Lời giải:

$\frac{6}{4}\times \frac{19}{10}-\frac{3}{4}\times \frac{7}{10}+\frac{3}{4}:\frac{10}{69}$

$=\frac{6}{4}\times \frac{19}{10}-\frac{3}{4}\times \frac{7}{10}+\frac{3}{4}\times \frac{69}{10}$

$=\frac{6}{4}\times \frac{19}{10}+\frac{3}{4}\times (\frac{69}{10}-\frac{7}{10})$

$=\frac{3}{2}\times \frac{19}{10}+\frac{3}{4}\times \frac{62}{10}$

$=\frac{3}{2}\times \frac{19}{10}+\frac{3}{2}\times \frac{31}{10}$
$=\frac{3}{2}\times (\frac{19}{10}+\frac{31}{10})$

$=\frac{3}{2}\times \frac{50}{10}=\frac{3}{2}\times 5=\frac{15}{2}$

Kết quả = 

\(\frac{6}{4}\cdot\frac{19}{10}-\frac{3}{4}\cdot\frac{7}{10}+\frac{3}{4}:\frac{10}{69}=2^{ }_{ }\)\(\frac{15}{46}\)

vế 1   (6:4 =1.5 )x(19:10 =1.9)1,5x1,9 =2,85
vế 2   (3/4=0,75)x(7:10=0,7)0,75x0,7=0,525
vế 3   (3:4=0,75):(10:69=0,14492753623 lấy 3 chữ số ở hàng thập phân =0,144) 0,75:0,144=6,57894736842 lấy 3 chữ số ở hàng thập phân =6,578 
2,85 -0,525+6,578
=2,325+6,578
=8.903
(hơi rườm rà nếu có sai thông cảm)

vế 1   6/4 x 19/10=57/20
vế 2   3/4 x 7/10=21/40
vế 3   3/4 : 10/69 =207/40 
57/20 - 21/40 + 207/40
= 93/40 + 207/40
=15/2

3 x 15 + 21 x 15 + 85 x 5

= 45 + 315 + 425

= 785

15 - 30 + 40 

= 25

21 + 19 - 50 + 10

= 0

\(\dfrac{1}{5}-\dfrac{1}{4}+2\)

\(=-\dfrac{1}{20}+2\)

\(=\dfrac{39}{20}\)

\(\left(\dfrac{1}{4}+\dfrac{1}{6}\right)\times\left(\dfrac{1}{2}-\dfrac{1}{4}\right)\)

\(=\dfrac{5}{12}\times\dfrac{1}{4}\)

\(=\dfrac{5}{12}\times\dfrac{3}{12}\)

\(=\dfrac{5}{48}\)

\(\dfrac{1}{10}+\dfrac{1}{5}-\dfrac{3}{4}\)

\(=-\dfrac{9}{20}\)

\(3\times15+21\times15+85\times5\\ =15\times\left(3+21\right)+425\\ =15\times24+425\\ =360+425\\ =785\)

\(15-30+40\\ =\left(15+40\right)-30\\ =55-30\\ =25\)

\(21+19-50+10\\ =\left(21+19\right)-\left(50-10\right)\\ =40-40\\ =0\)

\(\dfrac{1}{5}-\dfrac{1}{4}+2\)

\(=\dfrac{4}{20}-\dfrac{5}{20}+\dfrac{40}{20}\)

\(=\dfrac{\left(4+40\right)}{20}-\dfrac{5}{20}\)

\(=\dfrac{44}{20}-\dfrac{5}{20}\)

\(=\dfrac{39}{20}\)

\(\left(\dfrac{1}{4}+\dfrac{1}{6}\right)\times\left(\dfrac{1}{2}-\dfrac{1}{4}\right)\)

\(=\dfrac{5}{12}\times\dfrac{1}{4}\)

\(=\dfrac{5}{48}\)

\(\dfrac{1}{10}+\dfrac{1}{5}-\dfrac{3}{4}\)

\(=\dfrac{2}{20}+\dfrac{4}{20}-\dfrac{15}{20}\)

\(=\dfrac{6}{20}-\dfrac{15}{20}\)

\(=-\dfrac{9}{20}\)

\(\frac{1}{9\cdot10}+\frac{2}{10\cdot12}+\frac{3}{12\cdot15}+\frac{4}{15\cdot19}+\frac{5}{19\cdot24}+\frac{6}{24\cdot30} \)
\(=\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{12}+\frac{1}{12}-\frac{1}{15}+\frac{1}{15}-\frac{1}{19}+\frac{1}{19}-\frac{1}{24}+\frac{1}{24}-\frac{1}{30}\)
\(=\frac{1}{9}-\frac{1}{30}\)
\(=\frac{10}{90}-\frac{3}{90}\)
\(=\frac{7}{90}\)
 

1: =72/90+65/90=137/90

2: =24/56-77/56=-53/56

3: =-7/10+4/5=1/10

4: =15/100-4/100=11/100

5: =4/6-5/6=-1/6

6: =10/40-15/40-76/40=-81/40

7: =-9/10+7/18

=-81/90+35/90=-46/90=-23/45

8: =27/90-55/90=-28/90=-14/45

9: =36/60-50/60-35/60=-49/60

10: =-4/9+5/6-3/8

=-32/72+60/72-27/72

=1/72