Problem 37 - Prealgebra

Question

The following problems can be solved by the same method you used in Problems \(1-24\) \(4.89 \%\) of \(2,000\) is what number?

Step-by-Step Solution

Answer

4.89% of 2000 is 97.8.

Step 1: Understanding the Problem

We need to find what 4.89% of 2000 is. The term 'of' typically means multiplication when dealing with percentages.

Step 2: Convert Percentage to Decimal

To work with percentages, convert the percentage to a decimal. This is done by dividing by 100. Hence, 4.89% becomes \( \frac{4.89}{100} = 0.0489 \).

Step 3: Set Up the Multiplication

Now we multiply the decimal form of the percentage by the number we are interested in. This gives us: \( 0.0489 \times 2000 \).

Step 4: Perform Multiplication

Calculate the multiplication: \( 0.0489 \times 2000 = 97.8 \).

Step 5: Conclusion

Therefore, 4.89% of 2000 is 97.8.

Key Concepts

Multiplication in Math

Multiplication is a fundamental concept in math that involves finding the total of one number added a specific number of times. It's not only used when you hear the word "multiply" but often shows up in practical applications, such as in area calculations and percentage problems.

• When you see the word "of" in percentage problems, it usually means you need to multiply — for example, "4.89% of 2000".
• Think of multiplication as repeated addition. For instance, if you multiply 3 by 4, it's like adding 3 four times.
• Multiplication can be performed using different strategies, such as using a calculator, writing out the computation on paper, or using mental math for simpler numbers.
• Understanding the basics of multiplication is essential, especially when solving percentage problems, as they often depend on this operation to find the part of the whole.

To solve multiplication problems effectively, practice is key. The more familiar you are with the process, the easier it becomes to handle larger and more complex numbers.

Decimal Conversion

Converting percentages to decimals is a crucial step in percentage calculations. To convert a percentage into a decimal, divide by 100. This is because "percent" means "per hundred." Let's simplify this further:

• If you have 50%, think of it as 50 per 100, which is 50 divided by 100. This results in 0.50.
• Similarly, for 4.89%, divide 4.89 by 100 to get 0.0489. This small step makes it easier to multiply when solving problems.
• Converting percentages to decimals allows for straightforward multiplication with whole numbers.
• This method of conversion is an important tool in your math toolbox, making many percentage problems simpler to resolve.

Practice converting various percentages to decimals to boost your confidence. After some time, it will become second nature.

Percentage Problems

Percentage problems may seem tricky at first, but they follow a straightforward method once you understand the basics. Here's a guide to tackling these problems:

• A percentage problem typically involves finding how much of a number is represented by a certain percentage. For instance, 4.89% of 2000.
• The first step is to convert the percentage to a decimal. For example, 4.89% becomes 0.0489.
• Next, multiply this decimal by the number in question — in our case, 2000.
• The result of the multiplication gives you the answer. So, 0.0489 multiplied by 2000 equals 97.8.
• Remember, practice is essential. Work through different problems to see how percentages change the whole.

By breaking down the problem into these steps — conversion, multiplication, and calculation — you'll be able to solve percentage problems with ease. Each time, confirm your understanding and practice with real-world examples, such as financial or statistical data, to see how these calculations are used practically.