Problem 50 - Algebra 2

Question

Find each percent. 68% of 500

Step-by-Step Solution

Answer

68% of 500 is 340.

Step 1: Convert Percentage to Decimal

First, we need to convert the percentage into a decimal. To do this, divide the percentage by 100. Thus, the decimal form of 68% is \( \frac{68}{100} = 0.68 \).

Step 2: Multiply Decimal by Number

Now, multiply the decimal obtained in Step 1 by the number given (500 in this case). Perform the multiplication: \( 0.68 \times 500 \).

Step 3: Calculate the Product

Continuing from Step 2, perform the multiplication: \( 0.68 \times 500 = 340 \). This result represents 68% of 500.

Key Concepts

Decimal Conversion

When you're dealing with percentages, the first step is often converting the percentage into a decimal. This transformation is essential because it simplifies many arithmetic operations, such as multiplication, which we'll explore later.
To convert a percentage to a decimal, you need to divide the percentage value by 100. This works because "percent" literally means per hundred. Hence, 68% can be converted into a decimal by calculating \( \frac{68}{100} \). This gives us a result of 0.68.
By understanding the basic idea that percentages are just parts out of a hundred, the conversion to decimals becomes logical and straightforward. Always remember:

• Move the decimal point two places to the left when converting percentages to decimals.
• This process maintains the value but changes the form, making calculation easier.

Mastering this conversion is a foundational skill for various calculations, especially in problem-solving scenarios involving percentages.

Multiplication

Once the percentage is converted to a decimal, the next step in finding a portion of a number is to perform multiplication. Instead of using a direct percentage calculation, multiplying by decimals provides a more straightforward and efficient method.
Continuing with our example, we converted 68% into the decimal 0.68. To find 68% of 500, multiply the decimal by the number:

• Calculate \( 0.68 \times 500 \).

This tells us that you are finding 0.68 * the total (500), which gives the specific part we want to find.
Multiplication in this context works by allocating the portion-sized representation (the decimal) of the whole number accurately. This is why it's important to ensure the conversion step was correctly executed. This method can easily be adapted to other figures, providing you maintain a strong understanding of how multiplication extends the concept of parts of a whole.

Problem Solving Steps

Solving a percentage problem involves a logical series of steps that ensure accuracy and simplicity. Each step has its purpose in solving these problems efficiently.
Here's a summary of the steps used:

• Step 1: Start by converting the percentage to a decimal, as described in the 'Decimal Conversion' section.
• Step 2: Use the decimal to multiply by the number you are finding the percentage of. This step involves standard multiplication, transforming concepts into calculation.
• Step 3: Finally, calculate the product to arrive at the answer, completing the problem-solving process.

Following these steps ensures that you cover all necessary parts of the problem systematically. It simplifies the concept into manageable parts, providing confidence that you're approaching the solution correctly.
Understanding these steps not only helps in carrying out the exercise but also builds a deeper comprehension of how percentages interact with basic arithmetic operations.