a) 2.4 = 1.8

⇒ 2/1 = 8/4

2/8 = 1/4

1/2 = 4/8

9/2 = 4/1

b) (-2).6 = 3.(-4)

⇒ -2/3 = -4/6

-2/(-4) = 3/6

3/(-2) = 6/(-4)

-4/(-2) = 6/3

c) -18.(-5) = 9.10

⇒ -18/9 = 10/(-5)

-18/10 = 9/(-5)

9/(-18) = -5/10

10/(-18) = -5/9

Từ các số 2; 3; -6; -4; -9 ta có:

2.(-9) = 3.(-6) và 2.(-6) = 3.(-4)

*) 2.(-9) = 3.(-6)

⇒ 2/3 = -6/(-9)

2/(-6) = 3/(-9)

3/2 = -9/(-6)

-6/2 = -9/3

*) 2.(-6) = 3.(-4)

⇒ 2/3 = -4/(-6)

2/(-4) = 3/(-6)

3/2 = -6/(-4)

-4/2 = -6/3

3 ngày 15 giờ + 5 ngày 25 giờ = 9 ngày 16 giờ.

\(D=\dfrac{8}{3.11}+\dfrac{8}{11.19}+...+\dfrac{8}{187.195}\)

\(=\dfrac{11-3}{3.11}+\dfrac{19-11}{11.19}+...+\dfrac{195-187}{187.195}\)

\(=\dfrac{1}{3}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{19}+...+\dfrac{1}{187}-\dfrac{1}{195}\)

\(=\dfrac{1}{3}-\dfrac{1}{195}\)

\(=\dfrac{64}{195}\)

\(M=\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{99.101}\)

\(=\dfrac{3-1}{1.3}+\dfrac{5-3}{3.5}+\dfrac{7-5}{5.7}+...+\dfrac{101-99}{99.101}\)

\(=\dfrac{3}{1.3}-\dfrac{1}{1.3}+\dfrac{5}{3.5}-\dfrac{3}{3.5}+\dfrac{7}{5.7}-\dfrac{5}{5.7}+...+\dfrac{101}{99.101}-\dfrac{99}{99.101}\)

\(=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{99}-\dfrac{1}{101}\)

\(=1-\dfrac{1}{101}\)

\(=\dfrac{100}{101}\)

Tui đang cần gấp mong người giúp !

\(\dfrac{3}{5}+\dfrac{3}{45}+\dfrac{3}{117}+\dfrac{3}{221}\)

\(=\dfrac{3}{1.5}+\dfrac{3}{5.9}+\dfrac{3}{9.13}+\dfrac{3}{13.17}\)

\(=\dfrac{3}{4}\left(\dfrac{4}{1.5}+\dfrac{4}{5.9}+\dfrac{4}{9.13}+\dfrac{4}{13.17}\right)\)

\(=\dfrac{3}{4}\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{17}\right)\)

\(=\dfrac{3}{4}\left(1-\dfrac{1}{17}\right)\)

\(=\dfrac{12}{17}\)

make the sentences from the cues
1. My sister/ likes/ swim/ the sea/ in/ morning/ .
2. I/ often/ swimming/ summer.
3. Huy/ read/ book/ his room/ now.
4. How much/ shoes ?
5. Peter/ tall/ Tony

\(\dfrac{3}{5}=\dfrac{24}{40}\) ; \(\dfrac{3}{4}=\dfrac{30}{40}\)

4 phân số đó là: \(\dfrac{25}{40};\dfrac{26}{40};\dfrac{27}{40};\dfrac{28}{40}\)

\(ax^4-2x^3+3x^2-2x^4-7x+1=\left(a-2\right)x^4-2x^3+3x^2-7x+1\)

Do đa thức đã cho có bậc 4 \(\Rightarrow a-2\ne0\)

\(\Rightarrow a\ne2\)

Mà a là số nguyên tố nhỏ hơn 5

\(\Rightarrow a=3\)

\(a,\dfrac{5}{3}.x-\dfrac{2}{5}=\dfrac{1}{4}\\ \Rightarrow\dfrac{5}{3}.x=\dfrac{13}{20}\\\Rightarrow x=\dfrac{39}{100}\\ b,\dfrac{4}{7}.x-\dfrac{8}{5}=\dfrac{1}{2}\\ \Rightarrow\dfrac{4}{7}.x=\dfrac{21}{10}\\ \Rightarrow x=\dfrac{147}{40}. \)

a. \(\dfrac{5}{3}\).x . \(\dfrac{-2}{5}\) =\(\dfrac{1}{4}\)

    \(\dfrac{5}{3}\).x          = \(\dfrac{1}{4}\) : \(\dfrac{-2}{5}\)

    \(\dfrac{5}{3}\).x          = \(\dfrac{1}{4}\) . \(\dfrac{5}{-2}\)

    \(\dfrac{5}{3}\).x          =\(\dfrac{5}{-8}\)

        x          = \(\dfrac{5}{-8}\) : \(\dfrac{5}{3}\)

        x          = \(\dfrac{5}{-8}\) .\(\dfrac{3}{5}\)

       x           = \(\dfrac{3}{-8}\)

b.\(\dfrac{4}{7}\).x - \(\dfrac{8}{5}\)    = \(\dfrac{1}{2}\)

   \(\dfrac{4}{7}\).x          = \(\dfrac{1}{2}\)+\(\dfrac{8}{5}\)

   \(\dfrac{4}{7}\).x          = \(\dfrac{21}{10}\)

       x          = \(\dfrac{21}{10}\) : \(\dfrac{4}{7}\)

       x          = \(\dfrac{147}{140}\)

3S = 3-3²+3³-3⁴+...+3⁹⁸-3⁹⁹+3¹⁰⁰

4S = 3S+S = 1-3¹⁰⁰

-4S = 3¹⁰⁰-1

Mà SϵZ

=> 3¹⁰⁰-1⋮4

=> 3¹⁰⁰:4 dư 1

\(\dfrac{2^4\cdot125}{2^7\cdot50}=\dfrac{2^4\cdot5^3}{2^8\cdot5^2}=\dfrac{5}{2^4}=\dfrac{5}{16}\)