- A percentage \(P\%\) of a value \(V\) is defined as \(\frac{P}{100} \times V\).
- The expression \(6\% \times \$1,200\) can be written as \(\frac{6}{100} \times \$1,200\), which is equal to \(0.06 \times \$1,200\).
- All three given expressions are mathematically equivalent and correctly represent the 6% sales tax calculation.
- The correct expressions are: \(\boxed{0.06(\$1,200), \frac{6}{100}(\$1,200), 6\%(\$1,200)}\).
Explanation
- Analyzing the Problem and Definitions
The task is to identify expressions that correctly calculate the sales tax for a computer repair at Store A. We are given the repair cost of \(\$1,200\) and a sales tax rate of \(6\%\). To calculate the amount of sales tax, we need to find \(6\%\) of \(\$1,200\). A percentage \(P\%\) of a value \(V\) is equivalent to \(\frac{P}{100} \times V\). Since the percentage is \(6\%\), the calculation is \(\frac{6}{100} \times \$1,200\).
- Evaluating the Expressions
We examine the three provided expressions to see if they represent \(6\%\) of \(\$1,200\):
- Expression 1: \(0.06(\$1,200)\)
Since \(6\% = \frac{6}{100} = 0.06\), multiplying by \(0.06\) is equivalent to finding \(6\%\) of the value. Therefore, \(0.06 \times \$1,200 = \$72\). This is a correct expression.
- Expression 2: \(\frac{6}{100}(\$1,200)\)
This expression directly represents the definition of a percentage: taking \(6\) parts out of \(100\), which is \(\frac{6}{100}\), and multiplying it by the total cost. This is also a correct expression.
- Expression 3: \(6\%(\$1,200)\)
This is the standard way of writing "6 percent of 1,200". It is mathematically synonymous with the previous two forms. This is also a correct expression.
- Conclusion
We have verified that each of the three given expressions is a valid mathematical representation of the sales tax calculation. They all result in \(\$72\), which is \(6\%\) of \(\$1,200\). Thus, all three provided options are correct. The final answer is that all three expressions are correct.
Examples
Understanding how to calculate percentages is an essential skill in everyday life, whether you are shopping, dining out, or managing a budget. For instance, when you see a store offering a 6% discount or charging a 6% sales tax, you can quickly determine the final price by converting the percentage into a decimal (e.g., 6% to 0.06) or a fraction (e.g., 6/100). Being able to represent percentages in these different ways allows you to perform mental math easily or set up equations for more complex financial planning.