S=4/5.7+4/7.9+..+4/59.61

=>S=4/2.(2/5.7+2/7.9+...+2/59.61)

=>S=2.(1/5-1/7+1/7-1/9+...+1/59-1/61)

=>S=2.(1/5-1/61)=2.56/305=112/305

vậy S=112/305

Mot bai toan hay day

\(S=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{99.100}\)

   \(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{99}-\frac{1}{100}\)

     \(=1-\frac{1}{100}=\frac{99}{100}\)

a) 21: 25 =\(\dfrac{21}{25}\)

30: 43 = \(\dfrac{30}{43}\)              

61: 69 = \(\dfrac{61}{69}\) 

17: 100 = \(\dfrac{17}{100}\)

b)9 : 4 = \(\dfrac{9}{4}\)

51: 7 = \(\dfrac{51}{7}\)

60 : 39 = \(\dfrac{60}{39}\)                  

200 : 163 = \(\dfrac{200}{163}\)

A

4/ 5 * 7 + 4 / 7 * 9 + .. + 4 / 59 * 61

= 2/5 - 2/7 + 2/7 - 2/9 + ... + 2/59 - 2/61

= 2/5 - 2/61

= 112/305

Đặt 

\(S=\frac{4}{5.7}+\frac{4}{7.9}+...+\frac{4}{59.61}\)

\(S=2.\left(\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{59.61}\right)\)

\(S=2.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{59}-\frac{1}{61}\right)\)

\(S=2.\left(\frac{1}{5}-\frac{1}{61}\right)\)

\(S=2.\frac{56}{305}=\frac{112}{305}\)

\(1/\)

\(\frac{12}{49}:\frac{16}{21}\)

\(=\frac{12}{49}\times\frac{21}{16}\)

\(=\frac{12\times21}{49\times16}\)

\(=\frac{252}{784}=\frac{9}{28}\)

\(2/\)

\(a,\frac{5}{11}-\left(\frac{39}{61}+\frac{12}{61}\right)\)

\(=\frac{5}{11}-\frac{51}{61}\)

\(=-\frac{256}{671}\)

\(b,\frac{17}{12}+\frac{9}{7}-\left(\frac{2}{7}-\frac{7}{12}\right)\)

\(=\frac{17}{12}+\frac{9}{7}-\frac{2}{7}+\frac{7}{12}\)

\(=\left(\frac{17}{12}+\frac{7}{12}\right)+\left(\frac{9}{7}-\frac{2}{7}\right)\)

\(=2+1\)

\(=3\)

\(c,\frac{16}{17}\times\frac{12}{19}+\frac{16}{17}\times\frac{7}{19}\)

\(=\frac{16}{17}\times\left(\frac{12}{19}+\frac{7}{19}\right)\)

\(=\frac{16}{17}\times1\)

\(=\frac{16}{17}\)

\(3/\)

\(a,x:\frac{4}{5}=\frac{25}{8}:\frac{5}{4}\)

\(x:\frac{4}{5}=\frac{5}{2}\)

\(x=2\)

\(b,\frac{22}{5}:x=\frac{44}{5}:\frac{5}{2}\)

\(\frac{22}{5}:x=\frac{88}{25}\)

\(x=\frac{5}{4}\)

\(c,x\times\frac{4}{9}\times\frac{15}{18}=\frac{25}{18}\)

\(x\times\frac{4}{9}=\frac{5}{3}\)

\(x=\frac{15}{4}\)

a: \(B=\frac12-\left\lbrack\frac38+\left(-\frac74\right)\right\rbrack\)

\(=\frac12-\frac38+\frac74\)

\(=\frac48-\frac38+\frac{14}{8}=\frac{15}{8}\)

b: \(-\frac{4}{12}-\left(-\frac{13}{39}-0,25\right)+0,75\)

\(=-\frac13+\frac13+0,25+0,75\)

=0,25+0,75

=1

c: \(\frac12-\frac13+\frac{1}{23}+\frac16\)

\(=\left(\frac12-\frac13+\frac16\right)+\frac{1}{23}\)

\(=\left(\frac16+\frac16\right)+\frac{1}{23}=\frac13+\frac{1}{23}=\frac{26}{69}\)

d: \(\left(-\frac{13}{7}-\frac49\right)-\left(-\frac{10}{7}-\frac49\right)\)

\(=-\frac{13}{7}-\frac49+\frac{10}{7}+\frac49\)

\(=-\frac{13}{7}+\frac{10}{7}=-\frac37\)

e: \(\left(\frac78-\frac52+\frac47\right)-\left(-\frac37+1-\frac{13}{8}\right)\)

\(=\frac78-\frac52+\frac47+\frac37-1+\frac{13}{8}\)

\(=\frac{20}{8}-\frac52=0\)

f: \(-\frac37+\left(3-\frac34\right)-\left(2,25-\frac{10}{7}\right)\)

\(=-\frac37+3-\frac34-2,25+\frac{10}{7}\)

\(=\frac77+0,75-\frac34\)

=1
g: \(\left(\frac53-\frac37+9\right)-\left(2+\frac57-\frac23\right)+\left(\frac87-\frac43-10\right)\)

\(=\frac53-\frac37+9-2-\frac57+\frac23+\frac87-\frac43-10\)

\(=\left(\frac53+\frac23-\frac43\right)+\left(-\frac37-\frac57+\frac87\right)+\left(9-2-10\right)\)

\(=\frac33+7-10=1-3=-2\)

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{99.100}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.....+\frac{1}{99}-\frac{1}{100}\)

\(=1-\frac{1}{100}\)

\(=\frac{99}{100}\)

Dấu chấm là nhân

a) \(\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{99.100}\) \(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{99}-\frac{1}{100}=1-\frac{1}{100}=\frac{99}{100}\)

b) \(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{97.99}\) \(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+....+\frac{1}{97}-\frac{1}{99}=1-\frac{1}{99}=\frac{98}{99}\)

c) Đặt \(C=\frac{4}{5.7}+\frac{4}{7.9}+....+\frac{4}{59.61}\)

\(\Rightarrow\frac{1}{2}C=\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+....+\frac{1}{59}-\frac{1}{61}\)

\(\Rightarrow\frac{1}{2}C=\frac{1}{5}-\frac{1}{61}=\frac{56}{305}\)

\(\Rightarrow C=\frac{56}{305}:\frac{1}{2}=\frac{112}{305}\)

CHÚC BẠN HỌC TỐT NHA! ĐÚNG THÌ NHA!

= 0 nha

1 - 2 - 3 + 4 + 5 - 6 - 7 + 8 + 9 - 10 - 11 + 12 + ... + 61 - 62 - 63 + 64 ( 64 số )

= ( 1 - 2 - 3 + 4 ) + ( 5 - 6 - 7 + 8 ) + ( 9 - 10 - 11 + 12 ) + ... + ( 61 - 62 - 63 + 64 )   ( 16 nhóm )

= 0 + 0 + 0 + ... + 0         ( 16 số 0 )

= 0 . 16

= 0