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When adding or subtracting fractions, the concept of a common denominator is key. A denominator is the number below the fraction line, indicating the total number of equal parts. For example, in the fraction \(\frac{3}{4}\), 4 is the denominator. To add fractions together smoothly, they need to share the same denominator.
In the expression \(\frac{1}{a} + \frac{4}{a} + \frac{5}{a}\), all fractions already have a common denominator, which in this case is \(a\). This makes the problem much simpler, as you can directly add the numerators (the top numbers of the fractions). If the fractions had different denominators, you would first need to find a common denominator, often the least common multiple, to make the additions or subtractions possible.

Reducing fractions means simplifying them to their smallest possible form. A fraction is in its simplest form when the numerator and denominator have no common factors, except for 1. This process makes the fraction easier to read and work with.
After combining the numerators of the original expression \(\frac{1}{a} + \frac{4}{a} + \frac{5}{a}\), you get \(\frac{10}{a}\). To check if this fraction can be reduced, look for any common factors between 10 and \(a\). Since 10 is a constant and unless \(a\) is a multiple of 2 or 5 (the factors of 10), \(\frac{10}{a}\) is already in its simplest form. If, however, \(a\) had a factor that is common with 10, you could divide both the numerator and the denominator by this factor to provide a reduced version.

Simplifying algebraic expressions is an essential skill in algebra. It involves reducing expressions to their simplest form, making them easier to interpret and use in calculations or further equations. This simplification process often includes combining like terms and reducing fractions.
In our example, \(\frac{10}{a}\) represents a simplified form of the given expression, as the addition of like fractions with a common denominator was completed. Simplifying might involve additional steps in more complex expressions, such as expanding or factoring. However, in this case, each fraction shares the denominator, simplifying the process to just combining the numerators. Ensuring expressions are in their simplest form is crucial for efficiency and accuracy, particularly when solving equations or comparing results. Simplification is a gateway to clearer and more straightforward mathematical work.