Problem 12 - Elementary Algebra

Question

Find \(6 \%\) of 42 .

Step-by-Step Solution

Answer

2.52

Step 1: Understand the Problem

The task is to find 6% of 42. This can be written mathematically as 6% of 42 or 0.06 * 42.

Step 2: Convert Percentage to Decimal

To find a percentage of a number, convert the percentage to a decimal. Since 6% is the same as 6 out of 100, converted to a decimal, it is 0.06.

Step 3: Multiply the Decimal by the Number

Multiply the decimal value by the given number: 0.06 * 42 = 2.52.

Key Concepts

Converting Percentages to Decimals

When working with percentages in calculations, the first step is usually converting the percentage to a decimal. This makes it easier to perform mathematical operations like multiplication. To convert a percentage to a decimal, you divide the percentage by 100. For example, 6% becomes 0.06 since \( \frac{6}{100} = 0.06 \). Another way to think about this is simply moving the decimal point two places to the left. So, 15% becomes 0.15 and 125% becomes 1.25. Remember, converting percentages to decimals is essential before you can use them in algebraic calculations.

When you convert percentages this way, it simplifies other calculations, especially when working with large data sets or complex equations.

Multiplication of Decimals

Once you've converted the percentage to a decimal, the next crucial step is to multiply that decimal by the number in question. This process is straightforward, but let's break it down for clarity.

For instance, in the exercise, we need to find 6% of 42. After converting 6% to 0.06, we multiply it by 42. Mathematically, this is shown as \( 0.06 \times 42 = 2.52 \).

Here's a simple way to approach this:

• Ignore the decimal points initially and multiply the numbers as if they were whole numbers.
• Count the total number of decimal places in both numbers being multiplied.
• In the result, place the decimal point so that the number of decimal places matches the total counted in the previous step.

For instance, with 0.06 and 42, zero additional decimal places are needed in 42, while 0.06 has two decimal places. Thus, the final result should have two decimal places, giving us 2.52.

Elementary Algebra

Algebra involves working with symbols and numbers to solve equations and problems. In this particular exercise, elementary algebra is used to represent the task simply and solve it efficiently.

The problem 'Find 6% of 42' can be translated into an algebraic expression. Here, '6% of 42' is represented as \( 0.06 \times 42 \), breaking down the problem into a simple multiplication task. This method of representing word problems algebraically makes it easier to visualize and solve complex issues.

In general, when solving algebraic expressions involving percentages:

• First, convert the percentage to a decimal.
• Then, substitute the decimal into the algebraic expression.
• Perform the necessary operations to find the solution.

Understanding these basics is crucial for tackling more advanced algebraic problems and helps build a strong mathematical foundation.