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Many students get tripped up by the concept of converting percentages to decimals, but it's actually quite simple! A percentage is simply a fraction expressed as a part of 100. For example, 4% means 4 out of 100.
To convert a percentage to a decimal, divide the percentage by 100. This effectively moves the decimal point two places to the left. So, 4% becomes 0.04 when it's converted.
This conversion is crucial in solving problems involving percentages, especially when setting up equations. By using the decimal form, you can easily incorporate percentages into mathematical operations such as multiplication or division.

Solving equations is a fundamental skill in algebra, and it often involves isolating the variable to find its value. In our problem, the equation was set up as

Writing the Equation

The equation for this problem was based on converting the percentage to a decimal: \[0.04x = 60\] This equation states that 4% of some number \(x\) is equal to 60.

Isolating the Variable

To solve for \(x\), we need to get \(x\) alone on one side of the equation. We do this by performing operations that will leave \(x\) by itself. In this case, to remove the coefficient 0.04, we divide both sides of the equation by 0.04:\[x = \frac{60}{0.04}\]Performing this division gives us the value of \(x\) as 1500. Practicing these steps helps build confidence in tackling more complex algebraic problems.

After solving an equation, it's always a good idea to verify your solution. This ensures that you didn't make any mistakes and that your answer is indeed correct.

In this context, once we solved for \(x\) and found that it equals 1500, we can check this by calculating 4% of 1500 and verifying it equals 60.

Performing the Check

Use the decimal conversion of 4%, which is 0.04, and multiply it by 1500:\[0.04 \times 1500\]Calculating this gives 60, which confirms our solution is correct.
This step of multiplication verification not only affirms your solution but also helps understand how percentages work in practical terms.
It's like double-checking your work to ensure everything makes sense and that your solution is reliable.