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Understanding common factors is crucial when simplifying rational expressions. A factor is a number that divides into another number without leaving a remainder. For instance, factors of 12 include 1, 2, 3, 4, 6, and 12 itself.

When we talk about common factors, we're looking for numbers that are factors of both the numerator and the denominator in a fraction. Identifying common factors allows us to reduce a fraction to its simplest form. In the exercise \(\frac{28}{35}\), the common factor is 7 because it is the highest number that divides evenly into both 28 and 35. By finding and dividing by common factors, we make the numbers smaller and the expression simpler while keeping the value the same.

Essentially, common factors serve as a 'bridge' allowing us to streamline complex numbers into more manageable ones, making calculations easier and the relationships between numbers clearer.

The process of simplifying fractions is a fundamental skill in math that involves reducing fractions to their simplest form. This means making the numerator and the denominator as small as possible without changing the value of the fraction. Simplifying can be achieved by dividing both the numerator and the denominator by their greatest common divisor.

For example, the fraction \(\frac{28}{35}\) can be simplified by observing that both numbers share a common factor of 7. By dividing both the numerator (28) and the denominator (35) by 7, we get \(\frac{28 \div 7}{35 \div 7} = \frac{4}{5}\), which is the simplest form of the original fraction.

Simplifying fractions not only makes them easier to work with but also helps in comparing their sizes and understanding ratios. Furthermore, it's especially useful in higher-level algebra where simpler expressions can make it easier to manipulate equations and solve for variables.

Fractions are comprised of two parts: the numerator, which is the top number, and the denominator, which is the bottom number. The numerator represents the number of parts we have, while the denominator indicates the total number of equal parts into which the whole is divided.

In the fraction \(\frac{28}{35}\), 28 is the numerator, and 35 is the denominator. When simplifying, always keep in mind that changes to either the numerator or the denominator affect the fraction as a whole. The objective in simplification is to reduce both to their lowest terms while maintaining the proportion between them.

It's important to distinguish between numerators and denominators as they dictate the fraction's value. Remember, a fraction is simply a way to express division: \(\frac{28}{35}\) indicates that 28 is being divided by 35. Understanding this can really help in both simplifying fractions and performing operations like addition, subtraction, multiplication, and division of fractions.