Question

Perform the indicated operations. \(\frac{1}{2}\) is what percentage of \(60 ?\)

Short answer

\( \frac{1}{2} \) is approximately \( 0.83\% \) of \( 60 \).

Step-by-step solution

Understand the Problem

The question asks us to find out what percentage \( \frac{1}{2} \) is of \( 60 \). This means we need to figure out how much \( \frac{1}{2} \) is out of \( 60 \) in terms of percentage.

Convert the Fraction to a Number

First, we need to convert \( \frac{1}{2} \) into a decimal or a number. We know that \( \frac{1}{2} = 0.5 \).

Calculate the Percentage

To find out what percentage \( 0.5 \) is of \( 60 \), use the formula: \[ \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \] Here, the part is \( 0.5 \) and the whole is \( 60 \).

Substitute Values and Solve

Substitute the given values into the percentage formula: \[ \text{Percentage} = \left( \frac{0.5}{60} \right) \times 100 \] Now, calculate the value: \[ \text{Percentage} = \left( \frac{1}{120} \right) \times 100 = \frac{100}{120} = 0.8333\ldots \] This decimal can be approximated as \( 0.83 \).

Convert Decimal to Percentage

The decimal \( 0.0083 \) corresponds to \( 0.83 \% \). Therefore, \( \frac{1}{2} \) is approximately \( 0.83 \% \) of \( 60 \).

Key concepts

Understanding Fractions

Fractions are a way to express parts of a whole. In a fraction, the top number is called the numerator, and the bottom number is the denominator. For instance, in the fraction \( \frac{1}{2} \), 1 is the numerator, representing the part we have, and 2 is the denominator, indicating how many equal parts make up the whole. When you're asked to find what percentage a fraction is of a number like 60, you're essentially determining how big the fraction is compared to that number. It's all about balancing and comparing these parts to a new whole. The next step after grasping the concept of fractions is usually to convert them into a format that's easier to work with, like decimals, especially when talking about percentages.

Converting Fractions to Decimals

Converting a fraction to a decimal makes it easier to perform calculations like percentage operations. To convert a fraction, divide the numerator by the denominator. Take \( \frac{1}{2} \) as an example. Here, you simply divide 1 by 2, which equals 0.5.Decimals simplify many mathematical operations because they eliminate the need for handling multiple parts like in fractions. Plus, decimals are more directly related to percentages since 100% = 1.0 in decimal form. So, when you convert \( \frac{1}{2} \) to 0.5, you're laying the groundwork to uncover what percentage it represents of another whole number, like 60.

Performing Mathematical Operations

Mathematical operations are the processes we perform in math to find answers, like addition, subtraction, multiplication, and division. In our example, the operation needed is division to find out what percentage a decimal (0.5) is of another number (60).We use the formula to find percentages: \[ \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \] Here's how it works in this context:

• "Part" is your decimal, 0.5.
• "Whole" is the number you compare it to, which is 60 in this problem.

You substitute these values into the formula to get:\[ \text{Percentage} = \left( \frac{0.5}{60} \right) \times 100 \] Carrying out the math gives:\[ \text{Percentage} = \left( \frac{1}{120} \right) \times 100 = 0.83\ldots \] This means \( \frac{1}{2} \) represents an approximate 0.83% of 60.Understanding these operations helps you navigate through basic math problems efficiently.