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Understanding how to convert a percentage to a decimal is an essential skill for solving many types of math problems. To perform this conversion, simply divide the percentage by 100. Why do we do this? It's because the word 'percent' actually means 'per hundred'. So, when we have a number like 45%, it is equivalent to saying 45 per 100 or 45/100.

Let's consider the example: when we convert 45% to a decimal, we divide 45 by 100, which gives us 0.45. Another way to visualize this is by moving the decimal point two places to the left, which is the same as dividing by 100. Thus, 45% becomes 0.45 in decimal form.

Solving percentage problems involves a basic formula that can be very handy: part = percent × whole. This formula allows us to find any of the three variables (part, percent, or whole) if we have the other two.

For example, to find out what 45% of 30 is, we first convert 45% to its decimal form, which is 0.45, and then we multiply it by the whole, which in this case is 30. By applying the formula, we calculate the part as 0.45 × 30, resulting in 13.5. Therefore, the part, which is the unknown amount in our question, is 13.5. This straightforward approach serves well for a vast array of percentage problems.

Mathematical reasoning involves a logic-based approach to solving math problems. When we approach a problem, we first need to understand what is being asked. In our example, identifying the unknown amount as percent, part, or whole guides our method. Once we recognize that we are looking for the 'part', we then use the appropriate formula and follow a step-by-step process to solve it.

In applying mathematical reasoning, we ensure our calculations are logical and systematic. For the problem 45% of 30, we deduce that since we are given a percent and a whole, the percentage formula is our tool for finding the part. After we calculate it, we consider the context to check if 13.5 makes sense as a 'part' of 30 when considering 45%, confirming that our reasoning and thus our answer is correct.