Thực hiện phép tính ( tính nhanh nếu có thể)
\(\dfrac{20^4.15^5}{12^5.25^4}\)
Bài 1: Thực hiện phép tính: (tính nhanh nếu có thể)
f) \(\dfrac{4}{15}.\dfrac{1}{3}.\dfrac{15}{20}\)
`4 / 15 . 1 / 3 . 15 / 20`
`= [ 4 . 1 . 15 ] / [ 15 . 3 . 20 ]`
`= [ 4 . 1 . 15 ] / [ 15 . 3 . 4 . 5 ]`
`= 1 / [ 3 . 5 ]`
`= 1 / 15`
\(=\left(\dfrac{4}{15}.\dfrac{15}{20}\right).\dfrac{1}{3}=\dfrac{60}{300}.\dfrac{1}{3}=\dfrac{60}{900}=\dfrac{1}{15}\)
\(=\dfrac{4.1.15}{15.3.5.4}=\dfrac{1}{3.5}=\dfrac{1}{15}\)
Bài 1: Thực hiện các phép tính (Tính nhanh nếu có thể)
a) \(\dfrac{-5}{9}\) - \(\dfrac{-5}{12}\) b) \(\dfrac{-5}{12}\) : \(\dfrac{15}{4}\) c) \(\dfrac{1}{13}\) x \(\dfrac{8}{13}\) + \(\dfrac{5}{13}\) x \(\dfrac{1}{13}\) - \(\dfrac{14}{13}\)
Bài 2: Tìm \(x\), biết:
a) \(x=\dfrac{1}{5}+\dfrac{-3}{7}\) b) \(\dfrac{3}{5}-\dfrac{4}{7}\)\(:\)\(x=\dfrac{-9}{10}\) c) \(x-\left(\dfrac{-3}{4}\right)=\dfrac{-2}{3}-\dfrac{1}{2}\)
d) \(\dfrac{-5}{9}-x=\dfrac{1}{3}+\dfrac{7}{18}\)
Bài 3: Cho S = \(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{10^2}\). Chứng minh rằng: \(S>\dfrac{9}{22}\)
Thực hiện phép tính (tính nhanh nếu có thể):
\(\dfrac{4^{20}-2^{20}+6^{20}}{6^{20}-3^{20}+9^{20}}\)
Thực hiện phép tính ( tính nhanh nếu có thể ) :
a) \(\dfrac{3}{5}+\dfrac{1}{5}.\dfrac{-17}{9}\)
b) \(\left(-\dfrac{4}{15}-\dfrac{18}{19}\right)-\left(\dfrac{20}{19}+\dfrac{11}{15}\right)\)
\(a,\dfrac{3}{5}+\dfrac{1}{5}.\dfrac{-17}{9}=\dfrac{3}{5}-\dfrac{17}{45}=\dfrac{27}{45}-\dfrac{17}{45}=\dfrac{10}{45}=\dfrac{2}{9}\\ b,\left(-\dfrac{4}{15}-\dfrac{18}{19}\right)-\left(\dfrac{20}{19}+\dfrac{11}{15}\right)=-\dfrac{4}{15}-\dfrac{18}{19}-\dfrac{20}{19}-\dfrac{11}{15}=\left(-\dfrac{4}{15}-\dfrac{11}{15}\right)-\left(\dfrac{18}{19}+\dfrac{20}{19}\right)=-1-2=-3\)
\(a,=\dfrac{3}{5}+\left(-\dfrac{17}{45}\right)=\dfrac{2}{9}\)
\(b,=-\dfrac{4}{15}-\dfrac{18}{19}-\dfrac{20}{19}-\dfrac{11}{15}=-3\)
a. 3/5+1/5.-17/9
=3/5+-17/45
=27/45+-17/45
=2/9
b. (-4/15-18/19)-(20/19+11/15)
=-4/15-18/19-20/19-11/15
=(-4/15-11/15)-(18/19-20/19)
=(-1)-(-2/19)
=(-19/19)-(-2/19)
=-17/19
Thực hiện phép tính (tính nhanh nếu có thể):
a/ \(\dfrac{3}{5}+\dfrac{1}{5}.\dfrac{-17}{9}\) b/ \(\left(-\dfrac{4}{15}-\dfrac{18}{19}\right)\)-\(\left(\dfrac{20}{19}+\dfrac{11}{15}\right)\)
Bài 1: Thực hiện phép tính ( tính nhanh nếu có thể )
a) ( 12,36 - 0,61 ) - ( 50,39 - 12,64 )
b) \(\left[\dfrac{-1}{12}\right]^2-1\dfrac{1}{2}+0,5.\dfrac{12}{5}+5\%\)
a) = 11,75 - 37,75 = -26
b) = 1/144 - 3/2 + 1/2 . 12/5 + 1/20 = 1/144 - 3/2 + 6/5 + 1/20 =-35/144
Thực hiện phép tính (tính nhanh nếu có thể)
c) \(5\dfrac{2}{5}\)✖\(4\dfrac{2}{7}\)+\(5\dfrac{5}{7}\)✖\(5\dfrac{2}{5}\)
d) 75%-\(1\dfrac{1}{2}\)+0,5:\(\dfrac{5}{12}\)-\(\left(\dfrac{-1}{2}\right)^2\)
Thực hiện phép tính (tính hợp lý nếu có thể): \(\dfrac{-5}{6}.\dfrac{4}{19}+\dfrac{-7}{12}.\dfrac{4}{19}-\dfrac{40}{57}\)
\(=\dfrac{4}{19}\left(\dfrac{-5}{6}-\dfrac{7}{12}-\dfrac{10}{3}\right)\)
\(=\dfrac{4}{19}\cdot\left(\dfrac{-10-7-40}{12}\right)=\dfrac{4}{19}\cdot\dfrac{-57}{12}=-\dfrac{3}{3}=-1\)
=\(\dfrac{4}{19}.\left(-\dfrac{5}{6}+-\dfrac{7}{12}\right)-\dfrac{40}{57}\)
=\(-\dfrac{4}{19}-\dfrac{40}{57}\)
=\(-\dfrac{52}{57}\)
Thực hiện phép tính (tính nhanh nếu có thể)
\(\dfrac{11}{15}.\dfrac{4}{11}+\dfrac{11}{15}.\dfrac{5}{11}+\dfrac{11}{15}.\dfrac{2}{11}\)
= \(\dfrac{11}{15}\). \(\left(\dfrac{4}{11}+\dfrac{5}{11}+\dfrac{2}{11}\right)\)
= \(\dfrac{11}{15}\). 1
=\(\dfrac{11}{15}\)
\(=\dfrac{11}{15}\cdot\left(\dfrac{4}{11}+\dfrac{5}{11}+\dfrac{2}{11}\right)=\dfrac{11}{15}\cdot\dfrac{11}{11}=\dfrac{11}{15}\)
11/15 . ( 4/11 +5/11 + 2/11 )
= 11/15 . 1
= 11/15