`a// [-3]/5+7/21+[-4]/5+7/5=([-3]/5+[-4]/5+7/5)+7/21=0/5+7/21=7/21`

`b// [-3]/17+(2/3+3/17)=[-3]/17+2/3+3/17=([-3]/17+3/17)+2/3=0/17+2/3=2/3`

`c// [-5]/21+([-16]/21+1)=[-5]/21+[-16]/21+1=([-5]/21+[-16]/21)+1=[-21]/21+1=-1+1=0`

a) \(\dfrac{-3}{5}+\dfrac{7}{21}+\dfrac{-4}{5}+\dfrac{7}{5}\)

\(=\left(-\dfrac{3}{5}+\dfrac{-4}{5}+\dfrac{7}{5}\right)+\dfrac{7}{21}\)

\(=0+\dfrac{7}{21}\)

\(=\dfrac{7}{21}\)

b) `-3/17 + ( 2/3 + 3/17)`

` = -3/17 +  2/3 + 3/17`

` = 2/3 + ( -3/17 +3/17)`

` = 2/3 + 0`

` = 2/3`

c) 

` -5/21 + ( -16/21 +1)`

\(=\dfrac{-5}{21}+\dfrac{-16}{21}+1\)

\(=\left(\dfrac{-5}{21}+\dfrac{-16}{21}\right)+1\)

\(=-1+1=0\)

\(\dfrac{41}{66}\)

\(\dfrac{67}{30}\)

a, =5/11+1/6=41/66

b, = 5/2-4/15=67/30

a. 41/66

b. 67/30

a. Áp dụng tính chất dãy tỉ số bằng nhau:

$\frac{x}{2}=\frac{y}{5}=\frac{x+y}{2+5}=\frac{-21}{7}=-3$

$\Rightarrow x=2(-3)=-6; y=5(-3)=-15$

b. Áp dụng tính chất dãy tỉ số bằng nhau:

$7x=3y=\frac{x}{\frac{1}{7}}=\frac{y}{\frac{1}{3}}=\frac{x-y}{\frac{1}{7}-\frac{1}{3}}=\frac{16}{\frac{-4}{21}}=-84$

$\Rightarrow x=(-84):7=-12; y=-84:3=-28$

c. $\frac{x}{y}=\frac{5}{9}\Rightarrow \frac{x}{5}=\frac{y}{9}$

Áp dụng tính chất dãy tỉ số bằng nhau:

$\frac{x}{5}=\frac{y}{9}=\frac{3x}{15}=\frac{2y}{18}=\frac{3x+2y}{15+18}=\frac{66}{33}=2$

$\Rightarrow x=2.5=10; y=9.2=18$

d. Áp dụng tính chất dãy tỉ số bằng nhau:

$\frac{x}{15}=\frac{y}{7}=\frac{2y}{14}=\frac{x-2y}{15-14}=\frac{16}{1}=16$

$\Rightarrow x=16.15=240; y=7.16=112$

e.

Đặt $\frac{x}{5}=\frac{y}{2}=k\Rightarrow x=5k ; y=2k$

Khi đó: $xy=5k.2k=10k^2=1000\Rightarrow k^2=100\Rightarrow k=\pm 10$

Với $k=10$ thì $x=5k=50; y=2k=20$

Với $k=-10$ thì $x=5k=-50; y=2k=-20$

Bài 2:

Áp dụng tính chất dãy tỉ số bằng nhau:

$\frac{x}{13}-\frac{y}{7}-\frac{z}{5}=\frac{x-y-z}{13-7-5}=\frac{6}{1}=6$

$\Rightarrow x=13.6=78; y=7.6=42; z=5.6=30$

\(=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+...+\frac{1}{61}-\frac{1}{66}\)

\(=\frac{1}{11}-\frac{1}{66}=\frac{6}{66}-\frac{1}{66}=\frac{5}{66}\)

Thank you

\(\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+...+\frac{5}{61.66}=5\left(\frac{1}{11.16}+\frac{1}{16.21}+\frac{1}{21.26}+...+\frac{1}{61.66}\right)\)

\(=5\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+....+\frac{1}{61}-\frac{1}{66}\right)=5\left(\frac{1}{11}-\frac{1}{66}\right)=5.\frac{5}{66}=\frac{25}{66}\)

\(\dfrac{5}{3}\cdot\dfrac{7}{25}+\dfrac{5}{3}\cdot\dfrac{21}{25}-\dfrac{5}{3}\cdot\dfrac{7}{25}\)

\(=\dfrac{5}{3}\cdot\left(\dfrac{7.}{25}+\dfrac{21}{25}-\dfrac{7}{25}\right)\)

\(=\dfrac{5}{3}\cdot\dfrac{21}{25}=\dfrac{7}{5}\)

b) \(250\%+19\dfrac{3}{11}\cdot\dfrac{7}{26}-6\dfrac{3}{11}\cdot\dfrac{7}{26}\)

\(=\dfrac{5}{2}+\dfrac{212}{11}\cdot\dfrac{7}{26}-\dfrac{69}{11}\cdot\dfrac{7}{26}\)

\(=\dfrac{7}{26}\cdot\left(\dfrac{212}{11}-\dfrac{69}{11}\right)+\dfrac{5}{2}\)

\(=\dfrac{7}{26}\cdot13+\dfrac{5}{2}\)

\(=\dfrac{7}{2}+\dfrac{5}{2}\)

\(=\dfrac{12}{2}=6\)

\(=\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{21}+...+\dfrac{1}{61}-\dfrac{1}{66}\)

\(=\dfrac{1}{11}-\dfrac{1}{66}=\dfrac{5}{66}\)

a) 

\(\dfrac{-5}{21}+\left(\dfrac{-16}{21}+1\right)=\dfrac{-5}{21}+\dfrac{-16}{21}+1\)=\(-1+1=0\)

`(-5)/21+((-16)/21+1)`

`=(-5)/21-16/21+1`

`=-1+1=0`

`(-3)/8*1/6+3/(-8)*5/6+(-1)/16`

`=-3/8*(1/6+5/6)-10/16`

`=-3/8-10/16`

`=-6/16-10/16=-16/16=-1`

\(\dfrac{-3}{8}.\dfrac{1}{6}+\dfrac{-3}{8}.\dfrac{5}{6}+\dfrac{-10}{16}\)

=\(\dfrac{-3}{8}.\left(\dfrac{1}{6}+\dfrac{5}{6}\right)+\dfrac{-10}{16}\)

=\(\dfrac{-3}{8}+\dfrac{-5}{8}=-1\)=

\(\dfrac{-15}{3}.\dfrac{26}{7}.\dfrac{-21}{5}.\dfrac{15}{16}\)

\(=5.\dfrac{2.13}{7}.\dfrac{3.7}{5}.\dfrac{3.5}{2.8}\)

\(=\dfrac{5.13.3.3}{4}=\dfrac{585}{4}\)