91Ó°ÊÓ

When working with fractions, one of the first things you need to verify is whether the denominators (the bottom numbers in fractions) are the same. In this exercise, we observe that both fractions, \( \frac{6}{7} \) and \( \frac{2}{7} \), have the same denominator, which is 7.
Having a common denominator is crucial because it allows you to directly subtract the numerators (the top numbers) without needing any further adjustments to the fractions. This simplifies the subtraction process significantly.
For fractions with different denominators, you would need to find a common denominator before performing any operations. This often involves finding the least common multiple (LCM) of the denominators. But in this case, you’re already set because the denominators are the same.

After you perform operations with fractions, such as addition or subtraction, you might end up with a result that is not in its simplest form. Simplifying a fraction means reducing it to the lowest possible terms. In our example, we have already subtracted to get \( \frac{4}{7} \).
To simplify, you look for common factors in the numerator and denominator besides 1. For \( \frac{4}{7} \), the numerator is 4 and the denominator is 7, which do not share any common factors other than 1.
This means \( \frac{4}{7} \) is already simplified. Always remember: a fraction is in its simplest form when you cannot divide the numerator and denominator by the same number other than 1.

In fraction subtraction, you primarily focus on the numerators when the denominators match. With a common denominator, subtract the numerators directly. For our problem, you subtract 2 from 6, getting the result, 4.
The subtraction only affects the numerators, so the denominator remains unchanged. You then write the new numerator over this unchanged denominator, forming a new fraction: \( \frac{4}{7} \).
Remember, the denominator determines the size of the parts you divided the whole into, and altering it before ensuring compatibility can lead to incorrect results. But when subtracting the numerators, ensure precision to maintain the integrity of your final answer.