Question

How do you evaluate `(5/9 - 3)/(5/6) -:3/2 -: 3/4`?

Answer 1

`(5/9-3)/(5/6)-:3/2-:3/4=-352/135`

Explanation:

Dividing a fraction by a fraction, whether as in `(a/b)/(c/d)` or `a/b-:c/d`, is equivalent to multiplying by the reciprocal or multiplicative inverse of denominator (or the fraction written after sign ''`-:` and hence

`(a/b)/color(red)(c/d)=a/bcolor(red)(-:c/d)=a/bcolor(red)(xx(d/c))`

Now `5/9-3=5/9-(3xx9)/(1xx9)=5/9-27/9=(5-27)/9=-22/9`

Hence `(5/9-3)/(5/6)-:3/2-:3/4`

= `(-22/9)/(5/6)-:3/2-:3/4`

= `-22/9xx6/5xx2/3xx4/3`

= `-22/9xx(2cancel6)/5xx2/(1cancel3)xx4/3`

= `-(22xx2xx2xx4)/(9xx5xx3)`

= `-352/135`