Problem 11 - Elementary Algebra

Question

Find \(8 \%\) of 32 .

Step-by-Step Solution

Answer

8% of 32 is 2.56.

Step 1: Understand the Problem

The goal is to find 8% of the number 32.

Step 2: Convert the Percentage to a Decimal

A percentage can be converted to a decimal by dividing it by 100. So, convert 8% to a decimal: \( 8\text{\text{ per hundred}} = \frac{8}{100} = 0.08 \)

Step 3: Multiply the Decimal by the Number

Now multiply 0.08 by 32 to find 8% of 32. \( 0.08 \times 32 = 2.56 \)

Step 4: Write the Final Answer

Thus, 8% of 32 is 2.56.

Key Concepts

Convert Percentage to Decimal

When working with percentages in math problems, it's essential to know how to convert them to decimals. This process makes calculations much more manageable.

To convert a percentage to a decimal, divide the percentage by 100. This is because 'percent' means per hundred. For example, to convert 8% to a decimal:

• Take the number 8.
• Divide it by 100.
• This gives you 0.08.

So, 8% as a decimal is 0.08. This conversion is crucial for performing further calculations such as multiplication.

Multiplication of Decimals

After converting the percentage to a decimal, the next step involves multiplying that decimal by the given number.

In our problem, we need to find 8% of 32. We already converted 8% to 0.08. Now, we multiply 0.08 by 32.

Here’s a simple way to do it:

• Write down the numbers 0.08 and 32.
• Multiply them as you would with whole numbers:
  \( 0.08 \times 32 = 2.56 \).

Remember, when multiplying decimals, count the total number of decimal places in the factors. In this case, there are two decimal places in 0.08. Your result, 2.56, should also reflect this by having two decimal places.

This multiplication helps us determine parts of a whole in problems involving percentages.

Elementary Algebra

Elementary algebra often introduces concepts that can be challenging at first but are powerful tools for solving mathematical problems. In this case, we are using basic algebraic techniques to find the percentage of a number.

Understanding expressions and their simplifications forms the core of elementary algebra.

In our problem, we set up the expression:
\( 8\text{\text{\text{ percent of }} } 32 \).

By converting and multiplying, we actually solved a simple algebraic equation:
\( 0.08 \times 32 = 2.56 \).

This is a straightforward application but demonstrates how algebra enables you to break down and solve real-world problems step by step.

Practicing these steps can enhance your problem-solving skills and deepen your understanding of algebraic concepts.