Problem 71 - Elementary Algebra

Question

$$ \text { Find } 5 \% \text { of } 60 $$

Step-by-Step Solution

Answer

3

Step 1: Understand the Problem

You need to find 5% of 60. This means determining what 5 out of every 100 parts of 60 are.

Step 2: Convert Percentage to Decimal

To find a percentage of a number, convert the percentage to a decimal by dividing by 100. So, 5% becomes 0.05.

Step 3: Multiply by the Number

Multiply the decimal equivalent of the percentage by the given number: \[ 0.05 \times 60 = 3 \]

Step 4: Conclusion

Therefore, 5% of 60 is 3.

Key Concepts

Converting Percentages to Decimals

Understanding how to convert percentages to decimals is essential in percentage calculations. A percentage represents a part out of 100, so converting it to a decimal means expressing it in a form ready for multiplication.

To convert a percentage to a decimal, you simply divide it by 100. For example, to convert 5% to a decimal:

5% = 5 ÷ 100 = 0.05

By doing this, you turn the percentage into a value that is easier to work with when performing arithmetic operations. This step ensures that your subsequent calculations are accurate.

Multiplication in Percentage Problems

Once you have converted the percentage into a decimal, the next step involves multiplication. This is a crucial part of finding the actual value represented by the percentage.

Multiplication allows you to scale the decimal according to the number you are interested in. Continuing with our 5% example, if we need to find 5% of 60, we multiply the decimal 0.05 by 60:

\[ 0.05 \times 60 = 3 \]

The multiplication step takes the fraction of the whole number represented by the percentage and scales it to find the part of that whole. It's important to perform this operation accurately to avoid errors in the final result.

Finding Percentages of Numbers

Finding a percentage of a number combines both converting percentages to decimals and multiplying. This two-step process can be straightforward if you follow each step carefully.

Let's summarize the process using our example, finding 5% of 60:

1. **Convert the percentage to a decimal:** 5% becomes 0.05.

2. **Multiply by the number:** Take the decimal and multiply it by the number you're interested in: \[ 0.05 \times 60 = 3 \]

This approach can be used for any percentage calculation. Just replace 5% and 60 with your specific values. By mastering these steps, you can accurately determine any percentage of any given number.