Fraction Help...math? How can I solve : 5/9 - (-2/3) + (-5/6) Please explain to me step by step.  

Expert Answers

An illustration of the letter 'A' in a speech bubbles

First, the eventual answer to this question is 7/18.

Let me go through this step by step like you asked.  The first thing you need to do is to make it so you can actually add or subtract these fractions.  To do this, you must make them have the same...

Unlock
This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Start your 48-Hour Free Trial

First, the eventual answer to this question is 7/18.

Let me go through this step by step like you asked.  The first thing you need to do is to make it so you can actually add or subtract these fractions.  To do this, you must make them have the same denominator.  In this case, the one to use is 18 because it is the least common multiple of the three denominators you now have.

So you must multiply each fraction by one, but each time you have to do so in a way that gets the denominator to be 18.  Like this

5/9 becomes 10/18 because you multiplied top and bottom by 2.  2/3 becomes 12/18 because you multiplied top and bottom by 6.

So now you have

10/18 - (-12/18) + (-15/18)

Subtracting a negative number is the same as adding, adding a negative is the same as subtracting.  So

10/18 - (-12/18) = 22/18

22/18 - 15/18

which simplifies to 7/18

Approved by eNotes Editorial Team