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Chapter 7: Problem 68

Convert the given fraction to a percent. $$ \frac{13}{2} $$

Short Answer

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650%

Step by step solution

01

Understand Percentage Conversion

Converting a fraction to a percentage involves finding an equivalent number out of 100. The basic idea is to multiply the fraction by 100 to convert it to a percentage.
02

Multiply the Fraction by 100

Take the fraction \( \frac{13}{2} \) and multiply it by 100 to convert it to a percentage: \( \frac{13}{2} \times 100 \).
03

Perform the Multiplication

Simplify the expression by multiplying the numbers: \( \frac{13 \times 100}{2} = \frac{1300}{2} \).
04

Divide to Simplify

Complete the division: \( \frac{1300}{2} = 650 \).
05

Obtain the Final Percentage

The result of the division is the percentage: \( 650\% \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Fraction to Percentage
Converting a fraction to a percentage involves a simple yet essential math process. It's all about transforming a particular fraction into a number expressed out of 100. This evaluation helps in understanding how a part relates to the whole on a standardized scale.
For example, if you have the fraction \( \frac{13}{2} \), you might be wondering how this measures up in terms of percentage.
  • Start by considering what percentage stands for - a fraction of 100.
  • The process involves multiplying the fraction by 100.
This will allow you to directly compare the fraction to the standardized 100 percent scale. It's like adjusting the lens on a camera to get a clearer picture of parts per hundred.
Percentage Calculation
Once you're set to convert a fraction into a percentage, you'll need to perform what we call a percentage calculation. This involves a few easy arithmetic operations.
First, take your fraction; in our case, it is \( \frac{13}{2} \).
  • Next, multiply it by 100 to shift the scale from fractions to percentages.
  • This step transforms the calculation as follows: \( \frac{13}{2} \times 100 \).
This makes the fraction look like a number per every hundred units, directly showing its percentage. At this point, you perform the arithmetic operation needed to simplify and solve the equation.
Multiplying Fractions
When multiplying fractions, you multiply the numerators together and the denominators together. Yet, in cases such as our example, we're multiplying by a whole number, so there's just slightly more to consider.
Here鈥檚 how you handle it:
  • The multiplication goes as: \( 13 \times 100 = 1300 \).
  • Then, divide the result by the original fraction's denominator, making it: \( \frac{1300}{2} \).
This solves the ongoing multiplication process and leads us directly into simplifying the equation. Ultimately, you get a clean, understandable result as a percentage. It simplifies the problem and concludes the conversion process neatly.

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