Question

How do you evaluate `-\frac { 4} { 9} + ( - \frac { 5} { 6} )`?

Answer 1

`=-23/18`

Explanation:

We must first find the Least common denominator (LCD) of `9` and `6`

If we write out a list of factors of both `9` and `6` we can easily find the LCD

`9: 9, color(blue)18, 27, 36`
`6: 6, 12, color(blue)18,24`

We find that the LCD is `color(blue)18`

Now we must manipulate each fraction so that the denominator is `18` for both fractions.

For `-4/9` we can multiply `2` to `9` to get a denominator of `18` but we will also need to multiply the numerator by `2` to balance the fraction. Thus,

`-color(red)(2color(black)(*4))/(color(red)2*9) = -8/18`

Similarly for the fraction `-5/6`, we can multiply both the numerator and denominator by `3`

`-color(red)(3color(black)(*5))/(color(red)3*6) = -15/18`

Now when we add the two fractions together...

`-8/18+(-15/18)`

`= -8/18-15/18`

`=-23/18`

Answer 2

The result is `-1 5/18`

Explanation:

First thing to do is to find the common denominator. For `9` and `6` the lowest common multiplier is `18`.

`-4/9+(-5/6)=-8/18-15/18=-23/18`

Last step is to turn the improper fraction to a mixed number:

`-23/18=-1 5/18`

Answer is:

`-1 5/18`