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When adding fractions, the first and crucial step is to make sure that the denominators are the same. A denominator represents the total number of equal parts into which something is divided. The common denominator serves as a shared base for combining fractions. This step is key because you can only add, subtract, or compare fractions when they're referring to the same sized parts.

In our exercise, we saw both fractions had the denominator of \(a b\), the product of the variables \(a\) and \(b\), which means they are already prepared for direct addition of numerators. When you encounter fractions with different denominators, you would typically adjust them through finding the least common denominator (LCD). However, in this case, the groundwork is already laid out perfectly for the next step of the process.

Once you have a common denominator, simplifying fractions is the process of reducing them to their simplest form. This means making the numerator (the top number) and the denominator (the bottom number) as small as possible while keeping the value of the fraction the same. Simplifying can involve dividing both the numerator and the denominator by their greatest common factor (GCF).

In the exercise provided, after adding the numerators, the fraction \(\frac{20}{ab}\) is already in its simplest form as long as \(a\) and \(b\) have no factors in common with 20. Simplifying is an important skill to master, because it makes working with fractions easier and ensures that your final answers are in the form that most teachers will request.

With a common denominator secured, adding fractions is straightforward. You simply add the numerators, the numbers above the fraction line that represent how many parts we have. The denominator stays the same since it continues to reflect the size of each part.

For instance, the exercise requires adding \(4\) and \(16\), which are the numerators. Just like regular addition, we combine them to get \(4+16=20\). This sum becomes the new numerator, while the denominator remains \(a b\). Numerator addition in fractions is just adding up individual pieces to find a new total number of pieces, keeping in mind that these pieces must be of the same size, hence the unchanged denominator. Remember, it’s only this simple when the denominators are common – a scenario that’s essential for direct addition of fractions.