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I am having problems with variables on both sides. I get most of the concepts but I need help with adding fractions into the equations.

I am one of the only seventh graders in an algebra 1 class she is basing her lessons on what the eighth graders learned last year in pre-algebra. My teacher calls the equations many different things and she is confusing me.


is there a specific problem you can post to use as an example for clarifying any questions you may have...?  

I am just going to address this part of what you said: "My teacher calls the equations many different things and she is confusing me"

When I come across a teacher that seems to use a lot of different ways to say this same things I create a a sheet of paper for their sayings. I draw like 4 boxes on the page and in one box I will put any sayings that actually mean the same thing.

I'm using this as an example and it is meant to be a little weird. You could put all of these into the same box:  soda, pop, coke, brown bubbly liquid, sweet brownish drink.

Where a math box might have all of these in there: multiply by the reciprocal, divide by the fraction, flip and multiply, flip and cross cancel.


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2 Answers

There are two ways for dealing with fractions in algebraic equations.

1. Multiply the whole equation with the LCM (lowest common denominator) of all fractions. This will then give you a whole number equation to work with.

Example: 1/2 x - 4 = 2/3 x + 5/6

Multiplying with the LCM of 6 gives

6*(1/2 x) - 6*4 = 6*(2/3 x) + 6*(5/6)

or     3x - 24 = 4x + 5

then solve as normal to get x = -29

2. Leave the equation as it is and work as you always do. Let's use the same example:

1/2 x - 4 = 2/3 x + 5/6

Work as always to collect the variables on one side and the non-variable terms on the other. I will do this here by subtracting 1/2 x from both sides and by subtracting 5/6 from both sides. That gives

-4 - 5/6 = 2/3 x - 1/2 x

or    -4 - 5/6 = (2/3- 1/2) x

Now again, you will need to use the LCM (although here you just need to find the LCM of the fractions you actually want to add/subtract; coincidentally this is also 6, but you may, in other problems, find smaller LCMs)

with a common denominator you get

    - 24/6 - 5/6  = (4/6 - 3/6)

or  -29/6  = 1/6 x

Divide both sides by 1/6 and you get

-29 = x


Hope this helps!

If the variable on both sides of the equal sign are the same you will have to get them together (combine like terms) this will get you to where I believe you are able to solve the equation since you stated you have a grasp of the concept, somewhat.

For example:   

2+x = 3+2x  

  • remember when you carry anything, including the x across the equal sign it's mathematical job.  If it is positive when you carry it across the equal sign it becomes negative or subtraction, multiplication turns in to division and visa versa.    

2+x -2x = 3.

  • You now can combine like terms      

2-x = 3 

  • the rest you should be able to do.  

-x = 3-2

  • (remember the 2 was positive then it became negative when you carry it across the equal sign) and solve for x;  

x= -1

Adding fractions requires the denominator to be the same. I recommend using the vin diagram method

For example:

2/4 + x = 1/6 + 2x---------Same rules apply as above we will focus on getting denominators                   the same

 Denominator                                        4                                       6

1.  Reduce to prime factors                       2*2                                     2*3

2.  What number do the denominators share                    2  This is what they have alike and do not need the other 2

3.  What numbers do they have left           2                     &                  3 These are how they are different

4.  Multiple the number they have alike with the numbers that are different and you have the lowest common denominator or LCD               2*2*3  =  12

5.  Now change the denominators in each fraction to 12

                 2/4*3              & 1/6*2   --------------   but to do this we also have to multiply the same   number