Đáp án + Giải thích các bước giải:
Câu 1:
a)
`\frac{3}{4} + \frac{-5}{4}`
`= \frac{3 + (-5)}{4}`
`= \frac{-1}{2}`
b)
`(\frac{3}{4} + \frac{-7}{2}) \times (\frac{2}{11} + \frac{6}{11})`
`=(\frac{3}{4} + \frac{-14}{4}) \times \frac{8}{11}`
`=\frac{-11}{4} \times \frac{8}{11}`
`= -2`
c)
`\frac{-2}{3} \times \frac{5}{11} + \frac{-6}{11} \times \frac{2}{3} + 5\frac{1}{3}`
`=\frac{-2}{3} \times \frac{5}{11} + \frac{6}{11} \times \frac{-2}{3} + \frac{16}{3}`
`=\frac{-2}{3} \times (\frac{5}{11} + \frac{6}{11}) + \frac{16}{3}`
`=\frac{-2}{3} \times 1 + \frac{16}{3}`
`=\frac{-2}{3} + \frac{16}{3}`
`=\frac(14}{3}`
d)
`(\frac{5}{7} \times 0,6 - 5 ÷ 3\frac{1}{2}) \times (40% - 1,4) \times (-2)^3`
`=(\frac{5}{7} \times \frac{3}{5} - 5 ÷ \frac{7}{2}) \times (\frac{2}{5} - \frac{7}{5}) \times (-8)`
`=(\frac{5}{7} \times \frac{3}{5} - \frac{10}{7}) \times (-1) \times (-8)`
`=(\frac{3}{7} - \frac{10}{7}) \times (-1) \times (-8)`
`= -1 \times (-1) times (-8)`
`= -8`
Câu 2:
a)
`x - \frac{3}{4} = \frac{1}{2}`
`x = \frac{1}{2} + \frac{3}{4}`
`x = \frac{2}{4} + \frac{3}{4}`
`x = \frac{5}{4}`
b)
`3\frac{1}{3}x + 16\frac{3}{4} = 1,75`
`\frac{10}{3}x + \frac{67}{4} = \frac{7}{4}`
`\frac{10}{3}x = \frac{7}{4} - \frac{67}{4}`
`\frac{10}{3}x = -15`
`x = -15 ÷ \frac{10}{3}`
`x = \frac{-9}{2}`
c)
`\frac{x -1}{12} = \frac{-5}{3}`
`\Rightarrow x - 1 \times 3 = 12 \times (-5)`
`\Rightarrow 3x - 3 = -60`
`\Rightarrow 3x = 60 + 3`
`\Rightarrow 3x = 63`
`\Rightarrow x = 21`
d)
`\frac{3x}{4} + \frac{3x}{28} + \frac{3x}{70} +...+ \frac{3x}{304} = \frac{18}{19}`
`x(1 - \frac{1}{4} + \frac{1}{4} - \frac{1}{7} + \frac{1}{7} - \frac{1}{10} +...+ \frac{1}{16} - \frac{1}{19}) = \frac{1}{19}`
`x(1 - \frac{1}{19}) = \frac{18}{19}`
`x \times \frac{18}{19} = \frac{18}{19}`
`x = \frac{18}{19} ÷ \frac{18}{19}`
`x = 1`
