\(\dfrac{3}{31}\)+\(\left(\dfrac{1}{6}+\dfrac{-5}{9}\right)\):\(\left(\dfrac{7}{24}-\dfrac{13}{18}\right)\)
1. So sánh các tích sau hợp lý nhất:
P = \(\left(-\dfrac{21}{34}\right)\)\(\left(-\dfrac{13}{27}\right)\)\(\dfrac{7}{9}\)
Q = \(\left(-0,5\right)\)\(\dfrac{3}{19}\)\(\left(-\dfrac{24}{41}\right)\)\(\left(\dfrac{8}{31}\right)\)
M = \(\dfrac{-6}{17}.\dfrac{-5}{17}.\) ... \(.\dfrac{5}{17}.\dfrac{6}{17}\)
2. Tính hợp lý:
A = \(\left(-\dfrac{3}{11}\right).\dfrac{7}{10}.\dfrac{11}{-13}.\left(-20\right)\)
B = \(\dfrac{-4}{9}:\dfrac{2}{13}+\left(\dfrac{-5}{18}\right).\dfrac{2}{13}\)
C = \(\left(2\dfrac{1}{15}.\dfrac{3}{19}.\dfrac{2}{31}\right):\left(-\dfrac{5}{19}\right)\)
Help me!
Tính :
\(6.\dfrac{-5}{18};\dfrac{-13}{24}+\dfrac{-5}{21}.\dfrac{7}{25};\dfrac{-5}{13}-\dfrac{3}{26}.\dfrac{-2}{3};\left(\dfrac{2}{3}+\dfrac{-7}{6}\right).\left(\dfrac{3}{8}+\dfrac{-3}{24}\right)\)
\(6.-\dfrac{5}{18}=-\dfrac{5}{3}\)
\(-\dfrac{13}{24}+-\dfrac{5}{21}.\dfrac{7}{25}=-\dfrac{13}{24}+-\dfrac{1}{15}=-\dfrac{73}{120}\)
\(-\dfrac{5}{13}-\dfrac{3}{26}.-\dfrac{2}{3}=-\dfrac{5}{13}-\left(-\dfrac{1}{13}\right)=-\dfrac{4}{13}\)
\(\left(\dfrac{2}{3}+-\dfrac{7}{6}\right).\left(\dfrac{3}{8}+-\dfrac{3}{24}\right)=-\dfrac{1}{2}.\dfrac{1}{4}=\dfrac{1}{8}\)
Kết quả lần lượt của các phép tính là :
\(\dfrac{-5}{3}\) , \(\dfrac{-73}{120}\) , \(\dfrac{-4}{13}\) , \(\dfrac{-1}{8}\)
a) Tìm tập hợp các số nguyên x, biết rằng\(4\dfrac{5}{9}:2\dfrac{5}{18}-7< x< \left(3\dfrac{1}{5}:3,2+4,5.1\dfrac{31}{45}\right):\left(-21\dfrac{1}{2}\right)\)
b) tìm x, biết \(\left|x+\dfrac{1}{2}\right|+\left|x+\dfrac{1}{6}\right|+\left|x+\dfrac{1}{12}\right|+\left|x+\dfrac{1}{20}\right|+....+\left|x+\dfrac{1}{110}\right|-11x\)
c)Tính gt biểu thức \(C=2x^3-5y^3+2015\) tại x,y thỏa mãn \(\left|x-1\right|+\left(y+2\right)^{20}=0\)
Bài 1.( 2 điểm)Tính bằng cách hợp lí:
a) \(\dfrac{1}{2}+\dfrac{9}{10}+\dfrac{5}{6}-\dfrac{11}{14}-\dfrac{1}{3}+\dfrac{-4}{35}\)
b) \(\left(\dfrac{18}{23}+\dfrac{7}{12}\right)+\left(\dfrac{-13}{19}-\dfrac{3}{4}\right)+\left(\dfrac{-6}{19}+\dfrac{5}{23}\right)\)
c) \(\dfrac{4}{3}+\dfrac{-5}{6}+\dfrac{-1}{4}\)
d) \(\dfrac{5}{6}-\dfrac{7}{5}+\dfrac{17}{30}\)
1: \(\dfrac{1}{2}+\dfrac{9}{10}+\dfrac{5}{6}-\dfrac{11}{14}-\dfrac{1}{3}+\dfrac{-4}{35}\)
\(=\left(\dfrac{1}{2}+\dfrac{5}{6}-\dfrac{1}{3}\right)+\dfrac{9}{10}-\left(\dfrac{11}{14}+\dfrac{4}{35}\right)\)
\(=\dfrac{3+5-2}{6}+\dfrac{9}{10}-\dfrac{55+8}{70}\)
\(=1+\dfrac{9}{10}-\dfrac{9}{10}\)
=1
Bài 2: tính
a, \(\dfrac{11}{24}-\dfrac{5}{41}+\dfrac{13}{24}+0,5-\dfrac{36}{41}\)
b,\(-12:\left(\dfrac{3}{4}-\dfrac{5}{6}\right)^2\)
c,\(\dfrac{7}{23}.[\left(-\dfrac{8}{6}\right)-\dfrac{45}{18}]\)
d,\(23\dfrac{1}{4}.\dfrac{7}{5}-13\dfrac{1}{4}:\dfrac{5}{7}\)
e,\(\left(1+\dfrac{2}{3}-\dfrac{1}{4}\right).\left(0,8-\dfrac{3}{4}\right)^2\)
a. \(\dfrac{11}{24}-\dfrac{5}{41}+\dfrac{13}{24}+0,5-\dfrac{36}{41}\)
\(=\left(\dfrac{11}{24}+\dfrac{13}{24}\right)+\left(\dfrac{-5}{41}-\dfrac{36}{41}\right)+0,5\)
\(=1+\left(-1\right)+0,5\)
\(=0,5\)
b. \(-12:\left(\dfrac{3}{4}-\dfrac{5}{6}\right)^2\)
\(=-12:\left(\dfrac{-1}{12}\right)^2\)
\(=-12:\dfrac{1}{144}\)
\(=-1728\)
c. \(\dfrac{7}{23}.\left[\left(-\dfrac{8}{6}\right)-\dfrac{45}{18}\right]\)
\(=\dfrac{7}{23}.\dfrac{-23}{6}\)
\(=\dfrac{-7}{6}\)
d. \(23\dfrac{1}{4}.\dfrac{7}{5}-13\dfrac{1}{4}:\dfrac{5}{7}\)
\(=23\dfrac{1}{4}.\dfrac{7}{5}-13\dfrac{1}{4}.\dfrac{7}{5}\)
\(=\left(23\dfrac{1}{4}-13\dfrac{1}{4}\right).\dfrac{7}{5}\)
\(=10.\dfrac{7}{5}\)
\(=14\)
e. \(\left(1+\dfrac{2}{3}-\dfrac{1}{4}\right).\left(0,8-\dfrac{3}{4}\right)^2\)
\(=\dfrac{17}{12}.\left(\dfrac{1}{20}\right)^2\)
\(=\dfrac{17}{12}.\dfrac{1}{400}=\dfrac{17}{4800}\)
Tính hợp lý:
a, \(\dfrac{-3}{4}.5\dfrac{3}{13}-0,75.\dfrac{36}{13}\)
b, \(4\dfrac{5}{9}:\left(\dfrac{-5}{7}\right)+\dfrac{49}{9}:\left(\dfrac{-5}{7}\right)\)
c, \(\left(\dfrac{-3}{5}+\dfrac{4}{9}\right):\dfrac{7}{11}+\left(\dfrac{-2}{5}+\dfrac{5}{9}\right):\dfrac{7}{11}\)
d, \(\dfrac{6}{7}:\left(\dfrac{3}{26}-\dfrac{3}{13}\right)+\dfrac{6}{7}:\left(\dfrac{1}{10}-\dfrac{8}{5}\right)\)
*Trả lời :
a) \(-\dfrac{3}{4}.5\dfrac{3}{13}-0,75.\dfrac{36}{13}\)
= \(-\dfrac{3}{4}.\dfrac{68}{13}-\dfrac{3}{4}.\dfrac{36}{13}\)
=\(\dfrac{3}{4}.\dfrac{-68}{13}-\dfrac{3}{4}.\dfrac{36}{13}\)
=\(\dfrac{3}{4}.\cdot\left(\dfrac{-68}{13}-\dfrac{36}{13}\right)\)
=\(\dfrac{3}{4}.\left(-8\right)\)
= \(-6\)
b)\(4\dfrac{5}{9}:\left(-\dfrac{5}{7}\right)+\dfrac{49}{9}:\left(-\dfrac{5}{7}\right)\)
=\(\dfrac{41}{9}-\left(-\dfrac{5}{7}\right)+\dfrac{49}{9}:\left(-\dfrac{5}{7}\right)\)
=\(\left(\dfrac{41}{9}+\dfrac{49}{9}\right):\left(-\dfrac{5}{7}\right)\)
=\(\dfrac{90}{9}:\left(-\dfrac{5}{7}\right)\)
=\(10:\left(-\dfrac{5}{7}\right)\)
=\(-14\)
c)\(\left(-\dfrac{3}{5}+\dfrac{4}{9}\right):\dfrac{7}{11}+\left(-\dfrac{2}{5}+\dfrac{5}{9}\right):\dfrac{7}{11}\)
=\(\left(-\dfrac{3}{5}\right)+\dfrac{4}{9}:\dfrac{7}{11}+\left(-\dfrac{2}{5}\right)+\dfrac{5}{9}:\dfrac{7}{11}\)(áp dụng tính chất phá ngoặc )
=\(\left\{\left[-\dfrac{3}{5}+\left(-\dfrac{2}{5}\right)\right]+\left(\dfrac{4}{9}+\dfrac{5}{9}\right)\right\}:\dfrac{7}{11}\)
=\(\left(-\dfrac{5}{5}+\dfrac{9}{9}\right):\dfrac{7}{11}\)
=\(\left(-1+1\right):\dfrac{7}{11}\)
\(=0:\dfrac{7}{11}\)
=0.
d)\(\dfrac{6}{7}:\left(\dfrac{3}{26}-\dfrac{3}{13}\right)+\dfrac{6}{7}:\left(\dfrac{1}{10}-\dfrac{8}{5}\right)\)
=\(\dfrac{6}{7}:\left[\dfrac{3}{26}+\left(-\dfrac{6}{26}\right)\right]+\dfrac{6}{7}:\left[\dfrac{1}{10}+\left(-\dfrac{16}{10}\right)\right]\)
=\(\dfrac{6}{7}:\left(-\dfrac{3}{26}\right)+\dfrac{6}{7}:\left(-\dfrac{3}{2}\right)\)
=\(\dfrac{6}{7}:\left[\left(-\dfrac{3}{26}\right)+\left(-\dfrac{39}{26}\right)\right]\)
=\(\dfrac{6}{7}:\left(-\dfrac{21}{13}\right)\)
=\(-\dfrac{26}{49}\)
\(\left(\dfrac{-9}{13}\right)\left(\dfrac{-4}{5}\right)\)
\(-0,7:\dfrac{3}{2}\)
\(\dfrac{7}{6}.3\dfrac{1}{4}+\dfrac{7}{6}.\left(-0,25\right)\)
a: \(=\dfrac{9}{13}\cdot\dfrac{4}{5}=\dfrac{36}{65}\)
b: \(=\dfrac{-7}{10}:\dfrac{3}{2}=\dfrac{-7}{10}\cdot\dfrac{2}{3}=\dfrac{-14}{30}=-\dfrac{7}{15}\)
c: \(=\dfrac{7}{6}\left(3+\dfrac{1}{4}-\dfrac{1}{4}\right)=\dfrac{7}{6}\cdot3=\dfrac{7}{2}\)
A=\(\left[\dfrac{1\dfrac{11}{31}.4\dfrac{3}{7}-\left(15-6\dfrac{1}{3}.\dfrac{2}{19}\right)}{4\dfrac{5}{6}+\dfrac{1}{6}\left(12-5\dfrac{1}{3}\right)}.\left(-1\dfrac{14}{93}\right)\right].\dfrac{31}{50}\)
BT2: Tính nhanh
7) \(\left(-\dfrac{1}{2}\right)-\left(-\dfrac{3}{5}\right)+\left(-\dfrac{1}{9}\right)+\dfrac{1}{71}-\left(-\dfrac{2}{7}\right)+\dfrac{4}{35}-\dfrac{7}{18}\)
8)\(\left(3-\dfrac{1}{4}+\dfrac{2}{3}\right)-\left(5-\dfrac{1}{3}-\dfrac{6}{5}\right)-\left(6-\dfrac{7}{4}+\dfrac{3}{2}\right)\)