a) \(\dfrac{-5}{9}-\dfrac{4}{15}+\dfrac{2}{9}-\dfrac{11}{15}\)

\(=\left(\dfrac{-5}{9}+\dfrac{2}{9}\right)-\left(\dfrac{4}{15}+\dfrac{11}{15}\right)\)

\(=\dfrac{-3}{9}-\dfrac{15}{15}\)

\(=-\dfrac{1}{3}-1\)

\(=-\dfrac{4}{3}\)

b) \(\dfrac{-8}{13}-\dfrac{7}{16}+\dfrac{21}{13}-\dfrac{1}{6}\)

\(=\left(\dfrac{-8}{13}+\dfrac{21}{13}\right)-\dfrac{7}{16}-\dfrac{1}{6}\)

\(=\dfrac{13}{13}-\dfrac{29}{48}\)

\(=1-\dfrac{29}{48}\)

\(=\dfrac{19}{48}\)

c) \(\dfrac{-15}{25}-\dfrac{14}{21}+\dfrac{8}{5}-\dfrac{5}{3}\)

\(=\dfrac{-3}{5}-\dfrac{2}{3}+\dfrac{8}{5}-\dfrac{5}{3}\)

\(=\left(\dfrac{-3}{5}+\dfrac{8}{5}\right)-\left(\dfrac{2}{3}+\dfrac{5}{3}\right)\)

\(=\dfrac{5}{5}-\dfrac{7}{3}\)

\(=1-\dfrac{7}{3}\)

\(=-\dfrac{4}{3}\)

a: =-5/9+2/9-11/15-4/15

=-3/9-1

=-12/9=-4/3

b: =-8/13+21/13-7/16-1/6

=1-1/6-7/16

=5/6-7/16

=19/48

c: =-15/25+8/5-2/3-5/3

=-7/3+1

=-4/3

a) \(-\dfrac{5}{9}-\dfrac{4}{15}+\dfrac{2}{9}-\dfrac{11}{15}\)

\(=\left(-\dfrac{5}{9}+\dfrac{2}{9}\right)+\left(-\dfrac{4}{15}-\dfrac{11}{15}\right)\)

\(=-\dfrac{1}{3}-1=-\dfrac{4}{3}\)

b) \(-\dfrac{8}{13}-\dfrac{7}{16}+\dfrac{21}{13}-\dfrac{1}{16}\)(sửa đề)

\(=\left(-\dfrac{8}{13}+\dfrac{21}{13}\right)+\left(-\dfrac{7}{16}-\dfrac{1}{16}\right)\)

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

c) \(-\dfrac{15}{25}-\dfrac{14}{21}+\dfrac{8}{5}-\dfrac{5}{3}\)

\(=-\dfrac{3}{5}-\dfrac{2}{3}+\dfrac{8}{5}-\dfrac{5}{3}\)

\(=\left(-\dfrac{3}{5}+\dfrac{8}{5}\right)-\left(\dfrac{2}{3}+\dfrac{5}{3}\right)\)

\(=1-\dfrac{7}{3}=\dfrac{-4}{3}\)

a,= 32.(11+67) +78.68

      32.78+78.68

      78.(32+68)

      78.100

      = 7800

b,76.(41-20)+21.24

   =76.21+21.24

   =21.(76+24)

   =21.100

   =2100

a)=-374                   b)=-5250

c)=-2323                  d)=-3069

a: Số số hạng là 100-50+1=51 số

Tổng là (100+50)*51/2=51*75=3825

b: Số số hạng là (223-21):2+1=102(số)

Tổng là (223+21)*102/2=12444

c: Số số hạng là (72-12):4+1=16(số)

Tổng là (72+12)*16/2=672

d: Số số hạng là (124-4):6+1=21(số)

Tổng là (124+4)*21/2=1344

a) Đặt A= \(\dfrac{1}{3}+\dfrac{1}{6}+...+\dfrac{1}{36}\)

\(\dfrac{1}{2}\)A=\(\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{72}\)

\(\dfrac{1}{2}\)A=\(\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{8.9}\)

\(\dfrac{1}{2}\)A=\(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{8}-\dfrac{1}{9}\)

\(\dfrac{1}{2}\)A=\(\dfrac{1}{2}-\dfrac{1}{9}\)

\(\dfrac{1}{2}\)A=\(\dfrac{7}{18}\)

A=\(\dfrac{7}{9}\)

a) \(52^2\)

\(=\left(50+2\right)^2\)

\(=50^2+2\cdot2\cdot50+2^2\)

\(=2500+200+4\)

\(=2704\)

b) \(98^2\)

\(=\left(100-2\right)^2\)

\(=100^2-2\cdot100\cdot2+2^2\)

\(=10000-400+4\)

\(=9604\)

`a, 52^2 = (50+2)^2 = 2500 + 200 + 4 = 2704`

`b, 98^2  = (100-2)^2 = 100^2 - 2 . 100 . 2 + 4 = 10000 - 400 + 4`

`= 9604`

a) \(A=\dfrac{3}{4}.\dfrac{8}{9}.\dfrac{15}{16}.\dfrac{24}{25}.....\dfrac{120}{121}.\dfrac{143}{144}\)

= \(\dfrac{1.3.2.4.3.5.4.6....10.12.11.13}{2^2.3^2.4^2.5^2...11^2.12^2}\)

= \(\dfrac{1.2.12.13}{2^2.12^2}=\dfrac{13}{2.12}=\dfrac{13}{24}\)

b) \(B=\dfrac{5}{9}.\dfrac{21}{25}.\dfrac{45}{49}.\dfrac{77}{81}....\dfrac{357}{361}.\dfrac{437}{441}\)

= \(\dfrac{1.5.3.7.5.9.7.11.....17.21.19.23}{3^2.5^2.7^2....19^2.21^2}=\dfrac{1.3.21.23}{3^2.21^2}\)

= \(\dfrac{23}{3.21}=\dfrac{23}{63}\)

a. 2.54

b. 0.5

a) \(82\cdot78\)

\(=\left(80+2\right)\cdot\left(80-2\right)\)

\(=80^2-2^2\)

\(=6400-4\)

\(=6396\)

b) \(87\cdot93\)

\(=\left(90-3\right)\left(90+3\right)\)

\(=90^2-3^2\)

\(=8100-9\)

\(=8091\)

c) \(125^2-25^2\)

\(=\left(125-25\right)\left(125+25\right)\)

\(=100\cdot150\)

\(=15000\)