Tính nhanh :
72 . 56 - 12 . 44 + 72 . 44 - 12 . 5
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72 * (56 + 44) + 12 * (44 + 56)
= 72 * 100 + 12* 100
= 7200 + 1200
= 8400
72.56 - 12.44 + 72.44 - 12.56 = 72.(56 + 44) - 12.(44 + 56) = 72.100 - 12.100 = 100.(72 - 12) = 100.60 = 6000
a) \(56^2+44^2+2.56.44=56^2+2.56.44+44^2=\left(56+44\right)^2=100^2=10000\)
b) \(36^2+64^2+72.64=36^2+2.36.64+64^2=\left(36+64\right)^2=100^2=10000\)
c) \(136^2+36^2-72.136=136^2-2.36.136+36^2=\left(136-36\right)^2=100^2=10000\)
a) $56^2+44^2+2.56.44=56^2+2.56.44+44^2=\left(56+44\right)^2=100^2=10000$562+442+2.56.44=562+2.56.44+442=(56+44)2=1002=10000
b) $36^2+64^2+72.64=36^2+2.36.64+64^2=\left(36+64\right)^2=100^2=10000$362+642+72.64=362+2.36.64+642=(36+64)2=1002=10000
c) $136^2+36^2-72.136=136^2-2.36.136+36^2=\left(136-36\right)^2=100^2=10000$
a) \(21^{15}=21^{3.5}=\left(21^3\right)^5=9261^5\)
Vì \(9261>27\Rightarrow9261^5>27^5\Rightarrow21^{15}>27^5\)
b) \(15^{12}=\left(3.5\right)^{12}=3^{12}.5^{12}\)
\(81^3.125^5=\left(3^4\right)^3.\left(5^3\right)^5=3^{4.3}.5^{3.5}=3^{12}.5^{15}\)
Vì \(3^{12}=3^{12}\)mà \(5^{12}< 5^{15}\Rightarrow3^{12}.5^{12}< 3^{12}.5^{15}\Rightarrow15^{12}< 81^3.125^5\)
1: 243^5=(3^5)^5=3^25
3*27^8=3*(3^3)^8=3^25
=>243^5=3*27^8
6: 125^5=(5^3)^5=5^15
25^7=(5^2)^7=5^14
=>125^5>25^7(15>14)
5: 78^12-78^11=78^11(78-1)=78^11*77
78^11-78^10=78^10*77
mà 11>10
nên 78^12-78^11>78^11-78^10
Bài 1: Đặt tính rồi tính :
23,45 x 8,2 = 192,29
37,9 x 3,04 = 115,216
56,2 x 1,003 = 56,3686
72,4 x 3,05 = 220,82
Bài 5: Tính nhanh:
23,14 x 56 + 44 x 23,14
= 23,14 x (56 + 44)
= 23,14 x 100
= 2314
12,25 x 109 – 9 x 12,25
= 12,25 x (109 - 9)
= 12,25 x 100
= 1225
2,75 x 36 – 14 x 2,75 + 2,75 x 78
= 2,75 x (36 - 14 + 78)
= 2,75 x 100
= 275
1,56 x 67 + 34 x 1,56 – 1,56
= 1,56 x (67 + 34) - 1,56
= 1,56 x 101 - 1,56
= 157,56 - 1,56
= 156
Bài 1:
a.
$-12-(-46)=-12+46=46-12=34$
b.
$-(-8)-54=8-54=-(54-8)=-46$
c.
$-15-(-72)=-15+72=72-15=57$
Bài 2:
a. $(156-812)-(156-12)=156-812-156+12$
$=(156-156)-(812-12)=0-800=-800$
b.
$-(-72+83)-(72+17)=72-83-72-17=(72-72)-(83+17)$
$=0-100=-100$
c.
$-(-23-78)+(77-178)=23+78+77-178$
$=(23+77)-(178-78)=100-100=0$
d.
$(-213-156)-(-213+44)=-213-156+213-44=(-213+213)-(156+44)$
$=0-200=-200$
\(=\left(1-\dfrac{1}{2}\right)+\left(1-\dfrac{1}{6}\right)+\left(1-\dfrac{1}{12}\right)+...+\left(1-\dfrac{1}{90}\right)\\ =\left(1+1+1+1+1+1+1+1+1\right)-\left(\dfrac{1}{2}+\dfrac{1}{6}+...+\dfrac{1}{90}\right)\\ =9-\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{9\cdot10}\right)\\ =9-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{9}-\dfrac{1}{10}\right)\\ =9-\left(1-\dfrac{1}{10}\right)=9-\dfrac{9}{10}=\dfrac{81}{10}\)
a) \(\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+...+\frac{89}{90}\)
\(=1-\frac{1}{6}+1-\frac{1}{12}+...+1-\frac{1}{90}\)
\(=\left(1+1+1+...+1\right)-\left(\frac{1}{6}+\frac{1}{12}+...+\frac{1}{90}\right)\)
\(=\left(1+1+1+...+1\right)-\left(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{9\cdot10}\right)\)
Từ 2 đến 9 có : ( 9 - 2 ) / 1 + 1 = 8 ( số hạng ) => có 8 số 1
\(\Rightarrow8-\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(=8-\left(\frac{1}{2}-\frac{1}{10}\right)\)
\(=8-\frac{2}{5}=\frac{38}{5}\)
b) \(\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+...+\frac{109}{110}\)
\(=1-\frac{1}{2}+1-\frac{1}{6}+...+1-\frac{1}{110}\)
\(=\left(1+1+1+...+1\right)-\left(\frac{1}{2}+\frac{1}{6}+...+\frac{1}{110}\right)\)
\(=\left(1+1+...+1\right)-\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{10\cdot11}\right)\)
Từ 1 đến 10 có : ( 10 - 1 ) / 1 + 1 = 10 ( số hạng ) => có 10 số 1
\(\Rightarrow10-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{10}-\frac{1}{11}\right)\)
\(=10-\left(1-\frac{1}{11}\right)\)
\(=10-\frac{10}{11}=\frac{100}{11}\)
72 . 56 - 12 . 44 + 72 . 44 - 12 . 5
=72 x (56 + 44) + 12 x (44 + 56)
= 72 x 100 + 12 x 100
= 7200 + 1200
= 8400