Question

How do you simplify `3\frac { 2} { 3} - 2\frac { 4} { 11}`?

Answer 1

`43/33`

Explanation:

First we have to change the mixed numbers into fractions using the
`" "`
following property:

`color(blue)(m a/b=(mb+a)/b)`
`" "`
So,
`" "`
`3 2/3=(3*3+2)/3=color(blue)(11/3)`
`" "`
`2 4/11=(2*11+4)/11=color(blue)(26/11)`
`" "`
`" "`
To subtract fractions we should find common denominator which is
`" "`
the least common multiple of `(11,3)`.

Because `color(red)11` and `color(red)3` are prime numbers then denominator is `color(red)(11*3)`
`" "`
`" "`
`3 2/3-2 4/11`
`" "`
`=color(blue)( 11/3-26/11)`
`" "`
`=(11*color(red)11-26*color(red)3)/color(red)(11*3)`
`" "`
`=(121-78)/33`
`" "`
`=43/33`

`43/33` is the simplest form.