\(\dfrac{-5}{7}:\dfrac{15}{31}\)

\(=\dfrac{-5}{7}\cdot\dfrac{31}{15}\)

\(=\dfrac{-5\cdot31}{7\cdot15}\)

\(=\dfrac{-31}{7\cdot3}\)

\(=\dfrac{-31}{21}\)

Tuổi của con hiện nay:

40 : 5 = 8 (tuổi)

Số tuổi mẹ hơn con:

40 - 8 = 32 (tuổi)

Hiệu số phần bằng nhau:

3 - 1 = 2 (phần)

Tuổi của mẹ lúc tuổi con bằng 1/3 tuổi mẹ:

32 : 2 × 3 = 48 (tuổi)

Số năm để tuổi con bằng 1/3 tuổi mẹ:

48 - 40 = 8 (năm)

Tuổi con hiện nay là:

\(40\times\dfrac{1}{5}=8\left(tuổi\right)\)

Sau số năm thì tuổi con bằng \(\dfrac{1}{3}\) tuổi mẹ là:

\(\left(40-8\right)\div\left(3-1\right)\times1-8=8\left(năm\right)\)

-1-2-3-4-5-6-7-8-9-10=-55

\(\dfrac{-49}{81}\cdot\dfrac{27}{-77}\)

\(=\dfrac{-7^2}{3^2\cdot9}\cdot\dfrac{3\cdot9}{-7\cdot11}\)

\(=\dfrac{7}{3\cdot11}\)

\(=\dfrac{7}{33}\)

Bài 3:

\(A=\dfrac{1}{2}+\dfrac{3}{2}+\left(\dfrac{3}{2}\right)^2+...+\left(\dfrac{3}{2}\right)^{2012}\)

Đặt: \(C=\dfrac{3}{2}+\left(\dfrac{3}{2}\right)^2+...+\left(\dfrac{3}{2}\right)^{2012}\)

\(\dfrac{3}{2}C=\left(\dfrac{3}{2}\right)^2+\left(\dfrac{3}{2}\right)^3+...+\left(\dfrac{3}{2}\right)^{2013}\)

\(\dfrac{3}{2}C-C=\left[\left(\dfrac{3}{2}\right)^2+\left(\dfrac{3}{2}\right)^3+...+\left(\dfrac{3}{2}\right)^{2013}\right]-\left[\dfrac{3}{2}+\left(\dfrac{3}{2}\right)^2+...+\left(\dfrac{3}{2}\right)^{2012}\right]\)

\(\dfrac{1}{2}C=\left(\dfrac{3}{2}\right)^{2013}-\dfrac{3}{2}\)

\(C=2\left[\left(\dfrac{3}{2}\right)^{2013}-\dfrac{3}{2}\right]\)

\(A=\dfrac{1}{2}+2\left[\left(\dfrac{3}{2}\right)^{2013}-\dfrac{3}{2}\right]\)  

\(\Rightarrow B-A=\left(\dfrac{3}{2}\right)^{2023}:2-\dfrac{1}{2}-2\left[\left(\dfrac{3}{2}\right)^{2013}-\dfrac{3}{2}\right]\)

\(=\dfrac{\left(\dfrac{3}{2}\right)^{2023}}{2}-\dfrac{1+4\left[\left(\dfrac{3}{2}\right)^{2013}-\dfrac{3}{2}\right]}{2}\)

\(=\dfrac{\left(\dfrac{3}{2}\right)^{2023}-4\left(\dfrac{3}{2}\right)^{2013}-5}{2}\)

\(a=1-\dfrac{1}{2}+1-\dfrac{1}{6}+1-\dfrac{1}{12}+1-\dfrac{1}{20}+1-\dfrac{1}{30}+1-\dfrac{1}{42}+1-\dfrac{1}{56}+1-\dfrac{1}{72} =\left(1+1+1+1+1+1+1+1\right)-\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}\right)=8-\left(\dfrac{6}{12}+\dfrac{2}{12}+\dfrac{1}{12}+\dfrac{3}{60}+\dfrac{2}{60}+\dfrac{12}{504}+\dfrac{9}{504}+\dfrac{7}{504}\right)=8-\left(\dfrac{9}{12}+\dfrac{5}{60}+\dfrac{28}{504}\right)=8-\left(\dfrac{3}{4}+\dfrac{1}{12}+\dfrac{1}{18}\right)=8-\left(\dfrac{27}{36}+\dfrac{3}{36}+\dfrac{2}{36}\right)=8-\dfrac{32}{36}=8-\dfrac{8}{9}=\dfrac{72}{9}-\dfrac{8}{9}=\dfrac{64}{9} \)

Đáp số 64/9
CHÚC EM HỌC TỐT

-3/7 x 2/5= -3 x 2/7 x 5= -6/35

\(\dfrac{-3}{7}\times\dfrac{2}{5}=\dfrac{\left(-3\right)\times2}{7\times5}=\dfrac{-6}{35}\)

2009/2010 < 1

2010/2011 < 1

2011/2012 < 1

Cộng vế với vế ta được:

2009/2010 + 2010/2011 + 2011/2012 < 1 + 1 + 1

⇒ 2009/2010 + 2010/2011 + 2011/2012 < 3