Câu 13: (2,0 điểm) Thực hiện phép tính (tính theo cách hợp lý nếu có thể) a) $\frac{7}{8}$ : ($\frac{2}{3}$ - $\frac{1}{5}$) b) $\frac{-22}{17}$.$\frac{23}{31}$ + $\frac{-22}{17}$.$\frac{8}{31}$ + 2$\frac{5}{17}$ c) $\frac{8^{10}.9^{7}}{12^{15}}$ d) ($\frac{-2}{5}$ + $\frac{6}{13}$) : $\frac{11}{3}$ + ($\frac{7}{13}$ - $\frac{3}{5}$) : $\frac{11}{3}$

Đáp án+Giải thích các bước giải:

`a)` `7/8 : (2/3 - 1/5)`

`= 7/8 : (10/15 - 3/15)`

`= 7/8 : 7/15`

`= 7/8 * 15/7`

`= 15/8`

`b)` `(-22)/17 * 23/31 + (-22)/17 * 8/31 + 2 5/17`

`= (-22)/17 * (23/31 + 8/31) + 2 5/17`

`= (-22)/17 * 31/31 + 2 + 5/17`

`= (-22)/17 * 1 + 2 + 5/17`

`= (-22)/17 + 2 + 5/17`

`= ((-22)/17 + 5/17) + 2`

`= (-17)/17 + 2`

`= -1 + 2`

`= 1`

`c)` `(8^10 * 9^7)/(12^15)`

`= ((2^3)^10 * (3^2)^7)/((2^2 * 3)^15)`

`= (2^30 * 3^14)/(2^30 * 3^15)`

`= 1/3`

`d)` `((-2)/5 + 6/13) : 11/3 + (7/13 - 3/5) : 11/3`

`= ((-2)/5 + 6/13) * 3/11 + (7/13 - 3/5) * 3/11`

`= 3/11 * ((-2)/5 + 6/13 + 7/13 - 3/5)`

`= 3/11 * ((-5)/5 + 13/13)`

`= 3/11 * (-1 + 1)`

`= 3/11 * 0`

`= 0`

`\ttcolor{red}{#T2}`