1. Thực hiện phép tính:
a) 13$\frac{1}{4}$ : (-$\frac{5}{7}$) – 18$\frac{1}{4}$ : (-$\frac{5}{7}$)
b) (7 + $\frac{3}{2}$ – $\frac{1}{3}$) – ($\frac{1}{2}$ + $\frac{2}{3}$ – 2) – (5 + $\frac{1}{3}$)
c) $\frac{3}{5}$ + $\frac{13}{25}$ – $\frac{5}{9}$ – $\frac{6}{14}$
d) (-$\frac{7}{15}$ + $\frac{5}{7}$) : $\frac{4}{3}$ + ($\frac{2}{7}$ – $\frac{8}{15}$) : $\frac{4}{3}$
Đáp án + Giải thích các bước giải:
`a) 13 1/4:(-5/7)-18 1/4 :(-5/7)` $\\$ `=(13 1/4 – 18 1/4):(-5/7)=-5:(-5/7)=-5*(-7/5)=7`
`b)(7 + 3/2-1/3)-(1/2+2/3-2)-(5+1/3)` $\\$ `= 7 + 3/2 – 1/3 – 1/2 – 2/3 + 2 – 5 – 1/3` $\\$ `= (7+2-5)+(3/2-1/2)+(-1/3-2/3-1/3)` $\\$ `= 4+1-4/3=5-4/3 = 11/3`
`c) 3/5 + 13/25-5/9-6/14=3/5+13/25-5/9-3/7` $\\$ `= 15/25+13/25-5/9-3/7 = 28/25-5/9-3/7` $\\$ `= 1764/1575-875/1575-675/1575=214/1575`
`d) (-7/15+5/7):4/3+(2/7-8/15):4/3` $\\$ `=(-7/15+5/7+2/7-8/15):4/3` $\\$ `= [(-7/15 – 8/15) + (5/7 + 2/7)]:4/3` $\\$ `=(-1 + 1):4/3 = 0 : 4/3 = 0*3/4 = 0`
`a)`
`13 1/4 :(-5/7)-18 1/4 :(-5/7)`
`= (13 1/4 – 18 1/4):(-5/7)`
`= -5 :(-5/7)`
`=-5.(-7/5)`
`= 7`
`b)`
`(7 + 3/2-1/3)-(1/2+2/3-2)-(5+1/3)`
`= 7 + 3/2 – 1/3 – 1/2 – 2/3 + 2 – 5 – 1/3`
`= (7+2-5)+(3/2-1/2)+ (-1/3-2/3-1/3)`
`= 4 + 1 – 4/3 `
`= 5 – 4/3`
`= 11/3`
`c)`
` 3/5 + 13/25-5/9-6/14`
`=3/5+13/25-5/9-3/7`
`= 15/25+13/25-5/9-3/7`
`= 28/25-5/9-3/7`
`= 1764/1575-875/1575-675/1575`
`=214/1575`
`d)`
`(-7/15+5/7):4/3+(2/7-8/15):4/3`
`=(-7/15+5/7+2/7-8/15):4/3`
`= [(-7/15 – 8/15) + (5/7 + 2/7)]:4/3`
`=(-1 + 1):4/3`
`= 0 : 4/3`
`= 0`