91Ó°ÊÓ

When dealing with the subtraction of fractions, the first core concept you need to understand is the 'common denominator.' It is the shared bottom number in the fractions you are working with. For the problem at hand, both fractions \(\frac{5}{6}\) and \(\frac{1}{6}\) have the same denominator, which is 6. This makes it easier to subtract them.
The essence of having a common denominator is unifying the fractions under the same terms, allowing for easier manipulation. If the denominators were different, we would first need to convert them into equivalent fractions with a common denominator before proceeding with the subtraction. This often involves finding the least common multiple (LCM) of the denominators.
However, in our exercise, we already have a common denominator, so we can move on to the next step directly.

Once you have established a common denominator, the next important concept is 'numerator subtraction'. This is the process of subtracting the top numbers of your fractions while keeping the common bottom number unchanged.
Let's take the fractions \(\frac{5}{6}\) and \(\frac{1}{6}\). Since both fractions share the same denominator, you only need to subtract the numerators:
\[\ 5 - 1 = 4 \ \]
This results in \(\frac{4}{6}\). Remember, the denominator remains the same throughout the process.

The last concept is 'fraction simplification'. Simplification is all about reducing the fraction to its simplest form where the numerator and the denominator have no common factors other than 1.
For the fraction \(\frac{4}{6}\), we can simplify by determining the Greatest Common Divisor (GCD) of 4 and 6. The GCD of 4 and 6 is 2.
To simplify, you divide both the numerator and the denominator by the GCD:
\[ \frac{4 \div 2}{6 \div 2} = \frac{2}{3} \ \]
The fraction \(\frac{2}{3}\) is now in its simplest form. Simplifying fractions helps in making them easier to understand and quicker to work with in further calculations.