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Understanding the greatest common divisor (GCD) is essential when simplifying fractions. It is the largest number that can exactly divide two or more numbers without leaving a remainder.
When simplifying fractions, determining the GCD helps in reducing the fraction to its lowest terms. To find the GCD of two numbers, like 10 and 12 from our problem, list the factors of each number:

• Factors of 10: 1, 2, 5, 10
• Factors of 12: 1, 2, 3, 4, 6, 12

The GCD is the largest common factor found in both lists. In this case, it is 2.
Using this GCD, you can adjust both the numerator and the denominator of a fraction to make it simpler, which makes calculations easier and more efficient.

Every fraction consists of two parts: the numerator and the denominator.
These play a crucial role in defining the value of a fraction. The numerator is the top number in a fraction. It indicates how many parts of the whole are being considered. For example, in the fraction \(\frac{10}{12}\), 10 is the numerator, representing 10 parts of a certain whole.
The denominator, on the other hand, is the bottom number. It shows into how many equal parts the whole is divided. In our example, 12 is the denominator, meaning the whole is divided into 12 equal parts.
Understanding these two components is key to performing operations on fractions, such as addition, subtraction, and particularly simplification.

Simplifying fractions involves reducing them to their simplest form. This means changing a fraction so that the numerator and the denominator are as small as possible while still having the same value.
To simplify a fraction like \(\frac{10}{12}\), once you have the GCD (which we've found to be 2), divide both the numerator and the denominator by this number.

• \(\frac{10}{12} \rightarrow\) Divide both by 2
• New numerator: \(\frac{10}{2} = 5\)
• New denominator: \(\frac{12}{2} = 6\)

Now, you re-write the fraction with these new numbers, resulting in \(\frac{5}{6}\).
The simplified or lowest terms of the fraction \(\frac{10}{12}\) is \(\frac{5}{6}\). This not only makes the fraction easier to work with but also maintains its equality to the original expression.