tính nhanh tổng sau :
\(\frac{121212}{141414}\)x \(\frac{1313}{1212}\)x\(\frac{2424}{2424}\)
tính nhanh
\(2018\times(\frac{1}{2}+\frac{1212}{2424}\))
\(2018\times\left(\frac{1}{2}+\frac{1212}{2424}\right)=2018\times\left(\frac{1}{2}+\frac{12}{24}\right).\)
\(=2018\times\left(\frac{1}{2}+\frac{1}{2}\right)\)
\(=2018\times1=2018\)
2018.(1/2+1212/2424)
=2018.(1/2+1/2)
=2018.2/2
=2018.1
=2018
Hk tốt
\(2018\times\left(\frac{1}{2}+\frac{1212}{2424}\right)\)
\(=2018\times\left(\frac{1}{2}+\frac{1}{2}\right)\)
\(=2018\times1=2018\)
~ Hok tốt ~
Bài 1: Tính nhanh
a) \(\frac{1111+1212+1313+1414+1515+1616}{2020+2121+2222+2323+2424+2525}\)
b) \(\frac{5,4:0,4\cdot1420+4,5\cdot780\cdot3}{3+6+9+12+......+24+27}\)
c) \(\frac{7,2:2\cdot28,6+1,43\cdot2\cdot64}{2+2+4+6+10+16+......+110}\)
Bài 2: Tính tổng
D = 1 x 2 + 2 x 3 + 3 x 4 + ...... +99 x 100
TÍNH NHANH :
2018 x {\(\frac{1212}{1212}\):\(\frac{2424}{2424}\)}
Trả lời:
\(2018\times\left(\frac{1212}{1212}\div\frac{2424}{2424}\right)\)
\(=2018\times\left(1\div1\right)\)
\(=2018\times1\)
\(=2018\)
Tính nhanh
\(2018\times\left\{\frac{1212}{1212}\div\frac{2424}{2424}\right\}\)
\(=2018\times1\)
\(=2018\)
2018×(1212/1212×2424/2424)
2018×1
2018
Không quy đồng tử số và mẫu số hãy so sánh các p/s sau :
\(\displaystyle \frac{{12}}{{14}}
\) ; \(\displaystyle \frac{{1212}}{{1414}}
\) ; \(\displaystyle \frac{{121212}}{{141414}}
\)
\(\displaystyle \frac{{24}}{{35}} \) ; \(\displaystyle \frac{{2424}}{{3535}} \) ; \(\displaystyle \frac{{242424}}{{353535}} \)
\(\displaystyle \frac{{ab}}{{cd}} \) ; \(\displaystyle \frac{{abab}}{{cdcd}} \) ; \(\displaystyle \frac{{ababab}}{{cdcdcd}} \)
\(\frac{12}{14}=\frac{1212}{1414}=\frac{121212}{141414}\)
\(\frac{24}{35}=\frac{2424}{3535}=\frac{242424}{353535}\)
\(\frac{ab}{cd}=\frac{abab}{cdcd}=\frac{ababab}{cdcdcd}\)
bài 1: Tính biểu thức 1 cách hợp lý\(\frac{1010+1111+1212+1313+1414+1515+1616+1717}{2020+2121+2222+2323+2424+2525+2626+2727}\)
bài 2: Tím y là số tự nhiên
\(2< \)( \(\frac{1}{6}+\frac{2}{15}+\frac{3}{40}+\frac{4}{96}\)):5 x y \(< \frac{5}{6}\)
\(\frac{1010+1111+1212+1313+1414+1515+1616+1717}{2020+2121+2222+2323+2424+2525+2626+2727}\)
\(=\frac{101.10+101.11+...+101.17}{101.20+101.21+...+101.27}\)
\(=\frac{101.\left(10+11+...+17\right)}{101.\left(20+21+...+27\right)}\)
\(=\frac{108}{188}\)
\(=\frac{27}{47}\)
\(2>\left(\frac{1}{6}+\frac{2}{15}+\frac{3}{40}+\frac{4}{96}\right)\cdot5.y>\frac{5}{6}\)
\(\Rightarrow2>\left(\frac{1}{6}+\frac{2}{15}+\frac{3}{40}+\frac{1}{24}\right):5.y>\frac{5}{6}\)
\(\Rightarrow2>\left(\frac{20}{120}+\frac{16}{120}+\frac{9}{120}+\frac{5}{120}\right):5.y>\frac{5}{6}\)
\(\Rightarrow2>\frac{5}{12}:5.y>\frac{5}{6}\)
\(\Rightarrow2>\frac{1}{12}.y>\frac{5}{6}\)
Đặt :\(\frac{1}{12}.y=2\Rightarrow y=2:\frac{1}{12}=24\)
\(\frac{1}{12}.y=\frac{5}{6}\Rightarrow y=\frac{5}{6}:\frac{1}{12}=10\)
\(\Rightarrow24>y>10\)
\(\Rightarrow y\in\left\{11;12;...;23\right\}\)
Rút gọn các phân số sau:
a) − 1212 − 2424 ;
b) 120120 − 240240 ;
c) 1313 − 1414 .
a ) − 1212 − 2424 = ( − 1212 ) : ( − 1212 ) ( − 2424 ) : ( − 1212 ) = 1 2
b ) 120120 − 240240 = 120120 : ( − 120120 ) − 240240 : ( − 120120 ) = − 1 2
c) 1313 − 1414 = 1313 : ( − 101 ) − 1414 : ( − 101 ) = − 13 14
Tính
\(A=\frac{12}{13}+\frac{1212}{1313}+\frac{121212}{131313}+...+\frac{\underrightarrow{1212...12}2012số12}{\underrightarrow{1313...13}2012so13}\)
\(C=\frac{5}{2\times0,237237...}+\frac{5}{2\times0,0237237...}+\frac{5}{2\times0,00237237}\)
\(D=\) số các ước dương của 2492820
Rút gọn các phân số sau
a ) 33 66 ; b ) − 22 77 ; c ) 3030 6060
d ) − 1212 − 2424 ; e ) 120120 − 240240 ; f ) 1313 − 1414
a) 33 66 = 33 : 33 66 : 33 = 1 2 b ) − 22 77 = − 22 : 11 77 : 11 = − 2 7
c ) 3030 6060 = 3030 : 3030 6060 : 3030 = − 1 2 d ) − 1212 − 2424 = ( − 1212 ) : ( − 1212 ) ( − 2424 ) : ( − 1212 ) = 1 2
e ) 120120 − 240240 = 120120 : ( − 120120 ) − 240240 : ( − 120120 ) = − 1 2
f ) 1313 − 1414 = 1313 : ( − 101 ) − 1414 : ( − 101 ) = − 13 14
1111+1212+1313+1414+1515+1616 / 2020+2121+2222+2323+2424+2525 =?
\(\frac{2323+1313+1414+1515+1616}{4141+2222+2323+2424+2525}\)
=\(\frac{8181}{13635}\)