91Ó°ÊÓ

When adding or subtracting fractions, the concept of a common denominator is essential. The denominator is the bottom part of a fraction. For fractions to be added or subtracted, they need the same denominator or 'common denominator'. This makes it easy to combine the numerators (the top parts).
A common denominator is simply a shared multiple of the denominators of the fractions involved. When fractions already share a denominator, like the ones in our example, you can directly perform addition or subtraction!
In our exercise, fractions \(-\frac{11}{16}\) and \(\frac{-3}{16}\) already have a common denominator of 16. We saved a step since there's no need to modify either fraction, making the process much easier.

Once you've performed operations like addition or subtraction, the next step is often to simplify the fraction.
Simplifying means reducing the fraction to its simplest form. A fraction is simplified by dividing the numerator and the denominator by their greatest common divisor (GCD).
This process reduces the fraction to a form that is easier to understand or use. For example, simplifying \(-\frac{14}{16}\) involves finding a number that can evenly divide both 14 and 16. The result after simplification is \(-\frac{7}{8}\).
Simplification is crucial because it helps in better number management, making results more readable and problems involving these numbers easier to tackle.

The greatest common divisor, or GCD, is a key concept in simplifying fractions. It is the largest number that can perfectly divide both the numerator and the denominator of a fraction.
Finding the GCD helps in reducing fractions to their simplest form. In our context, the GCD of 14 and 16 is used to simplify \(-\frac{14}{16}\).
To find the GCD, one reliable method is listing the factors of each number and finding the largest number common to both lists. For example, factors of 14 are 1, 2, 7, and 14; and factors of 16 are 1, 2, 4, 8, and 16. Here, 2 is the greatest factor that appears in both lists, thus it's the GCD.
Using the GCD ensures your fractions are simplified correctly, providing a neat and manageable form.