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a ) − 1 < 1 ; b ) 9 15 > 7 15 ; c ) − 1 2 > − 7 12 ; d ) 71 20 < 4
a) 1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + 9 - 10 + 11
= (1 - 2) + (3 - 4) + (5 - 6) + (7 - 8) + (9 - 10) + 11
= -1 + (-1) + (-1) + (-1) + (-1) + 11
= -1 x 5 + 11
= -5 + 11
= 6
b) 98 + 87 + 76 + ... + 21 - 12 - 23 - 34 - ... - 89
= (98 89) + (87 - 78) + ... + (21 - 12) (có 8 nhóm)
= 9 + 9 + ... + 9 (có 8 số 9)
= 9 x 8
= 72
\(1-2+3-4+.....-10+11\)
\(=\left(1-2\right)+\left(3-4\right)+...\left(9-10\right)+11\)
\(=1+\left(-1\right)+\left(-1\right)+\left(-1\right)+\left(-1\right)+11\)
\(=-1\times5+11\)
\(=6\)
\(\left(\frac{12}{199}+\frac{23}{200}-\frac{34}{201}\right)\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)\)
\(=\left(\frac{12}{199}+\frac{23}{200}-\frac{34}{201}\right)\left(\frac{6}{12}-\frac{4}{12}-\frac{2}{12}\right)\)
\(=\left(\frac{12}{199}+\frac{23}{200}-\frac{34}{201}\right).0\)
\(=0\)
a) (x - 7) + 5 = 16
=> x - 7 = 11
=> x = 18
b) 4 : x - 34 = 6
=> 4 : x = 40
=> x = \(\frac{1}{10}\)
c) 120 : ( x - 1 ) + 3 = 23
=> 120 : ( x - 1 ) = 20
=> x - 1 = 6
=> x = 7
d) 170 - ( x-7) : 5 = 20
=> ( x - 7 ) : 5 = 150
=> x - 7 = 750
=> x = 757
e) x + 12 + 2 .x + 3 = 4.x + 3
=> 3x + 17 = 4x + 3
=> x = 15
\(a,x-7=11\)
\(x=18\)
\(b,x-36=\frac{2}{3}\)
\(x=\frac{110}{3}\)
\(c,120:\left(x-1\right)=20\)
\(x-1=6\)
\(x=7\)
\(d,\left(x-7\right):5=150\)
\(x-7=10\)
\(x=17\)
\(d,x+12+2.x+3-4.x-3=0\)
\(x.\left(1+2-4\right)+3-3+12=0\)
\(x.\left(-1\right)+12=0\)
\(x.\left(-1\right)=-12\)
\(x=12\)
a)\(\frac{7}{13}.\frac{7}{15}-\frac{5}{12}.\frac{21}{39}+\frac{49}{21}.\frac{8}{15}\)
=\(\frac{7}{13}.\frac{7}{15}-\frac{5}{12}.\frac{7}{13}+\frac{7}{13}.\frac{8}{15}\)
=\(\frac{7}{13}.\left(\frac{7}{15}-\frac{5}{12}-\frac{8}{15}\right)\)
=\(\frac{7}{13}.\frac{7}{12}\)
=\(\frac{49}{156}\)
b)\(\left(\frac{12}{199}+\frac{23}{200}-\frac{34}{201}\right).\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)\)
=\(a.\left(\frac{3}{6}-\frac{2}{6}-\frac{1}{6}\right)\)
=a . 0
=0
Bài 2
a)Có
\(3^{200}=3^{2.100}=\left(3^2\right)^{100}=9^{100}\)
\(2^{300}=2^{3.100}=\left(2^3\right)^{100}=8^{100}\)
Vì 8<9 =>\(8^{100}< 9^{100}\) =>\(3^{200}>2^{300}\)
a) -23 + 13 - (-7)
= 10 + 7 = 17
b) |-40| : 8 + 4(-2) + |7|
= 5 + (-8) + 7 = 4