Problem 47 - Algebra 1: Concepts and Skills

Question

Evaluate. $$ \frac{1}{2} \% \text { of } 200 $$

Step-by-Step Solution

Answer

The answer is 1.

Step 1: Convert the percentage to a decimal

To convert a percentage into a decimal, divide the percentage by 100. Here, we have \( \frac{1}{2} \% \), so we divide \( \frac{1}{2} \) by 100 to get \( \frac{1}{2} \times \frac{1}{100} = \frac{1}{200} \).

Step 2: Find the required percentage of the number

Multiply the number 200 by the decimal obtained in step 1. That is, \(\frac{1}{200} \times 200 = 1 \).

Key Concepts

Convert Percentage to Decimal

Understanding how to convert percentages to decimals is a key skill in mathematics. When you see a number with a '%' sign, it represents a fraction out of 100. To convert it into a decimal format, you divide by 100.
For instance, if you have a percentage like \( \frac{1}{2}\% \), you first think of it as the fraction \( \frac{1}{2} \). Then, to turn it into a decimal, you perform the division: \( \frac{1}{2} \div 100 \).
This can also be rewritten using multiplication with fractions: \( \frac{1}{2} \times \frac{1}{100} \). When you multiply these, you get \( \frac{1}{200} \). This result is your decimal version of the percentage.
Converting percentages to decimals simplifies many other calculations in math, like finding parts of a whole.

Multiplication of Fractions

Multiplying fractions might seem tricky at first, but it's pretty straightforward once you get the hang of it. The key thing to remember is that you multiply the numerators (top numbers) together and then the denominators (bottom numbers) together.
For the fraction \( \frac{1}{2} \times \frac{1}{100} \), you multiply as follows:

• Numerator: \( 1 \times 1 = 1 \)
• Denominator: \( 2 \times 100 = 200 \)

This gives you \( \frac{1}{200} \) as the product of the fractions. Keeping track of your numerators and denominators separately helps you stay organized.
Practice with different fractions, and you'll become more comfortable with the process over time.

Mathematical Operations

Mathematical operations include addition, subtraction, multiplication, and division. When dealing with percentages, multiplication plays a key role in determining parts of a whole, especially when you convert percentages to decimals.
In our example, once we have a decimal (\(\frac{1}{200}\)), we multiply it by the number you want to evaluate against—in this case, 200. So, the operation \( \frac{1}{200} \times 200 \) simplifies the decimal with the whole number.
The goal of these operations is to find just how much of something you have or need. Here, the result is 1, meaning \(\frac{1}{2}\%\) of 200 is indeed just 1.
Mastering these operations allows you to tackle a wide range of problems effortlessly. It's all about breaking down the problem and applying the right operation.