Calculating Sales Tax: Which Option Is Correct?

Hey guys! Ever wondered how sales tax is calculated? It's a pretty common thing we encounter when shopping, and understanding the math behind it can be super helpful. Let's dive into a specific example: figuring out the sales tax on a $14.29 purchase with a tax rate of 6 3/4%. We'll break down the steps, explain the concepts, and make sure you're a pro at calculating sales tax in no time!

Understanding Percentages and Decimals

To accurately calculate percentages, especially in the context of sales tax, it’s crucial to understand the relationship between percentages and decimals. Percentages are essentially fractions out of 100. So, when we say 6 3/4%, we mean 6.75 out of 100. The first key step is converting this percentage into its decimal equivalent. To do this, you divide the percentage by 100. So, 6.75% becomes 6.75 / 100 = 0.0675. This conversion is the foundation for calculating the actual tax amount. Think of it like translating a language; you need to convert the percentage language into a decimal language that your calculator can understand.

Why is this conversion so important? Because multiplying by a decimal is how we find a portion of a number. When we multiply the price of an item by the decimal form of the sales tax, we're essentially finding what that percentage of the price is. For instance, if you wanted to find 50% of something, you'd multiply by 0.50 (since 50/100 = 0.50). Similarly, for sales tax, we need to find the decimal equivalent to perform the calculation correctly. Understanding this fundamental concept is the key to avoiding common mistakes and ensuring accurate financial calculations, not just in sales tax scenarios but in many aspects of daily life.

Breaking Down 6 3/4% Sales Tax

Now, let's focus on the specific sales tax rate we have: 6 3/4%. This mixed number percentage might seem a bit tricky at first, but we can easily convert it into a decimal. The fraction 3/4 is equivalent to 0.75, so 6 3/4% is the same as 6.75%. As we discussed earlier, to convert this percentage to a decimal, we divide by 100. This gives us 6.75 / 100 = 0.0675. This decimal, 0.0675, represents the tax rate in a format we can use for calculation. It's the magic number that will help us find the tax amount.

It's important to be super precise when dealing with percentages and decimals, especially when money is involved. A small error in the decimal conversion can lead to a significant difference in the calculated tax amount. Imagine if you accidentally used 0.675 instead of 0.0675! You'd end up calculating ten times the actual sales tax, which is definitely not what anyone wants. So, double-checking your conversion and making sure you've divided by 100 correctly is always a good idea. Think of it as a crucial step in ensuring you're getting the right answer and not overpaying (or underpaying!) your taxes. This precision builds confidence in your calculations and prevents potential headaches down the line. Remember, accuracy is key when handling percentages and decimals in real-world scenarios.

Calculating the Tax Amount on $14.29

Alright, we've got our decimal representation of the sales tax (0.0675). Now, let's apply it to our purchase price of $14.29. To calculate the sales tax amount, we simply multiply the price by the decimal form of the tax rate. So, we have: Sales Tax = 0.0675 * $14.29. This is a straightforward multiplication problem, but it’s essential to understand what this calculation represents. We're essentially finding 6.75% of $14.29. This result will give us the amount of tax added to the original price.

Now, let's grab a calculator (or do the math manually if you're feeling ambitious!) and perform the multiplication. 0. 0675 multiplied by 14.29 equals approximately $0.964575. In a real-world scenario, sales tax is typically rounded to the nearest cent. So, $0.964575 would be rounded to $0.96. This $0.96 is the amount of sales tax that would be added to the $14.29 purchase. Understanding the process of multiplication in this context clarifies why we chose this particular operation. We're not adding, subtracting, or dividing; multiplication is the correct way to find a percentage of a value. This fundamental concept is crucial for not only sales tax calculations but also for understanding discounts, interest rates, and various other financial computations.

Identifying the Correct Expression

Now that we understand the calculation, let's look at how it's represented in the answer choices. We know that the correct calculation involves multiplying the decimal form of the sales tax (0.0675) by the price of the item ($14.29). So, we're looking for an expression that looks like this: (0.0675) * (14.29). The answer choices will likely present various combinations of these numbers, but only one will accurately represent the calculation we've just performed.

The key here is to avoid common mistakes, such as using the percentage directly (6.75 instead of 0.0675) or misplacing the decimal point. Carefully examine each option and make sure it aligns with the logic we've established. We're not looking for a sum, a difference, or a quotient; we're looking for a product – the result of multiplication. This step highlights the importance of understanding the mathematical operation required for a specific situation. Recognizing the correct operation, in this case, multiplication, is just as crucial as performing the calculation itself. By carefully analyzing the answer choices and relating them back to our calculated result, we can confidently select the correct expression and avoid falling for common distractors.

Why Other Options Are Incorrect

To truly master this concept, it's just as important to understand why the incorrect answer choices are wrong as it is to know why the correct answer is right. This deeper understanding will prevent you from making similar mistakes in the future and solidify your grasp on sales tax calculations. Let's consider some potential incorrect options and analyze why they don't represent the correct sales tax calculation.

One common mistake is to forget to convert the percentage to a decimal. If you used 6.75 directly instead of 0.0675, you'd end up with an expression like (6.75)(14.29). This would calculate 675% of $14.29, which is a drastically inflated number and clearly not the correct sales tax. Understanding this error highlights the importance of the percentage-to-decimal conversion step. Another potential mistake is misplacing the decimal point. For example, using 0.675 instead of 0.0675 would calculate 67.5% of $14.29, which is also significantly higher than the actual sales tax. This emphasizes the need for precision when working with decimals. By understanding the common errors that lead to incorrect answers, we strengthen our understanding of the correct process and build confidence in our ability to identify and avoid these pitfalls in future calculations.

Conclusion: Mastering Sales Tax Calculations

So, guys, calculating sales tax might seem a little intimidating at first, but by breaking it down into clear steps, it becomes much more manageable. We learned the importance of converting percentages to decimals, how to perform the multiplication, and how to identify the correct expression representing the calculation. Mastering these skills not only helps you with math problems but also gives you a practical understanding of everyday financial transactions. Remember, the key is to understand the underlying concepts and apply them consistently.

By working through this example, you've gained a solid foundation for tackling other sales tax problems and similar percentage-based calculations. Keep practicing, and you'll become a whiz at calculating sales tax in no time! And remember, understanding the “why” behind the math is just as important as knowing the “how.” So, the next time you’re at the store, take a moment to think about how the sales tax is calculated. You’ll be surprised at how much you already know! Understanding these financial concepts empowers you to make informed decisions and navigate the world of commerce with confidence. So, keep learning, keep practicing, and keep those calculations accurate!