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Converting percentages into decimals is often the first step in solving problems involving percentages, as it simplifies the calculations. Let’s take a quick dive into how you do it.

When you see a percentage, it's simply a way to express a fraction out of 100. Therefore, to convert a percentage to a decimal, you divide the percentage by 100.

Here's why: the term "percent" itself means "per hundred". For example, when you have 42%, it means 42 parts out of 100. Mathematically, you write this as:

• Divide 42 by 100
• Write it as \( \frac{42}{100} \)
• This equals 0.42

Thus, 42% as a decimal is 0.42. Remember, shifting the decimal point two places to the left for any percentage will give you the decimal format. This method is consistent for all percentage conversions.

Multiplication is a core operation when solving word problems involving percentages. Once you convert the percentage into a decimal, you multiply it by the number in question.

Let's break it down using our problem. We want to find 42% of 60. After converting 42% to the decimal 0.42, the next step is to multiply:

• Take the decimal 0.42
• Multiply it by 60: \( 0.42 \times 60 \)
• The result is 25.2

This multiplication operation calculates the part of the quantity (in this case, 60) represented by the percentage (42%).

Using multiplication in this way helps to solve percentage problems effectively and quickly by representing how much of a total quantity is taken up by a given percentage.

After completing your calculations, interpreting the results accurately is crucial. Math problems aren't just about finding numbers, they tell a story or answer a specific question. Let's interpret the result from our example.

We calculated that \( 0.42 \times 60 = 25.2 \). So, what does this number mean? In this context, 25.2 is the number that represents 42% of the total 60. This is particularly useful when you want to understand proportions in terms of real-world contexts or when analyzing data.

Interpreting results involves:

• Understanding what the answer represents in the context of the problem.
• Checking if the answer makes logical sense.
• Applying this understanding to inform further decisions or analyses.

Thus, interpretation transforms mere calculations into meaningful insights, enhancing the learning journey and ensuring accurate application of mathematical concepts.