1.Tính :
a.\(12+\left\{45-\left[36:\left(12-9\right)^2\right]\right\}\)
b.\(24:\left[48-\left(42:7\right)^2\right]\)
2.Viết tập hợp các số tự nhiên không quá 10 bằng hai cách.
a) tìm các Ư
\(Ư\left(12^2\right)\)
\(Ư\left(18^2\right)\)
\(Ư\left(24^2\right)\)
\(Ư\left(32^2\right)\)
\(Ư\left(36^2\right)\)
\(Ư\left(48^2\right)\)
\(Ư\left(50^2\right)\)
\(Ư\left(60^2\right)\)
\(Ư\left(64^2\right)\)
\(Ư\left(72^2\right)\)
\(Ư\left(90^2\right)\)
\(Ư\left(96^2\right)\)
\(Ư\left(100^2\right)\)
b) tìm các \(ƯC\) ở câu a
\(Ư\left(144\right)=\left\{1,2,3,4,6,8,9,12,16,18,24,36,48,72,144\right\}\)
\(Ư\left(324\right)=\left\{1,2,3,4,6,9,12,18,27,36,54,81,108,162,324\right\}\)
\(Ư\left(576\right)=\left\{1,2,3,4,6,8,9,12,16,18,24,32,36,48,64,72,96,144,192,288,576\right\}\)
\(Ư\left(1024\right)=\left\{1,2,4,8,16,32,64,128,256,512,1024\right\}\)
\(Ư\left(1296\right)=\left\{1,2,3,4,6,8,9,12,16,24,27,36,48,54,72,81,108,144,162,216,324,432,648,1296\right\}\)
\(Ư\left(2304\right)=\left\{1,2,3,4,6,8,9,12,16,18,24,32,48,64,72,96,128,144,192,256,288,384,576,768,1152,2304\right\}\)
\(Ư\left(2500\right)=\left\{1,2,4,5,10,20,25,50,100,125,250,500,625,1250,2500\right\}\)
\(Ư\left(10000\right)=\left\{1,2,4,5,8,10,16,20,25,40,80,100,125,200,250,400,500,625,1000,1250,2000,2500,5000,10000\right\}\)
Tính các thương sau:
a) \(12:6\)
b) \(24:\left( { - 8} \right)\)
c) \(\left( { - 36} \right):9\)
d) \(\left( { - 14} \right):\left( { - 7} \right)\)
Cách 1:
a) \(12:6 = 2\)
b) \(24:\left( { - 8} \right)=-(24:8)=-3\)
c) \(\left( { - 36} \right):9=-(36:9)=-4\)
d) \(\left( { - 14} \right):\left( { - 7} \right)=14:7=2\)
Cách 2:
a) Ta có \(12 = 6.2\) nên \(12:6 = 2\).
b) Ta có \(24 = \left( { - 8} \right).\left( { - 3} \right)\)\( \Rightarrow 24:\left( { - 8} \right) = \left( { - 3} \right)\).
c) Ta có \(\left( { - 36} \right) = 9.\left( { - 4} \right)\) nên \(\left( { - 36} \right):9 = \left( { - 4} \right)\).
d) Ta có \(\left( { - 14} \right) = \left( { - 7} \right).2\) nên \(\left( { - 14} \right):\left( { - 7} \right) = 2\)
1.Viết phân số \(\frac{14}{45}\)thành tổng hai phân số có tử số là 1,mẫu số khác nhau:
2.Tính bằng cách thuận tiện nhất:
\(\left(1-\frac{1}{12}\right)\times\left(1-\frac{1}{11}\right)\times\left(1-\frac{1}{10}\right)\times\left(1-\frac{1}{9}\right)\times\left(1-\frac{1}{8}\right)\)
Các bạn hãy giúp mình nhé!
1. \(\frac{14}{45}=\frac{1}{9}+\frac{1}{5}\)
2. \(\left(1-\frac{1}{12}\right).\left(1-\frac{1}{11}\right).\left(1-\frac{1}{10}\right).\left(1-\frac{1}{9}\right).\left(1-\frac{1}{8}\right)\)
\(=\frac{11}{12}.\frac{10}{11}.\frac{9}{10}.\frac{8}{9}.\frac{7}{8}\)
Triệt tử với mẫu:
\(=\frac{7}{12}\)
1.ket qua la 1/5+1/9
2.=11/12x10/11x9/10x8/9x7/8
=(11x10x9x8x7)/(12x11x10x9x8)
=7/12
1.
\(\frac{14}{45}=\frac{5+9}{45}=\frac{5}{45}+\frac{9}{45}=\frac{1}{9}+\frac{1}{5}.\)
2.
\(\left(1-\frac{1}{12}\right)\times\left(1-\frac{1}{11}\right)\times\left(1-\frac{1}{10}\right)\times\left(1-\frac{1}{9}\right)\times\left(1-\frac{1}{8}\right)\)
\(=\frac{11}{12}\times\frac{10}{11}\times\frac{9}{10}\times\frac{8}{9}\times\frac{7}{8}\)
\(=\frac{7}{12}\)
tính một cách hợp lí:
a) \(\dfrac{-5}{18}+\dfrac{32}{45}-\dfrac{9}{10}\)
b) \(\left(\dfrac{-1}{4}+\dfrac{51}{33}-\dfrac{5}{3}\right)-\left(\dfrac{-15}{12}+\dfrac{6}{11}-\dfrac{42}{29}\right)\)
c) \(1-\dfrac{1}{2}+2-\dfrac{2}{3}+3-\dfrac{3}{4}+4-\dfrac{1}{4}-3-\dfrac{1}{3}-2-\dfrac{1}{2}-1\)
giải chi tiết giúp mình nha
a) Ta có: \(\dfrac{-5}{18}+\dfrac{32}{45}-\dfrac{9}{10}\)
\(=\dfrac{-25}{90}+\dfrac{64}{90}-\dfrac{81}{90}\)
\(=\dfrac{-42}{90}=-\dfrac{7}{15}\)
b) Ta có: \(\left(-\dfrac{1}{4}+\dfrac{51}{33}-\dfrac{5}{3}\right)-\left(-\dfrac{15}{12}+\dfrac{6}{11}-\dfrac{42}{29}\right)\)
\(=\dfrac{-1}{4}+\dfrac{17}{11}-\dfrac{5}{3}+\dfrac{5}{4}-\dfrac{6}{11}+\dfrac{42}{29}\)
\(=\dfrac{-5}{3}+\dfrac{42}{29}\)
\(=\dfrac{-145}{87}+\dfrac{126}{87}=\dfrac{-19}{87}\)
c) Ta có: \(1-\dfrac{1}{2}+2-\dfrac{2}{3}+3-\dfrac{3}{4}+4-\dfrac{1}{4}-3-\dfrac{1}{3}-2-\dfrac{1}{2}-1\)
\(=\left(1-1\right)-\left(\dfrac{1}{2}+\dfrac{1}{2}\right)+\left(2-2\right)-\left(\dfrac{2}{3}+\dfrac{1}{3}\right)+\left(3-3\right)-\left(\dfrac{3}{4}+\dfrac{1}{4}\right)+4\)
\(=-1-1-1+4\)
=1
a) Ta có: =−2590+6490−8190=−2590+6490−8190
(−14+5133−53)−(−1512+611−4229)(−14+5133−53)−(−1512+611−4229)
=−53+4229=−53+4229
1−12+2−23+3−34+4−14−3−13−2−12−11−12+2−23+3−34+4−14−3−13−2−12−1
Cmr :
a) \(36^{36}-9^{10}\) chia hết cho 45
b) \(7^{1000}-3^{1000}\) chia hết cho 10
c)\(\left(2^{10}+2^{11}+2^{12}\right):7\)là 1 số tự nhiên
d)\(\left(8^{10}-8^9-8^8\right):55\) là 1 số tự nhiên
\(\text{Thực hiện các phép tính sau một cách hợp lý:}\)
\(a\)) \(\left(10^2+11^2+12^2\right):\left(13^2+14^2\right)\)
\(b\)) \(1.2.3...9-1.2.3...8-1.2.3...7.8^2\)
\(c\)) \(\dfrac{\left(3.4.2^{16}\right)^2}{11.2^{13}.4^{11}-16^9}\)
\(d\)) \(1152-\left(374+1152\right)+\left(-65+374\right)\)
\(e\)) \(13-12+11+10-9+8-7-6+5-4+3+2-1\)
Tính thương và viết kết quả ở dạng phân số tối giản:
a) \(\dfrac{3}{10}:\left(\dfrac{-2}{3}\right);\)
b) \(\left(-\dfrac{7}{12}\right):\left(-\dfrac{5}{6}\right);\)
c) \(\left(-15\right):\dfrac{-9}{10}.\)
\(a.\)
\(\dfrac{3}{10}:\left(-\dfrac{2}{3}\right)=\dfrac{3}{10}\cdot\dfrac{-3}{2}=-\dfrac{9}{20}\)
\(b.\)
\(\left(-\dfrac{7}{12}\right):\left(-\dfrac{5}{6}\right)=\left(-\dfrac{7}{12}\right)\cdot\left(-\dfrac{6}{5}\right)=\dfrac{\left(-7\right)\cdot\left(-6\right)}{12\cdot5}=\dfrac{7}{10}\)
\(c.\)
\(\left(-15\right):-\dfrac{9}{10}=\left(-15\right)\cdot-\dfrac{10}{9}=\dfrac{150}{9}=\dfrac{50}{3}\)
a) \(\dfrac{3}{10}:\dfrac{-2}{3}=\dfrac{3}{10}.\dfrac{-3}{2}=\dfrac{3.-3}{10.2}=\dfrac{-9}{20}\)
b) \(\dfrac{-7}{12}:\dfrac{-5}{6}=\dfrac{-7}{12}.\dfrac{-6}{5}=\dfrac{-7.-6}{12.5}=\dfrac{7}{10}\)
c)\(-15:\dfrac{-9}{10}=-15.\dfrac{-10}{9}=\dfrac{-15.-10}{9}=\dfrac{50}{3}\)
a,Tính \(\frac{2^{12}.27^3-15.\left(-4\right)^9.9^4}{6^9.2^{10}+\left(-12\right)^{10}}\)
b, Cho a,b,c là các số nguyên dương. CMR:
\(\frac{x}{x+y}+\frac{y}{y+z}+\frac{z}{z+x}\)> 1.
c, Tính bằng cách hợp lí:
\(\left(\frac{1}{2^2}-1\right)\left(\frac{1}{3^2}-1\right)...\left(\frac{1}{99^2}-1\right)\)
Tính:
\(-3^2+\left\{-54:\left[-2^8+7\right]\cdot\left(-2\right)^2\right\}\)
Tính hợp lí :
\(31\cdot\left(-18\right)+31\cdot\left(-81\right)-31\)
\(\left(-12\right)\cdot47+\left(-12\right)\cdot52+\left(-12\right)\)
\(13\cdot\left(23+22\right)-3\cdot\left(17+28\right)\)
\(-48+48\cdot\left(-78\right)+48\cdot\left(-21\right)\)
`#3107.101107`
`-3^2 + {-54 \div [-2^8 + 7] * (-2)^2}`
`= -9 + [-54 \div (-256 + 7) * 4]`
`= -9 + [-54 \div (-249) * 4]`
`= -9 + (18/83 * 4)`
`= -9 + 72/83`
`= -675/83`
______
`31 * (-18) + 31 * (-81) - 31`
`= 31 * (-18 - 81 - 1)`
`= 31 * (-100)`
`= -3100`
___
`(-12) * 47 + (-12) * 52 + (-12)`
`= (-12) * (47 + 52 + 1)`
`= (-12) * 100`
`= -1200`
___
`13 * (23 + 22) - 3 * (17 + 28)`
`= 13 * 45 - 3 * 45`
`= 45 * (13 - 3)`
`= 45 * 10`
`= 450`
____
`-48 + 48 * (-78) + 48 * (-21)`
`= 48 * (-1 - 78 - 21)`
`= 48 * (-100)`
`= -4800`