Question

Evaluate: `((-4)/5 xx 3/2) + (9/-5 xx 10/3) - ((-3)/2 xx (-1)/4)`

Answer 1

`((-4)/5 xx 3/2) + (9/-5 xx 10/3) - ((-3)/2 xx (-1)/4)`

`= ((-2 xx 3)/(5 xx 1)) + ((3 xx 2)/(-1 xx 1)) - ((- 3 xx (- 1))/(2 xx 4))`

`= ((-6)/5) + ((-6)/1) - (3/8)`

`= (- 6 xx 8)/(5 xx 8) - (6 xx 40)/(1 xx 40) - (3 xx 5)/(8 xx 5)`

`= (- 48 - 240 - 15)/40`

`= (- 288 - 15)/40`

`= (-303)/40`

Answer 2

`((-4)/5 xx 3/2) + (9/-5 xx 10/3) - ((-3)/2 xx (-1)/4)`

Simplify each product

`(-4)/5 xx 3/2 = (-4xx3)/(5xx2) = (-12)/10 = (-6)/5`

`9/-5xx10/3 = (9xx10)/(-5xx3) = 90/-15 = -6/1 = -6`

`(-3)/2xx(-1)/4 = (-3xx-1)/(2xx4) = 3/8`

The expression becomes: `(-6)/5+(-6)-3/8`

The denominators are 5, 1, and 8. The least common denominator (LCD) is 40. Rewrite each term with a denominator of 40:

1. `(-6)/5=(-48)/40`

2. `-6 = (-240)/40`

3. `(-3)/8 = (-15)/40`

`(-48)/40+(-240)/40-15/40`

`= (-48-240-15)/40`

`= (-303)/40`