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1.
a) \(\frac{-7}{9}.2\frac{3}{4}=\frac{-7}{9}.\frac{11}{4}=\frac{-77}{36}\)
b) \(\frac{2}{3}+\frac{1}{3}.\frac{-2}{5}=\frac{2}{3}+\frac{-2}{15}=\frac{8}{15}\)
c) \(\frac{3}{4}.15\frac{1}{3}-\frac{3}{4}.43\frac{1}{3}=\frac{3}{4}.\frac{46}{3}-\frac{3}{4}.\frac{130}{3}=\frac{23}{2}-\frac{65}{2}=-21\)
d) \(\left(-49,1\right).\frac{13}{27}-58,9.\frac{13}{27}=\frac{13}{27}.\left(-49,1-58,9\right)=\frac{13}{27}.\left(-108\right)=-52\)
e) \(0,375:\left(-4,5\right)=\frac{-1}{12}\)
f) \(3\frac{1}{7}:\left(-1\frac{3}{7}\right)=\frac{22}{7}:\frac{-10}{7}=\frac{-11}{5}\)
g) \(9\frac{1}{3}:4\frac{2}{3}-2=\frac{28}{3}:\frac{14}{3}-2=2-2=0\)
h) \(\left(7\frac{3}{4}:0,3125+4,5.2\frac{2}{45}\right):\left(-8,5\right)=\left(\frac{31}{4}:\frac{5}{16}+\frac{9}{2}.\frac{92}{45}\right):\frac{-17}{2}=\left(\frac{124}{5}+\frac{46}{5}\right):\frac{-17}{2}=34:\frac{-17}{2}=-4\)
Bài 1 : Tính:
a)
\(\frac{-7}{9}.2\frac{3}{4}=\frac{-7}{9}.\frac{11}{4}=\frac{-77}{36}\)
b)
\(\frac{2}{3}+\frac{1}{3}.\frac{-2}{5}=\frac{2}{3}+\frac{-2}{15}=\frac{10}{15}+\frac{-2}{15}=\frac{8}{15}\)
c)
\(\frac{3}{4}.15\frac{1}{3}-\frac{3}{4}.43\frac{1}{3}=\frac{3}{4}.\frac{46}{3}-\frac{3}{4}.\frac{130}{3}\)\(=\frac{23}{2}-\frac{65}{2}=\frac{-42}{2}=-21\)
....
Tự lm tiếp dạng như v
Bài 2 :
\(A=\frac{-6}{11}.\frac{7}{10}.\frac{11}{-6}.-20=\left(\frac{-6}{11}.\frac{11}{-6}\right).\left(\frac{7}{10}.-20\right)\)\(=1.\left(-14\right)=-14\)
.....
Bài 3 :
\(\frac{3}{7}.x-\frac{2}{5}.x=\frac{-17}{35}\)
\(\Leftrightarrow\frac{3}{7}-\frac{2}{5}.x=\frac{-17}{35}\)
\(\Leftrightarrow\frac{1}{35}x=\frac{-17}{35}\)
\(\Leftrightarrow x=\frac{-17}{35}:\frac{1}{35}\)
\(\Leftrightarrow x=\frac{-17}{35}.35=-17\)
A=\(2^2-9^3+4^{-2}.16-2.5^2\)
\(=4-729+1-50=-774\)
B=\(\left(2^3.2\right).\dfrac{1}{2}+3^{-2}.3^2-7.1+5\)
\(B=2^4.\dfrac{1}{2}+1-7+5=8+1-7+5=7\)
C = 2-3 + (52)3.5-3 + 4-3.16 - 2.32 - 105.(\(\dfrac{24}{51}\))0
C = \(\dfrac{1}{8}\) + 56.5-3 + 4-3.42 - 2.9 - 105.1
C = \(\dfrac{1}{8}\) + 53 + \(\dfrac{1}{4}\) - 18 - 105
C = (\(\dfrac{1}{8}\) + \(\dfrac{1}{4}\)) - (105 - 125 + 18)
C = \(\dfrac{3}{8}\) - (-20 + 18)
C = \(\dfrac{3}{8}\) + 2
C = \(\dfrac{19}{8}\)
a) 2n = 16/2=8= 23 => n =3
b) (-3)n = (-27).81 =(-3)3.34= (-3)7 => n = 7
c) 4 =22= 23n.2n = 23n-n = 22n => n =1
Bài 4 :
Gọi các số đó là a,a+1,a+2,a+3.......,a+45
Ta có
a+(a+1)+(a+2)+(a+3)+..........+(a+45)
46a+ (1+2+3+4+5+.........+45)
46a+1035
Ta thấy 46a chia hết cho 46 , 1035 không chia hết cho 46
=> 46a +1035 không chia hết cho 46
Vậy 46 số tự nhiên liên tiếp không chia hết cho 46
Nếu n chia 5 dư 1, 3 thì n^2 chia 5 dư 1
=> n^2 + 4 chia hết cho 5
Nếu n chia 5 dư 2,4 thì n^2 chia 5 dư 4
=> n^2 + 1 chia hết cho 5
Nếu n chia hết cho 5
=> A chia hết cho 5
a) Ta có:
C = 5/18 + 8/19 - 7/21 + (-10/36 + 11/19 + 1/3) - 5/8
C = 5/18 + 8/19 - 1/3 - 5/18 + 11/19 + 1/3 - 5/8
C = (5/18 - 5/18) + (8/19 + 11/19) - (1/3 - 1/3) - 5/8
C = 1 - 5/8
c = 3/8
b) F = 15/14 - (17/23 - 80/87 + 5/4) + (17/23 - 15/14 + 1/4)
F = 15/14 - 17/23 + 80/87 - 5/4 + 17/23 - 15/14 + 1/4
F = (15/14 - 15/14) - (17/23 - 17/23) + 80/87 - (5/4 - 1/4)
F = 80/87 - 1
F = -7/87
c) G = 1/25 - 4/27 + (-23/27 + -1/25 - 5/43) + 5/43 - 4/7
G = 1/25 - 4/27 - 23/27 - 1/25 - 5/43 + 5/43 - 4/7
G = (1/25 - 1/25) - (4/27 + 23/27) - (5/43 - 5/43) - 4/7
G = -1 - 4/7 = -11/7
Help me!