a, ( 1 + 2/3 - 1/4 ) . ( 4/5 - 3/4 )^2
=( 12/12 + 8/12 - 3/12 ) . (16/20 - 15/20 )^2
=17/12 . 1/20^2
=17/12 . 1/400
=17/4800
b, 2 : ( 1/2 - 2/3 )^3
=2 : (3/6 - 4/6 )^3
=2 : -1/6^3
=2 : -1/216
= -432
2 Thực hiện phép tính
\(\frac{17}{9}-\frac{17}{9}:\left(\frac{7}{3}+\frac{1}{2}\right)\)
\(\frac{4}{3}.\frac{2}{5}-\frac{3}{4}.\frac{2}{5}\)
\(-\frac{3}{4}.5\frac{3}{13}-0.75.\frac{36}{13}\)
\(3.\left(-\frac{4}{3}\right)^2-\frac{7}{3}\)
\(-\frac{5}{7}.\frac{3}{11}+\frac{-5}{7}.\frac{8}{11}+3\frac{5}{7}\)
\(32\frac{1}{7}:\left(\frac{-5}{4}\right)-47\frac{1}{7}:\left(\frac{-5}{4}\right)\)
\(\left(\frac{2}{3}+\frac{1}{2}\right)^2-\frac{1}{12}\\ \frac{1}{4}-\frac{5}{12}:\frac{1}{6}+\frac{-6}{5}\\ \frac{17}{21}+\frac{5}{23}-\frac{1}{2}+\frac{4}{21}-1\frac{5}{23}\)
\(\left(-3\right)^2+\sqrt{\frac{16}{25}}-\sqrt{9}+\frac{\sqrt{81}}{3}\)
tính :
a) \(\frac{4}{9}:\frac{-1}{7}+6\frac{5}{9}:\frac{-1}{7}\)
b) \(\left(2\frac{1}{3}+3\frac{1}{2}\right):\left(-4\frac{1}{6}+3\frac{1}{7}\right)+7\frac{1}{2}\)
c) \(\frac{\left(13\frac{1}{4}-2\frac{5}{27}-10\frac{5}{6}\right).230\frac{1}{25}+46\frac{3}{4}}{\left(1\frac{3}{7}+\frac{10}{3}\right):\left(12\frac{1}{3}-14\frac{2}{7}\right)}\)
Tính :
A = \(\left(1-\frac{2}{3}+\frac{4}{3}\right)-\left(\frac{4}{5}-1\right)+\left(\frac{7}{5}+2\right)\)
B = \(\left(-3+\frac{3}{4}-\frac{1}{3}\right):\left(5+\frac{2}{5}-\frac{2}{3}\right)\)
C = \(\left(\frac{3}{5}-\frac{4}{5}\right).\left(\frac{2}{7}-\frac{3}{14}\right)-\left(\frac{5}{9}-\frac{7}{27}\right).\left(1-\frac{3}{5}\right)+\left(1-\frac{11}{12}\right).\left(1-\frac{11}{12}\right)\)
Tính F=\(\frac{2.2016}{1+\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+4+5+...+2616}}\)
Tính:
a) \(\left(\frac{3}{7}+\frac{1}{2}\right)^2\)
b) \(\left(\frac{3}{4}-\frac{5}{6}\right)^2\)
c) \(\frac{5^4.20^4}{25^5.4^5}\)
d) \(\left(\frac{-10}{3}\right)^5.\left(\frac{-6}{5}\right)^4\)
e) \(\left(1+\frac{2}{3}-\frac{1}{4}\right).\left(\frac{4}{5}-\frac{3}{4}\right)^2\)
f) \(2:\left(\frac{1}{2}-\frac{2}{3}\right)^3\)
1.Chứng minh rằng: \(\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+\frac{7}{3^3.4^2}+...+\frac{19}{9^2.10^2}< 1\)
2.Chứng minh rằng: \(\frac{1}{3}+\frac{2}{3^2}+\frac{3}{3^3}+\frac{4}{3^4}+...+\frac{100}{3^{100}}< \frac{3}{4}\)
Làm nhanh giúp mình nhé mọi người !!!
Tính :
\(a,\left(\frac{4}{9}+\frac{1}{3}\right)^2\)
\(b,\left(\frac{1}{2}-\frac{3}{5}\right)^3\)
\(c,\left(\frac{-1}{5}\right)^5.\left(\frac{-6}{5}\right)^4\)
\(d,\left(\frac{3}{4}\right)^3:\left(\frac{3}{4}\right)^2:\left(\frac{-2}{5}\right)^3\)
\(a,\left|x-\frac{2}{5}\right|=0,5-\left(-\frac{1}{2}\right)\)
\(b,\frac{3}{2}\left|\frac{1}{4}-x\right|=\frac{5}{6}-1\)
\(c,\frac{4}{3}-\frac{5}{3}\left|x-\frac{1}{3}\right|=-\frac{1}{6}\div\frac{2}{3}\)
Bài 1 : Cho\(\frac{1}{2}a=\frac{3}{4}b\) và a-b=4,5 .tìm a,b
Bài 2: Tính
\(a,-\frac{3}{4}+\frac{3}{4}\div\frac{3}{5}\)
\(b,\frac{5}{6}-\left(\frac{5}{6}+\frac{1}{3}\right)-\frac{1}{2}\)
\(c,1\div\left(1-\frac{1}{2}\right)^2\)
\(\frac{\left(-\frac{1}{2}\right)^3-\left(\frac{3}{4}\right)^3-\left(-2\right)^2}{2.\left(-1\right)^5+\left(\frac{3}{4}\right)^2-\frac{3}{8}}\)