Question

How do you simplify fractions with variables?

Answer 1

Hint: From the given question we are asked how can we simplify fractions with variables. So, for solving this question we will take an example that contains variables in it and simplify it using basic mathematical operations like addition etc.. along with the explanation and solve the given question. So, we proceed with the solution as follows.

Complete step by step solution:
Let us take an example of a fraction that contains a variable in it.
So, let the fraction be $ \dfrac{2}{a}+\dfrac{3}{ab}$
When adding the fractions directly the denominator (size indicator of what we are counting) has to be the same. Then we can directly add the numerator.
So, we can see that the fraction we considered don’t have the same denominator.
So, now we try to make the denominator of the fraction the same using the basic mathematical operations which are multiplication and division.
So, we get,
$\Rightarrow \dfrac{2}{a}+\dfrac{3}{ab}$
Now let us multiply the first term that is $\dfrac{2}{a}$ with the fraction $\dfrac{b}{b}$. So, we get the expression reduced as follows.
$\Rightarrow \dfrac{b}{b}\times \dfrac{2}{a}+\dfrac{3}{ab}$
$\Rightarrow \dfrac{2b}{ab}+\dfrac{3}{ab}$
Now, we can observe that the denominator is the same in both the terms of the expression.
As said in the above now we can add the terms directly by adding the numerators and keep the denominator constant. So, we get as follows.
$\Rightarrow \dfrac{2b}{ab}+\dfrac{3}{ab}$
$\Rightarrow \dfrac{2b+3}{ab}$

Note: Students must do the calculations very carefully. Students must check that whether the denominator is the same in all the terms or not if not the solution will be wrong. For example, if we add like this $ \dfrac{2+3}{ab}$ instead if $ \dfrac{2b}{ab}+\dfrac{3}{ab}$ then our solution is wrong.