Solving Equations with Fractions Solving Equations with Fractions If we have any equation which has a fraction along with the variable and the constant value, then we have a different method of Solving Equations with Fractions. To solve the equation with the fraction, we will first make the denominators of all the terms same. For this we need to first find the lcm of all the denominators. In case the term does not have any denominator, then we will write one as the denominator for that term and thus find the LCM. Now once the LCM for all the terms is calculated, we will convert the terms into their equivalent form, such that the denominator becomes equal to the LCM which we have already calculated. Now all the fractions are in form of like fractions and now the constant terms are taken on one side of the equation and variables are taken to another side of the equation. Thus we separate the constant terms from the variables and we get the value of the variable. Let us understand it more clearly by the following example: 2x + ½ = 4
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Here in the given expression, we observe that ½ is the fraction and the other two terms of the equation are simple terms. SO we consider that the denominator of these two terms is 1. Thus we can write the above given expression in the following form, by writing the denominator as 1, for the terms which do not have the denominator. 2x / 1 + 1 / 2 = 4 / 1 Now we find the LCM of 1 and 2 and we get: 2 as the LCM of all the denominators. Now we need to change all the terms such that the denominator becomes 2. For this we will multiply the numerator and the denominator of the terms 2x and 4 by 2 and thus the new equation will be formed as follows: 2x * ( 2/2 ) + ½ = 4 * ( 2 / 2) 4x / 2 + ½ = 8 / 2 Now we find that the denominators of all the terms of the given equation becomes equal, which is 2. Or we can write it as : ( 4x + 1 ) / 2 = 8 / 2 Thus we observe that the denominators on both sides of the equation are same and equal, so they will be cancelled. Cancelling 2 from the denominator of both the sides, we get: 4x + 1 = 8
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In next step we will take the constant terms on one side of the equation and the variables will be written to another side of the equation. For this we will subtract 1 from both sides of the equation and we will get the following expression: 4x + 1 – 1 = 8 - 1 Or 4x = 8 – 1 Or 4x = 7 Now we need to remove 4 from the left side of the equation and we get the result by dividing both sides of the equation by 4 and thus we get : 4x / 4 = 7/4
Or x = 7 / 4 Ans.
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