BT1: Tính nhanh:
3) \(\left(\dfrac{1}{3}-\dfrac{1}{4}\right)^2+\left(\dfrac{1}{2}-\dfrac{1}{6}\right)^2+1\dfrac{1}{3}\)
BT1: Tính nhanh
2) \(\left(7-\dfrac{4}{3}+\dfrac{1}{3}\right)-\left(6+\dfrac{5}{4}-\dfrac{4}{3}\right)-\left(5-\dfrac{7}{4}+\dfrac{5}{3}\right)\)
\(=7-\dfrac{4}{3}+\dfrac{1}{3}-6-\dfrac{5}{4}+\dfrac{4}{3}-5+\dfrac{7}{4}-\dfrac{5}{3}\)
\(=\left(7-6-5\right)-\left(\dfrac{4}{3}-\dfrac{4}{3}+\dfrac{5}{3}-\dfrac{1}{3}\right)-\left(\dfrac{5}{4}-\dfrac{7}{4}\right)\)
\(=-4-\dfrac{4}{3}-\left(\dfrac{-1}{2}\right)\)
\(=-4-\dfrac{4}{3}+\dfrac{1}{2}\)
\(=-\dfrac{24}{6}-\dfrac{8}{6}+\dfrac{3}{6}\)
\(=-\dfrac{32}{6}+\dfrac{3}{6}\)
\(=-\dfrac{29}{6}\)
BT1: Tính nhanh
3) \(\dfrac{1}{2}-\dfrac{3}{2}.\left(\dfrac{1}{2}-\dfrac{1}{3}\right)+\left(\dfrac{-3}{-2^3}\right)\)
4) \(\dfrac{1}{12}.\dfrac{37}{39}+\dfrac{1}{12}.\dfrac{2}{39}+\dfrac{1}{4}\)
\(\dfrac{1}{12}\). \(\dfrac{37}{39}+\dfrac{1}{12}.\dfrac{2}{39}+\dfrac{1}{4}\)
=\(\dfrac{1}{12}.\left(\dfrac{37}{39}+\dfrac{2}{39}\right)+\dfrac{1}{4}\)
=\(\dfrac{1}{12}.1+\dfrac{1}{4}\)
=\(\dfrac{13}{12}+\dfrac{1}{4}\)
=\(\dfrac{16}{12}\)
Thực hiện phép tính (tính nhanh nếu có thể):
a) \(\left(\dfrac{1}{2}-\dfrac{1}{3}\right)-\left(\dfrac{5}{3}-\dfrac{3}{2}\right)+\left(\dfrac{7}{3}-\dfrac{5}{2}\right)\)
b) \(\left(\dfrac{3}{4}-1\dfrac{1}{6}\right)^2:\sqrt{\dfrac{25}{144}}\)
\(a.=\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{5}{3}+\dfrac{3}{2}+\dfrac{7}{3}-\dfrac{5}{2}=\dfrac{1+3-5}{2}-\dfrac{2+5-7}{3}=\dfrac{-1}{2}\)
\(b.\left(\dfrac{3}{4}-1\dfrac{1}{6}\right)^2:\sqrt{\dfrac{25}{144}}=\left(-\dfrac{5}{12}\right)^2:\dfrac{5}{12}=\dfrac{5}{12}\)
BT1: Tính
1) \(\dfrac{1}{2}-\text{|}\dfrac{1}{5}-\dfrac{1}{4}\text{|}+\left(-\dfrac{1}{3}\right)^2\)
2) \(\dfrac{1}{3}+\dfrac{4}{3}.\left(\dfrac{1}{2}-\dfrac{1}{3}\right)+\left(\dfrac{-2}{3}\right)^2\)
1) . \(\dfrac{1}{2}-\left|\dfrac{1}{5}-\dfrac{1}{4}\right|+\left(-\dfrac{1}{3}\right)^2\\ =\dfrac{1}{2}-\left(\dfrac{1}{4}-\dfrac{1}{5}\right)+\dfrac{1}{9}\\ =\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{9}\)
\(=\dfrac{61}{180}\)
2) . \(\dfrac{1}{3}+\dfrac{4}{3}\left(\dfrac{1}{2}-\dfrac{1}{3}\right)+\left(\dfrac{-2}{3}\right)^2\\ =\dfrac{1}{3}+\dfrac{4}{3}\cdot\dfrac{1}{6}+\dfrac{4}{9}\\ =\dfrac{1}{3}+\dfrac{2}{9}+\dfrac{4}{9}\\ =1\)
Thực hiện phép tính (tính nhanh nếu có thể):
4) \(4\cdot\left(\dfrac{-1}{2}\right)^3+\left|-1\dfrac{1}{2}+\sqrt{\dfrac{9}{4}}\right|:\sqrt{25}\)
5) \(\left[6-3\cdot\left(\dfrac{-1}{3}\right)^2+\sqrt{\dfrac{1}{4}}\right]:\sqrt{0,\left(9\right)}\)
BT1: Tính
1) \(\dfrac{1}{2011}+\dfrac{2012.2010}{2011}-2012\)
2) \(\left(2-\dfrac{2}{3}\right)\left(2-\dfrac{4}{3}\right)\left(2-\dfrac{5}{4}\right)\left(2-\dfrac{6}{5}\right)\)
1) \(\dfrac{1}{2011}+\dfrac{2012.2010}{2011}-2012\)=\(\dfrac{1+2012.2010-2012.2011}{2011}\)
= \(\dfrac{1+2012.\left(2010-2011\right)}{2011}\)= \(\dfrac{1+2012.\left(-1\right)}{2011}\)
= \(\dfrac{-2011}{2011}=-1\)
Thực hiện phép tính:
1, \(\left(\dfrac{-1}{2}\right)^2.\left|+8\right|-\left(-\dfrac{1}{2}\right)^3:\left|-\dfrac{1}{16}\right|\)
2, \(\left|-0,25\right|-\left(-\dfrac{3}{2}\right)^2:\dfrac{1}{4}+\dfrac{3}{4}.2017^0\)
3, \(\left|\dfrac{2}{3}-\dfrac{5}{6}\right|.\left(3,6:2\dfrac{2}{5}\right)^3\)
4, \(\left|\left(-0,5\right)^2+\dfrac{7}{2}\right|.10-\left(\dfrac{29}{30}-\dfrac{7}{15}\right):\left(-\dfrac{2017}{2018}\right)^0\)
5, \(\dfrac{8}{3}+\left(3-\dfrac{1}{2}\right)^2-\left|\dfrac{-7}{3}\right|\)
`1//([-1]/2)^2 . |+8|-(-1/2)^3:|-1/16|=1/4 .8+1/8 .16=2+2=4`
`2//|-0,25|-(-3/2)^2:1/4+3/4 .2017^0=0,25-2,25.4+0,75.1=0,25-9+0,75=-8,75+0,75-8`
`3//|2/3-5/6|.(3,6:2 2/5)^3=|-1/6|.(3/2)^3=1/6 . 27/8=9/16`
`4//|(-0,5)^2+7/2|.10-(29/30-7/15):(-2017/2018)^0=|1/4+7/2|.10-1/2:1=|15/4|.10-1/2=15/4 .10-1/2=75/2-1/2=37`
`5// 8/3+(3-1/2)^2-|[-7]/3|=8/3+(5/2)^2-7/3=8/3+25/4-7/3=107/12-7/3=79/12`
BT1: Tính nhanh
1) \(\left(\dfrac{-4}{9}+\dfrac{3}{7}\right):1\dfrac{1}{15}+\left(\dfrac{4}{7}-\dfrac{5}{9}\right):1\dfrac{1}{15}\)
2) \(3\dfrac{2}{9}.15\dfrac{4}{7}-3\dfrac{2}{9}.8\dfrac{1}{7}+3\dfrac{2}{9}.\dfrac{15}{7}-3\dfrac{2}{9}.\dfrac{1}{7}\)
1: \(=\dfrac{16}{15}\left(-\dfrac{4}{9}+\dfrac{3}{7}\right)+\dfrac{16}{15}\left(\dfrac{4}{7}-\dfrac{5}{9}\right)\)
\(=\dfrac{16}{15}\left(-\dfrac{4}{9}+\dfrac{3}{7}+\dfrac{4}{7}-\dfrac{5}{9}\right)=0\)
2: \(=\dfrac{29}{9}\left(15+\dfrac{4}{7}-8-\dfrac{1}{7}+\dfrac{15}{7}-\dfrac{1}{7}\right)\)
\(=\dfrac{20}{9}\cdot\left(7\cdot\dfrac{18}{7}\right)=\dfrac{20}{9}\cdot18=40\)
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)\(\left(3-\dfrac{1}{4}+\dfrac{2}{3}\right)-\left(5-\dfrac{1}{3}-\dfrac{6}{5}\right)-\left(6-\dfrac{7}{4}+\dfrac{3}{2}\right)\)