Solving Linear Equations with Fractions

Linear equations may be expressed in terms of fractions rather than whole numbers. These are called linear equations with fractions. In order to solve equations with fractions we need to transform it by transforming it into an equation without fractions. We call it ‘clearing the fractions’

x/3    +   (x-2) / 5  =  6

Step 1

Clear the fractions. Multiply both sides of the equation with the LCM of the denominators.  The LCM of the denominators 3 and 5 is 15. Therefore, multiply both sides with 15.

15 × x/3 + 15 × (x-2)/5 = 15 × 6

Step 2

We have to turn the fractions into whole numbers. Thus, solving the above step, we get,

5x + 3 (x-2) = 90

Or, 5x + 3x – 6= 90

Or, 8x -6= 90

Or 8x= 90 + 6

8x= 96

X= 96/8 or 12

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