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When adding fractions, it's important to understand the concept of like denominators. Denominators are the numbers located below the fractional line in a fraction.
For example, the denominators in the fractions \(-\frac{6}{20}\) and \(+\frac{1}{20}\) are both 20.
Like denominators mean that the fractions have the same denominator value. This similarity allows us to add the fractions directly by adding their numerators, without needing to change the denominators. With like denominators, you don't need to do any extra calculation to align the fractions. Just add or subtract the numerators, keeping the common denominator the same.
For example, in our exercise, \(-\frac{6}{20} + \frac{1}{20}\) allows us to clear a path straight to the numerators: -6 + 1. It's a straightforward process and is an essential first step in adding fractions.

Simplifying fractions means rewriting them in their simplest form, where the numerator and the denominator have no common divisors other than 1.
To simplify a fraction, you divide both the numerator and the denominator by the greatest common divisor (GCD).
Simplifying is an important part of working with fractions because it makes the number easier to understand and work with in later calculations. For instance, after adding \(-\frac{6}{20}\) and \(+\frac{1}{20}\), we obtain \(-\frac{5}{20}\). The fraction \-\frac{5}{20}\ can be simplified because both 5 and 20 share a common divisor, which is 5.
By dividing both the numerator and the denominator by 5, we achieve the simplest form: \(-\frac{1}{4}\).
No further simplification is possible because -1 and 4 have no common factors other than 1.

The greatest common divisor (GCD) is the largest positive integer that divides two or more integers without leaving a remainder.
Finding the GCD is crucial in simplifying fractions because it determines how much you can reduce a fraction. To find the GCD of two numbers, list out the factors of each number and identify the largest factor that they share.
For our exercise, to simplify \(-\frac{5}{20}\), we need the GCD of 5 and 20.
The factors of 5 are 1 and 5, while the factors of 20 are 1, 2, 4, 5, and 20.
The greatest common factor they share is 5. That’s why dividing both 5 (numerator) and 20 (denominator) by 5 results in \(-\frac{1}{4}\), the simplified form of the fraction.Understanding how to find the GCD is an essential skill in simplifying fractions, helping to complete the process quickly and accurately.