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When we talk about simplifying expressions, we refer to the process of making a mathematical expression easier to understand by reducing it to its simplest form. This could involve combining like terms, reducing fractions, or performing arithmetic operations.

Simplifying can be especially crucial when dealing with fractions in algebra. For example, look at the expression inside the parentheses in the given problem: \(1-\frac{3}{5}\). To simplify it, we aim to combine the 1, which can be thought of as \(\frac{5}{5}\) since any number divided by itself is 1, with \(-\frac{3}{5}\). This yields \(\frac{2}{5}\), which is the simplest form of this part of the expression.

Why go through this hassle? Because simplification generally makes all subsequent calculations easier and less error-prone. When working with more complicated algebraic expressions, always look for opportunities to simplify before moving to solve or manipulate the equation further.

Parentheses have a special place in algebra. They are used to indicate which operations should be completed first in an expression. According to the order of operations, also known as BIDMAS or PEMDAS, anything within parentheses must be worked out before moving on to other operations.

In our example, the parentheses group together \(1-\frac{3}{5}\). The simplification process inside these parentheses is essential because it affects the final result. Disregarding the parentheses could lead to significant errors. They are like a roadmap that guides the order in which you should address each part of the expression, ensuring every step in the solution is correctly followed.

Arithmetic with fractions can seem daunting, but it's based on the same principles as arithmetic with whole numbers. With fractions, you can add, subtract, multiply, and divide, just like with any other numbers. However, there are specific rules to follow to perform these operations correctly.

For multiplying fractions, as seen in the problem at hand, the rule is straightforward: you multiply the numerators with each other, and the denominators with each other. So, \(\frac{5}{4} * \frac{2}{5}\) becomes \(\frac{5 * 2}{4 * 5}\) which simplifies to \(\frac{10}{20}\), and then further reduced to \(\frac{1}{2}\) since both the numerator and the denominator can be divided by 10. This final simplified form is easier to read, use, and understand, showing the importance of simplifying wherever possible.

Remember, with fractions, simplifying before performing operations can often make those operations much easier. For instance, had we simplified the fraction \(\frac{5}{4}\) initially by noticing that 5 is in both the numerator of the first fraction and the denominator of the second fraction, the multiplication step would have been even simpler.