Thực hiện phép tính:
C = 23 . 3 – ( 110 + 15) : 42
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\(C=-\left[\dfrac{1}{3}\cdot\dfrac{\left(3+1\right)\cdot3}{2}+\dfrac{1}{4}\cdot\dfrac{\left(4+1\right)\cdot4}{2}+...+\dfrac{1}{50}\cdot\dfrac{\left(50+1\right)\cdot50}{2}\right]\\ C=-\left(\dfrac{1}{3}\cdot\dfrac{4\cdot3}{2}+\dfrac{1}{4}\cdot\dfrac{5\cdot4}{2}+...+\dfrac{1}{50}\cdot\dfrac{51\cdot50}{2}\right)\\ C=-\left(2+\dfrac{5}{2}+...+\dfrac{51}{2}\right)\\ C=-\dfrac{4+5+...+51}{2}=-\dfrac{\dfrac{\left(51+4\right)\left(51-4+1\right)}{2}}{2}=-\dfrac{55\cdot48}{4}=-660\)
a)156-4=152
b)42(39-37)]:42
=42.2:42
=2
c)2448:(119-17)
=2448:102
=24
Giải:
a) \(2\dfrac{17}{20}-1\dfrac{15}{11}+6\dfrac{9}{20}:3\)
\(=\dfrac{57}{20}-\dfrac{26}{11}+\dfrac{129}{20}:3\)
\(=\dfrac{107}{220}+\dfrac{43}{20}\)
\(=\dfrac{29}{11}\)
b) \(4\dfrac{3}{7}:\left(\dfrac{7}{5}.4\dfrac{3}{7}\right)\)
\(=\dfrac{31}{7}:\left(\dfrac{7}{5}.\dfrac{31}{7}\right)\)
\(=\dfrac{31}{7}:\dfrac{31}{5}\)
\(=\dfrac{5}{7}\)
c) \(\left(3\dfrac{2}{9}.\dfrac{15}{23}.1\dfrac{7}{29}\right):\dfrac{5}{23}\)
\(=\left(\dfrac{29}{9}.\dfrac{15}{23}.\dfrac{36}{29}\right):\dfrac{5}{23}\)
\(=\dfrac{60}{23}:\dfrac{5}{23}\)
\(=12\)
a: \(\left(-2\right)^3-45:\left(-3\right)^2+\left(-2019\right)^0\cdot1^{2019}\)
\(=-8-45:9+1\)
\(=-8-5+1\)
=-13+1
=-12
b: \(11^{25}:11^{13}-3^5:\left(1^{10}+2^3\right)-60\)
\(=11^{25-13}-3^5:3^2-60\)
\(=11^{12}-27-60\)
\(=11^{12}-87\)
#)Giải :
Bài 1 :
\(A=\frac{15}{6.16}+\frac{15}{16.26}+\frac{15}{26.36}\)
\(A=3\left(\frac{5}{6.16}+\frac{5}{16.26}+\frac{5}{26.36}\right)\)
\(A=3\left(\frac{1}{6}-\frac{1}{16}+\frac{1}{16}-\frac{1}{26}+\frac{1}{26}-\frac{1}{36}\right)\)
\(A=3\left(\frac{1}{6}-\frac{1}{36}\right)\)
\(A=3.\frac{5}{36}\)
\(A=\frac{15}{36}\)
\(B=\frac{33}{6.16}-\frac{63}{16.26}+\frac{93}{26.36}\)
\(B=\frac{3.11}{6.16}-\frac{3.21}{16.26}+\frac{3.31}{26.36}\)
\(B=\frac{1}{2.16}.11+\frac{1}{2.16}.\frac{3.21}{13}+\frac{3.31}{26.36}\)
\(B=\frac{1}{32}.\frac{143-63}{13}+\frac{3.31}{26.12.3}\)
\(B=\frac{1}{32}.\frac{80}{13}+\frac{31}{36.12}\)
\(B=\frac{5}{26}+\frac{31}{26.12}=\frac{60+31}{26.12}=\frac{91}{26.12}=\frac{13.7}{13.2.12}=\frac{7}{24}\)
Bài 2 :
a)\(28.157-28.267+28.10\)
\(=28\left(157-267+10\right)\)
\(=28.-100\)
\(=-2800\)
b)\(\left(-5\right).4.\left(-2\right).23.\left(-25\right)\)
\(=\left[4.\left(-25\right)\right].\left[\left(-5\right).2\right].23\)
\(=\left(-100\right).\left(-10\right).23\)
\(=23000\)
2)
28 . 157 - 28 .267 + 28.10
=28.( 157 - 267 + 10 )
= 28 . -100
= -2800
3)
[(-2).(-5)]. 4 .-25.23
= 10 . -100 .23
=-23000
còn câu 1 mik suy nghĩ đã
\(\text{(−1)+(−3)+...+(−199)+(−201)(−1)+(−3)+...+(−199)+(−201)}\)
=\(\text{−(1+3+...+199+201)=−(1+3+...+199+201)}\)
=\(\dfrac{\left(201+1\right).\left[\left(201-1\right)\right]:2+1}{2}\)
= \(\dfrac{-200.102}{2}=\dfrac{-20400}{2}=-10200\)
\(\text{17 + ( − 20 ) + 23 + ( − 26 ) + . . . + 53 + ( − 56 ) = [ 17 + ( − 20 ) ] + [ 23 + ( − 26 ) ] + . . . + [ 53 + ( − 56 ) ] = ( − 3 ) + ( − 3 ) + . . . + ( − 3 ) = ( − 3 ) . ( 7 ) = − 21}\)
\(\text{=17 + ( − 20 ) + 23 + ( − 26 ) + . . . + 53 + ( − 56 ) = [ 17 + ( − 20 ) ] + [ 23 + ( − 26 ) ] + . . . + [ 53 + ( − 56 ) ] = ( − 3 ) + ( − 3 ) + . . . + ( − 3 ) = ( − 3 ) . ( 7 ) = − 21}\)
\(\text{ = ( − 3 ) + ( − 3 ) + . . . + ( − 3 )}\)
\(\text{= ( − 3 ) . ( 7 ) = − 21}\)
\(2^3.3-\left(1^{10}+15\right):4^2\)
\(=8.3-16:16\)
\(=24-1=23\)