Ta có: \(\frac{1010}{1008\cdot8-994}\)

\(=\frac{1010}{8064-994}=\frac{1010}{7070}=\frac17\)

\(=\frac{1\cdot3}{7\cdot3}=\frac{3}{21}\)

\(\frac{1\cdot2\cdot3+2\cdot4\cdot6+3\cdot6\cdot9+5\cdot10\cdot15}{1\cdot3\cdot6+2\cdot6\cdot12+3\cdot9\cdot18+5\cdot15\cdot30}\)

\(=\frac{1\cdot2\cdot3+1\cdot2\cdot3\cdot2\cdot2\cdot2+1\cdot2\cdot3\cdot3\cdot3\cdot3+1\cdot2\cdot3\cdot5\cdot5\cdot5}{1\cdot3\cdot6+1\cdot3\cdot6\cdot2\cdot2\cdot2+1\cdot3\cdot6\cdot3\cdot3\cdot3+1\cdot3\cdot6\cdot5\cdot5\cdot5}\)

\(=\frac{1\cdot2\cdot3\left(1+2^3+3^3+5^3\right)}{1\cdot3\cdot6\cdot\left(1+2^3+3^3+5^3\right)}=\frac26=\frac13\)

\(=\frac{1\cdot7}{3\cdot7}=\frac{7}{21}\)

Kết quả rút gọn lần lượt là:  1 2 ; − 3 8 ; 1 2 ; 2 3 ; 3 2 ; − 15 17

10/11

10 phần 1 100%

1/7

tick cho mình tròn 85 nha

\(\frac{1010}{\left(1008.8-994\right)}=\frac{1010}{8064-994}=\frac{1010}{7070}=\frac{1}{7}\)

C = \(\frac{1010}{1008.8-994}\)

= \(\frac{1010}{1008.7+1008-994}\)

= \(\frac{1010}{1008.7+14}\)

= \(\frac{1010}{1008.7+2.7}\)

= \(\frac{1010}{7\left(1008+2\right)}=\frac{1010}{7.1010}=\frac{1}{7}\)

D = \(\frac{1.2.3+2.4.6+3.6.9+5.10.15}{1.3.6+2.6.12+3.9.18+5.15.30}\)

= \(\frac{1.2.3+2.4.6+3.6.9+5.10.15}{1.3.2.3+2.6.4.3+3.9.6.3+5.15.10.3}\)

= \(\frac{1.2.3+2.4.6+3.6.9+5.10.15}{3\left(1.2.3+2.4.6+3.6.9+5.10.15\right)}=\frac{1}{3}\)

BCNN(7,3) = 21

\(\frac{1}{7}=\frac{1.3}{7.3}=\frac{3}{21}\)

\(\frac{1}{3}=\frac{1.7}{3.7}=\frac{7}{21}\)

1010/1313=10/13

\(\frac{10}{13}\)

Giải:

Gọi phân số cần tìm là: \(\frac{a}{b}\)(a; b ∈ Z; a; b ≠ 0)

Theo bài ra ta có: \(\frac{a}{b}=\frac57\) và a + b = 4812

\(\frac{a}{b}\) = \(\frac57\)

\(\frac{a}{5}=\frac{b}{7}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\frac{a}{5}=\frac{b}{7}=\frac{a+b}{5+7}\) = = \(\frac{4812}{12}\) = 401

a = 401 x 5 = 2005

b = 401 x 7 = 2807

Phân số cần tìm là: \(\frac{2005}{2807}\)