\(\dfrac{1}{12}.\dfrac{4}{33}+\dfrac{3}{4}.\dfrac{12}{99}\)
= \(\dfrac{1}{12}.\dfrac{12}{99}+\dfrac{3}{4}.\dfrac{12}{99}\)
= \(\left(\dfrac{1}{12}+\dfrac{9}{12}\right).\dfrac{12}{99}\)
= \(\dfrac{5}{6}.\dfrac{12}{99}\)
= \(0,1010101010...\)
Chứng minh:
a. \(A=\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{8}-\dfrac{1}{16}+\dfrac{1}{32}-\dfrac{1}{64}< \dfrac{1}{3}\)
b.\(B=\dfrac{1}{3}-\dfrac{2}{3^2}+\dfrac{3}{3^3}-\dfrac{4}{3^4}+...+\dfrac{99}{3^{99}}< \dfrac{3}{16}\)
c. \(C=\dfrac{1}{41}+\dfrac{1}{42}+\dfrac{1}{43}+...+\dfrac{1}{79}+\dfrac{1}{80}>\dfrac{7}{12}\)
1, So sánh A và B, biết :
A=\(\dfrac{2^{19}.27^3.15.4^9.9^4}{6^9.2^{10}+12^{10}}\)
B=\(\dfrac{4}{35}+\dfrac{4}{63}+\dfrac{4}{99}+\dfrac{4}{143}+\dfrac{4}{195}\)
Thực hiện các phép tính :
a) \(9,6.2\dfrac{1}{2}-\left(2.125-1\dfrac{5}{12}\right):\dfrac{1}{4}\)
b) \(\dfrac{5}{18}-1,456:\dfrac{7}{25}+4,5.\dfrac{4}{5}\)
c) \(\left(\dfrac{1}{2}+0,8-1\dfrac{1}{3}\right)\left(2,3\right)+4\dfrac{7}{25}-1,28\)
d) \(\left(-5\right).12:\left[\left(-\dfrac{1}{4}\right)+\dfrac{1}{2}:\left(-2\right)\right]+1\dfrac{1}{3}\)
13 Tìm x, biết :
a) \(\dfrac{2}{3}x+4=-12\); b) \(\dfrac{3}{4}+\dfrac{1}{4}:x=-3\); c) \(\left|3x-5\right|=4\)
d) \(\dfrac{x+1}{10}+\dfrac{x+1}{11}+\dfrac{x+1}{12}=\dfrac{x+1}{13}+\dfrac{x+1}{14}\) ;
e) \(\dfrac{x+4}{2000}+\dfrac{x+3}{2001}=\dfrac{x+2}{2002}+\dfrac{x+1}{2003}\)
Thực hiện phép tính hợp lí;
a) \(\left(\dfrac{9}{25}-2,18\right):\left(3\dfrac{4}{5}+0,2\right)\)
b) \(\dfrac{3}{8}.19\dfrac{1}{3}-\dfrac{3}{8}.33\dfrac{1}{3}\)
c) \(1\dfrac{4}{23}+\dfrac{5}{21}-\dfrac{4}{23}+0,5+\dfrac{16}{21}\)
ĐỀ 2:
1. Tính:
A. \(\left(-\dfrac{2}{3}\right)^2+\left(-\dfrac{7}{8}\right)+\left(-\dfrac{11}{12}\right)\)
B. \(\left(\dfrac{-1}{3}\right)^2:\dfrac{1}{6}-2.\left(\dfrac{-1}{2}\right)^3\)\
C. \(\dfrac{-1}{5}-\left(\dfrac{1}{2}+\dfrac{3}{4}\right)^2:\dfrac{5}{8}\)
D. \(\left|\dfrac{-3}{2}+1,2\right|+1\dfrac{2}{3}:6\)
2. Tìm x, biết:
a. \(\dfrac{2}{3}x-\dfrac{1}{3}x=\dfrac{5}{12}\)
b. \(\left(x-\dfrac{12}{7}\right):1\dfrac{1}{5}=\dfrac{4}{7}\)
c. \(\dfrac{2}{5}+\left|x+1\right|=\dfrac{3}{4}\)
3. Tìm x, y biết:
a. \(\dfrac{x}{18}=\dfrac{y}{15}\)và x - y = -30
b. 7x = 9x và 10x - 8x = 68
c. \(\left(x-\dfrac{1}{2}\right)^{50}+\left(y+\dfrac{1}{3}\right)^{40}=0\)
* Lm nhanh nha
Tính :
a) \(5\dfrac{1}{3}+2,5.\left(\dfrac{1}{3}-\dfrac{5}{12}\right)\)
b) \(\sqrt{12^2-44}-\left(1\dfrac{3}{4}-2\right)^2+\left(-1.5\right)^5:\left(\dfrac{-3}{2}\right)^4\)
Bài 2: Tìm x biết:
1) \(\dfrac{x}{12}-\dfrac{5}{6}=\dfrac{1}{12}\) 2) \(\dfrac{2}{3}-1\dfrac{4}{15}x=\dfrac{-3}{5}\) 3) -2\(^3\)+ 0,5x =1,5
a,\(\dfrac{2}{3}+5\dfrac{3}{7}:2+\dfrac{9}{49}.\left(-7\right)+\dfrac{1}{12}.\left(-2\right)^4\)
b,\(2\dfrac{3}{4}.\left(-0,4\right)-1\dfrac{3}{5}.2,75+\left(-1,2\right):\dfrac{4}{11}\)
