Problem 15 - Elementary Algebra

Question

Find \(1.25 \%\) of 4500 .

Step-by-Step Solution

Answer

1.25% of 4500 is 56.25.

Step 1 - Understand the Problem

The task is to find what 1.25% of 4500 is. This means determining how much 1.25% of the total amount 4500 translates to.

Step 2 - Convert Percentage to Decimal

Percentages need to be converted into decimals before performing the multiplication. To convert 1.25% to a decimal, divide 1.25 by 100: \( 1.25 \div 100 = 0.0125 \).

Step 3 - Multiply by the Total Amount

Now, multiply the decimal form of the percentage by 4500: \( 0.0125 \times 4500 \).

Step 4 - Calculate the Multiplication

Perform the multiplication: \( 0.0125 \times 4500 = 56.25 \).

Step 5 - State the Final Answer

The result of finding 1.25% of 4500 is 56.25.

Key Concepts

Percent to Decimal Conversion

When dealing with percentages, the first step is often to convert the percentage to a decimal format. This makes mathematical operations more straightforward.
To convert a percentage to a decimal:

• Remove the percent sign (%)
• Divide by 100

For instance, to convert 1.25% to a decimal format:
The calculation is: \(\frac{1.25}{100} = 0.0125\)
This conversion is essential because percentages are essentially fractions of 100. By converting to decimal, we standardize the way we handle these values in multiplication and other operations.

Multiplication

Once the percentage is converted to a decimal, we multiply this by the total amount to find the portion represented by that percentage.
When multiplying decimals, remember:

• Align the numbers by their rightmost digits before multiplying.
• Ignore the decimal points initially and multiply as if these were whole numbers.
• Count the total number of decimal places in both the original numbers. Place the decimal point in the result accordingly.

For example, in our problem, we need to find 1.25% of 4500. After converting 1.25% to 0.0125, we perform: \(0.0125 \times 4500 = 56.25\).
Notice the multiplication and how the decimal placement is handled carefully.

Finding Percentages

Finding a percentage of a given number involves specific steps to maintain accuracy.
Here's a condensed version for clarity:

• Convert the percentage to a decimal (as discussed above).
• Multiply the decimal by the total amount.
• Review the result to ensure accuracy.

Let's recap with our exercise:
- We had to find 1.25% of 4500.
- We converted 1.25% to its decimal equivalent: \(0.0125\).
- We multiplied \(0.0125 \times 4500 = 56.25\).
Therefore, 1.25% of 4500 is 56.25. Following these steps ensures you consistently arrive at the correct answer when dealing with percentages.