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When adding fractions, the first thing to do is to find a common denominator. A common denominator is a shared multiple of the denominators of the fractions you are working with. This allows you to combine the fractions into a single fraction.
For example, if you are adding \(-\frac{1}{3} + (-\frac{4}{15})\), the denominators are 3 and 15. You need to determine the least common denominator (LCD) of these two numbers. The LCD is the smallest number that both denominators can divide into evenly.
In this case, 15 is the smallest number that both 3 and 15 can divide into without leaving a remainder. So, 15 is the common denominator.
Always remember to find this common base before proceeding to add fractions.

After finding a common denominator and performing the addition, you might end up with a fraction that can be simplified. Simplifying a fraction means reducing it to its lowest terms.
This typically involves dividing both the numerator and the denominator by their greatest common divisor (GCD).
For instance, after adding \(-\frac{5}{15} + (-\frac{4}{15})\), you get \(-\frac{9}{15}\).
To simplify \(-\frac{9}{15}\), divide both the top and bottom by their GCD (which is 3): \(-\frac{9 \div 3}{15 \div 3} = -\frac{3}{5}\).
The simplified fraction is easier to understand and work with.

The Greatest Common Divisor (GCD) of two numbers is the highest number that divides both of them without leaving a remainder.
Finding the GCD is essential when you need to simplify fractions. Use the GCD to reduce both the numerator and the denominator by their shared highest factor.
In our example, after calculating \(-\frac{9}{15}\), we need to simplify this fraction. To do this, we identify that the GCD of 9 and 15 is 3.
Divide both the numerator and the denominator by this GCD to get the simplified form: \(-\frac{9 \div 3}{15 \div 3} = -\frac{3}{5}\).
Understanding the GCD concept helps in making fractions clearer and easier to manage.