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

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted on

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

cgnlv | Student, Grade 11 | (Level 1) eNoter

Posted on

Alright Here We go. after you write out your problem like this:

5/9-(-2/3)+(-5/6)

Start out with your two negative fractions first:

(-2/3)+(-5/6)

Since in (-2/3) the numerator 2 is negative, it makes the entire fraction negative. The same goes for (-5/6).

Now you have: -(2/3) - (5/6)

Now you must get a common demominator. so multiply -(2/3) by -2 so you common denominator is now 6

Now you should have (4/6) -(5/6)

Just switch 5/6 and 4/6 around and subtract. you then have 1/6.

Now plug in 5/9 - 1/6 and get the common denominator. The common denominator is 18 so multiply 5/9 by 2 and 1/6 by 3.

5/9 * 2= 10/18

1/6 * 3 = 3/18

Now subtract

10/18- 3/18=  7\ 18

7/18 is your answer. Hope you understood this. Comment back to me.

krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted on

This problem needs to be solved in the following steps.

First step is to remove the parenthesis.

Thus the given fraction 5/9 - (-2/3) + (-5/6), after removing fraction becomes:

5/9 + 2/3 - 5/6

Then we find the least common multiple (LCM) of the denominators of all the fractions and replace all the fractions in equivalent fraction with this LCM as denominator.

In this case the LCM of denominators is 18, and using this as denominators the expression becomes:

5/9 + 2/3 - 5/6 = 10/18 + 12/18 - 15/18

Next we find equivalent single fraction for the expression by adding the numerators of the fraction and keeping the common denominator. Thus:

10/18 + 12/18 - 15/18 = (10 + 12 - 15)/18 = 7/18

rsarvar1a | Student, Grade 9 | (Level 1) Honors

Posted on

5/9 - (-2/3) + (-5/6)

This question needs to first be simplified. There are several things that we can do to simplify this. First of all, we can remove the brackets.

5/9 + 2/3 - 5/6

Remember that when you have two negative operations side by side, they become positive, but one positive and one negative stay as a negative.

Now, we want to find a common denominator so that we can add/subtract these fractions. A common denominator between 9, 3 & 6 is 18.

5/9 + 2/3 - 5/6 -> 10/18 + 12/18 - 15/18

To get the proper fractions, we have to multiply the numerator by the number that we multiplied the denominator by. For example, we turned 5/9 into 10/18 by multiplying both sides of the equation by 2:

5*2 / 9*2 = 10/18