When you add fractions, you must first make sure that the denominators are the same. If they are, great! You keep the denominator the same and just add the numerators together and simplify.
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
But if we are trying to add fractions with unlike denominators, then we need to find a common denominator for the fractions we wish to add.
One way to do this, which will always work, is to merely multiply the denominators with each other. But this might make things messy if the denominators contain large numbers or polynomials.
The more straightforward approach is to find Least Common Denominator (LCD) by first finding the Least Common Multiple (LCM).
Confused?
Here’s what you need to know…. the LCD and the LCM pretty much mean the same thing!
All you have to do is find the lowest number or smallest polynomial they all have in common, as Math Planet accurately states.
Adding Fractions with Like Denominators
How do we determine what is the smallest?
We factor!
So, now let’s talk about the steps for Adding and Subtracting Rational Expressions:
- If all denominators are the same, then add or subtract the numerators and simplify if needed.
- If the denominators are different, we must create common denominators by factoring each denominator into primes.
- Rewrite each fraction using the least common denominator (LCD), then add or subtract the numerators and simplify if needed.
Don’t worry; we will walk through countless examples in detail so that by the end of the lesson you will feel confident in adding and subtracting even the most complicated rational expressions.
Adding & Subtracting Fractions (How-To) – Video
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