Calculating Percentages in Mathematical Expressions

Understanding and calculating percentages in mathematical expressions is a fundamental skill in mathematics with numerous practical applications. This article will walk you through the steps of calculating a specific percentage in a given equation, breaking it down into simple, clear steps that are easy to follow. Using the Google SEO optimization techniques, we will ensure this content is optimized for search engines to enhance its visibility and reach.

Problem Statement: 200 of 4 of a

The problem at hand is to find out what percent 200 of 4 of a is of a/2. This involves a series of steps to break down the problem and arrive at an accurate and understandable solution.

Step 1: Calculate 4 of a

To begin, we need to calculate what 4 of a is. Mathematically, this can be represented as:

4 of a 4/100 × a 0.04a

Step 2: Calculate 200 of 0.04a

Next, we need to find out what 200 of 0.04a is:

200 of 0.04a 200/100 × 0.04a 2 × 0.04a 0.08a

Step 3: Determine the Percentage of 0.08a of a/2

Now, the question is what percent 0.08a is of a/2. We start by calculating a/2:

a/2 0.5a

Then, we set up the ratio to find the percentage:

Percentage

Simplifying the fraction:

0.08a/0.5a 0.08/0.5 0.08 ÷ 0.08/0.5 ÷ 0.08 1/6.25 0.16

Converting to percentage:

0.16 × 100 16

Therefore, 200 of 4 of a is 16 percent of a/2.

Alternative Approach

A simplified approach could also yield the same result. We know that:

200 of 4 of a 8 of a

Given that a/2 is 50 of a, then 8 of a is 16 of a/2.

Final Calculation

To double-check, we can use the proportion:

x of a/2 8 of a

100/100a/2 8/100a

100/100 8/100 × 2/1

100/100 16/100

Thus, x 16, confirming that 200 of 4 of a is 16 percent of a/2.

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Conclusion

Through this detailed breakdown, we have calculated 200 of 4 of a as 16 percent of a/2. This approach can be applied to a variety of similar problems, providing a solid foundation for understanding percentage calculations in mathematical expressions.