"If an equation has several fractions, how does..." solved and explained

smellmovinglz

Answered question

2021-11-15

If an equation has several fractions, how does multiplying both sides by the LCD make it easier to solve?

Answer & Explanation

Liek1993

Beginner2021-11-16Added 13 answers

There are several fractions given. Fractions may have same or different denominator. When the fractions have same denominator then it can be easily added.
If the given fractions are not having the same denominator, the LCD of the denominator can help to equalize all the denominator of the given fractions. If the denominator will get equal, all the basic operations like addition, subtraction and addition can be perfomed easily.
For example:
Add:

\frac{1}{2} + \frac{1}{3}

LCD of

{2, 3} = 6

\Rightarrow \frac{1}{2} + \frac{1}{3} = \frac{1}{2} \times \frac{3}{3} + \frac{1}{3} \times \frac{2}{2}

[Make the denominator of each fraction as 6(LCD)]

\Rightarrow \frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6}

\Rightarrow \frac{1}{2} + \frac{1}{3} = \frac{3 + 2}{6}

\Rightarrow \frac{1}{2} + \frac{1}{3} = \frac{5}{6}

This is how the LCD is used.

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