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Simplifying fractions is like cleaning up a messy room; it makes everything neat and easy to understand. A fraction is simplified when its numerator and denominator have no common factors other than 1. To simplify, we divide the numerator and denominator by their greatest common divisor (GCD).
For example, in Step 1 of the solution, the fraction \(\frac{-12}{18}\) is simplified to \(\frac{-2}{3}\) by dividing both 12 and 18 by their GCD, which is 6.
This process ensures that fractions are in their simplest form, making them easier to compare, add, or subtract. Always look for common factors before performing further operations.

Finding a common denominator is essential when adding or subtracting fractions. A denominator is the bottom number of a fraction, and fractions can only be added or subtracted directly when they have the same denominator.

To find a common denominator, look for the least common multiple (LCM) of the denominators involved. In the exercise, we had fractions \(\frac{-2}{3}\) and \(\frac{-56}{27}\).
To add them, you find a common denominator, which in this case is 27. Convert \(\frac{-2}{3}\) to \(\frac{-18}{27}\) by multiplying both the numerator and the denominator by 9, so both fractions share the denominator 27.
Working with common denominators simplifies the addition or subtraction of fractions.

Once the fractions have a common denominator, addition is straightforward. Only their numerators are added, and the sum retains the common denominator.
In our exercise, after simplifying and finding common denominators, we added \(\frac{-18}{27}\) and \(\frac{-56}{27}\).
The numerators, -18 and -56, are combined:

• Add -18 and -56 to get -74.
• The denominator remains 27.

The result is \(\frac{-74}{27}\).
Additions become easier once fractions are properly aligned with a common denominator, ensuring the operations are executed smoothly and accurately.