Equations that involve a combination of variables and fractions can make life difficult for most of the students. You may be good at solving simple equations but when you see fractions along with the variables in the equation, you tend to become nervous. Thus, the simplest way to deal with such equations is to first get rid of fractions and then solve it like a normal equation without any fractions.

Learning to Solve equations that involve fractions with the help of a few examples

Let us start with simpler equations where each fraction in the equation has the same number in the denominator. For example:
2/3 y +4/3  = 5 

In the above equation, there is a common denominator = 3. We can write the above equation as:
1/3 (2y +4) = 5

Now, multiplying both sides by common denominator I.e. 3
3 *1/3  (2y +4) = 3 * 5
=> 2y + 4 = 15
=> 2y = 15 – 4
=> 2y = 11 
=> y = 11/2

There can be more complex equations involving fractions with different denominators. For example:
2/3 y + 4/5 = 5 

In the above equation, there are two different denominators, 3 and 5. In such case, you need to make the denominators same by finding the LCM of the two denominators. LCM of 3 and 5 is 15.

Now, multiplying both sides by the LCM i.e. 15, we have
15 * ( 2/3 y +4/5 )=  15 *5 
=> 5*2 y + 3*4 = 75 
=> 10y + 12 = 75
=> 10y = 75 - 12
=> 10y = 63 
=> y = 63/10 = 6.3

You must now try to solve a few equations that involve variables and fractions to make sure that you can now handle such equations. 

The main things that you need to prepare yourself before looking for ‘How To Solve Equations With Fractions And Variables’ are:

1. You must be able to solve simple equations that do not contain fractions. 
2. You must be able to calculate the LCM of two or more numbers. 

You must have learnt to find LCM in your lower classes. Even if you do not know, how to calculate LCM, you can look for a chapter of LCM or Lowest Common Multiple in any book of basic mathematics. There are also several tutorials available online where you can learn to find out the LCM of two or more numbers.



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