Tính hợp lý
a. M=\(\left(\dfrac{1284}{1391}+\dfrac{212121}{656565}\right):\left(\dfrac{27}{13}\cdot3\right)\)
Tính hợp lý
a. M=\(\left(\dfrac{1284}{1391}+\dfrac{212121}{656565}\right):\left(\dfrac{27}{13}\cdot3\right)\)
a. \(M=\left(\frac{12}{13}+\frac{21}{65}\right):\frac{81}{13}\)
\(M=\left(\frac{120}{130}+\frac{42}{130}\right).\frac{13}{81}\)
\(M=\frac{81}{65}.\frac{13}{81}\)
\(M=\frac{1}{5}\)
M=(12.107/13.107 + 21.10101/65.10101):27.3/13=(12/13 + 21/65):27.3/13
=[(12.5+21)/65]:27.3/13
=81/13.5 : 27.3/13 =81/(5.27.3)=1/5
Đs: M=1/5
Bài 1: Tính hợp lí nếu có:
a) [ ( 17/15 - 4/30 ) :5/6 ] : [ 102/25 : ( 17/25 . 1/15 ) ]
b) ( 1284/1391 + 212121/656565) : ( 27/13 . 3 )
Thanks
Tính hợp lý:
\(A=\dfrac{7}{12}+\dfrac{5}{12}:6-\dfrac{11}{36}\) \(B=\left(\dfrac{4}{5}+\dfrac{1}{2}\right):\left(\dfrac{3}{13}-\dfrac{8}{13}\right)\)
\(C=\left(\dfrac{2}{3}-\dfrac{1}{4}+\dfrac{5}{11}\right):\left(\dfrac{5}{12}+1-\dfrac{7}{11}\right)\)
a: \(A=\dfrac{7}{12}+\dfrac{5}{72}-\dfrac{11}{36}=\dfrac{42}{72}+\dfrac{5}{72}-\dfrac{22}{72}=\dfrac{25}{72}\)
b: \(B=\dfrac{8+5}{10}:\dfrac{-5}{13}=\dfrac{13}{10}\cdot\dfrac{13}{-5}=-\dfrac{169}{100}\)
c: \(C=\left(\dfrac{88}{132}-\dfrac{33}{132}+\dfrac{60}{132}\right):\left(\dfrac{55}{132}+\dfrac{132}{132}-\dfrac{84}{132}\right)\)
\(=\dfrac{88-33+60}{55+132-84}=\dfrac{115}{103}\)
A=18\(\times\)\(\left(\dfrac{191919}{212121}+\dfrac{888}{999}\right)+27\times\left(\dfrac{171717}{272727}\right)\)
= 18 x ( \(\dfrac{19}{21}\)+\(\dfrac{8}{9}\))+27 x \(\dfrac{17}{27}\)
=18 x \(\dfrac{113}{63}\)+27 x \(\dfrac{17}{27}\)
=\(\dfrac{226}{7}\)+17
=\(\dfrac{345}{7}\)
Chúc bạn học tốt!!
\(\text{Thực hiện phép tính một cách hợp lý nhất (nếu có thể):}\)
\(1\)) \(\left(\dfrac{-8}{13}:\dfrac{3}{7}+\dfrac{-5}{13}:\dfrac{3}{7}\right).\dfrac{\left(-4\right)^3.\left|-3\right|}{7}\)
\(2\)) \(75\)\(\text{%}\)\(-\left(\dfrac{5}{2}+\dfrac{5}{3}\right)+\left(-\dfrac{1}{2}\right)^2\)
Giải:
1) (-8/13:3/7+-5/13:3/7).(-4)3.|-3|/7
=[7/3.(-8/13+-5/13)].-192/7
=[7/3.(-1)].-192/7
=-7/3.-192/7
=64
2) 75%-(5/2+5/3)+(-1/2)2
=3/4-25/6+1/4
=(3/4+1/4)-25/6
=1-25/6
=-19/6
Chúc bạn học tốt!
1) \(\left(\dfrac{-8}{13}:\dfrac{3}{7}+\dfrac{-5}{13}:\dfrac{3}{7}\right).\dfrac{\left(-4\right).|-3|}{7}\)
= \(\left[\left(\dfrac{-8}{13}+\dfrac{-5}{13}\right):\dfrac{3}{7}\right].\dfrac{-64.3}{7}\)
= \(\left[-1:\dfrac{3}{7}\right].\dfrac{-192}{7}\)
= \(\dfrac{-7}{3}.\dfrac{-192}{7}\)
= \(64\)
2) \(75\%-\left(\dfrac{5}{2}+\dfrac{5}{3}\right)+\left(-\dfrac{1}{2}\right)^2\)
= \(\dfrac{3}{4}-\dfrac{25}{6}+\dfrac{1}{4}\)
= \(\left(\dfrac{3}{4}+\dfrac{1}{4}\right)-\dfrac{25}{6}\)
= \(1-\dfrac{25}{6}\)
= \(\dfrac{-19}{6}\)
Chúc bạn học tốt !
\(\dfrac{99}{100}:\left(\dfrac{1}{4}-\dfrac{1}{12}+\dfrac{1}{3}\right)-\left(\dfrac{-7}{5}\right)^2\)
\(\dfrac{13}{15}\cdot0,25\cdot3+\left(\dfrac{8}{15}-1\dfrac{19}{60}\right):1\dfrac{23}{24}\)
a: \(=\dfrac{99}{100}:\left(\dfrac{3}{12}-\dfrac{1}{12}+\dfrac{4}{12}\right)-\dfrac{49}{25}\)
\(=\dfrac{99}{100}:\dfrac{1}{2}-\dfrac{49}{25}\)
\(=\dfrac{99}{50}-\dfrac{98}{50}=\dfrac{1}{50}\)
b: \(=\dfrac{13}{15}\cdot\dfrac{1}{4}\cdot3+\left(\dfrac{32}{60}-1-\dfrac{19}{60}\right):\dfrac{47}{24}\)
\(=\dfrac{39}{60}+\dfrac{-19}{60}\cdot\dfrac{24}{47}\)
=459/940
Tính giá trị của các biểu thức sau 1) \(A=1+2+2^2+...+2^{2015}\) 2) \(B=\left(\dfrac{1}{4}-1\right)\cdot\left(\dfrac{1}{9}-1\right)\cdot\left(\dfrac{1}{16}-1\right)\cdot\cdot\cdot\cdot\cdot\left(\dfrac{1}{400}-1\right)\) 3) \(C=\left(\dfrac{1}{4\cdot9}+\dfrac{1}{9\cdot14}+\dfrac{1}{14\cdot19}+...+\dfrac{1}{44\cdot49}\right)\cdot\dfrac{1-3-5-7-...-49}{89}\) 4) \(D=\dfrac{2^{12}\cdot3^5-4^6\cdot9^2}{\left(2^2\cdot3\right)^6+8^4\cdot3^5}-\dfrac{5^{10}\cdot7^3-25^5\cdot49^2}{\left(125\cdot7\right)^3+5^9\cdot14^3}\) 5) \(E=\dfrac{\dfrac{1}{2003}+\dfrac{1}{2004}-\dfrac{1}{2005}}{\dfrac{5}{2003}+\dfrac{5}{2004}-\dfrac{5}{2005}}-\dfrac{\dfrac{2}{2002}+\dfrac{2}{2003}-\dfrac{2}{2004}}{\dfrac{3}{2002}+\dfrac{3}{2003}-\dfrac{3}{2004}}\) 6) Cho 13+23+...+103=3025 Tính S= 23+43+63+...+203
Tính hợp lý
\(A = \left(1-\dfrac{1}{25}\right)\left(1-\dfrac{1}{36}\right)\left(1-\dfrac{1}{49}\right)...\left(1-\dfrac{1}{10000}\right)\) B= \(\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{6}\right)\left(1-\dfrac{1}{10}\right)...\left(1-\dfrac{1}{50.101}\right)\)
Bài 1.Tính hợp lý
a) \(\text{(0,5)}^3\) .\(2^3\)
b) \(\text{(0,25)}^2\).16
c) \(\left(\dfrac{3}{5}\right)^3:\left(\dfrac{-27}{1000}\right)\)
d) \(\dfrac{4^2.25^2+32.125}{2^3.5^2}\)
e) \(\dfrac{4^5.21+4^5.19}{2^{10}.11+2^{10}.5}\)
a: \(\left(0.5\right)^3\cdot2^3=1\)
b: \(\left(0.25\right)^2\cdot16=1\)
c: \(\left(\dfrac{3}{5}\right)^3:\left(-\dfrac{27}{1000}\right)=\dfrac{3^3}{5^3}\cdot\dfrac{-1000}{27}=\dfrac{-1000}{125}=-8\)