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Chapter 7: Problem 15

Convert the given percent to a fraction, and simplify the result. $$ 130 \% $$

Short Answer

Expert verified
130% as a simplified fraction is \(\frac{13}{10}\).

Step by step solution

01

Convert Percent to Fraction

To convert a percentage to a fraction, divide the percentage by 100. Therefore, \(130\%\) can be written as \(\frac{130}{100}\).
02

Simplify the Fraction

Now, simplify \(\frac{130}{100}\). Find the greatest common divisor (GCD) of 130 and 100. The GCD of 130 and 100 is 10. Divide both the numerator and the denominator by 10.\[\frac{130 \div 10}{100 \div 10} = \frac{13}{10}\]
03

Write the Final Fraction

The simplified form of \(\frac{130}{100}\) is \(\frac{13}{10}\). Thus, 130% as a simplified fraction is \(\frac{13}{10}\).

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Key Concepts

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

Simplifying Fractions
When you start converting percentages into fractions, you'll often need to simplify the fraction to its smallest possible form. Simplifying fractions makes them easier to interpret and use in further calculations. A fraction is simplified when the numerator and the denominator have no common factors other than 1. To simplify a fraction:
  • Find the greatest common divisor (GCD) of the numerator and the denominator.
  • Divide both the numerator and the denominator by this GCD.
For example, in the conversion of 130% to a fraction, \(\frac{130}{100}\), simplification involves dividing both 130 and 100 by their GCD, which is 10. This results in the simplified fraction \(\frac{13}{10}\). By simplifying, the fraction becomes much more manageable for further operations.
Greatest Common Divisor (GCD)
The greatest common divisor (GCD) is a critical concept in simplifying fractions. It represents the largest number that can evenly divide both the numerator and the denominator of a fraction. Finding the GCD is essential for reducing fractions to their simplest form. To find the GCD of two numbers, employ these steps:
  • List the factors of each number.
  • Identify the largest factor that appears in both lists.
For instance, when simplifying the fraction \(\frac{130}{100}\), you look for the GCD of 130 and 100:
  • Factors of 130: 1, 2, 5, 10, 13, 26, 65, 130
  • Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
The GCD is 10, which is the largest factor common to both lists. By dividing 130 and 100 by 10, you achieve the simplified fraction \(\frac{13}{10}\). Understanding and finding the GCD is integral to mastering fraction simplification.
Percentages
Percentages are an everyday part of mathematics, representing a fraction with a denominator of 100. When you see a percentage, such as 130%, it tells you how many parts out of 100 a particular quantity represents. To convert percentages to fractions:
  • Write the percentage as a fraction with 100 as the denominator. For example, 130% is \(\frac{130}{100}\).
  • Simplify the fraction if necessary. This is where your understanding of the greatest common divisor (GCD) comes into play.
Remember, percentages can be greater than 100, just like in this example where 130% represents \(\frac{13}{10}\) after simplification. This fraction shows there are 13 parts out of a baseline of 10, indicating a value greater than the whole, which is common in various real-world contexts.

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Most popular questions from this chapter

In an election for class president, the vote distribution among three candidates is shown in the following table. $$ \begin{array}{c|c} \text { Candidate } & \text { Votes } \\ \hline \text { Hue } & 48 \\ \text { Lisa } & 48 \\ \text { Akbar } & 47 \end{array} $$ Use a protractor to help create a pie chart showing the distribution of votes.

A business owner borrows $2,400 for 4 months at a 8.25% per year simple interest rate. At the end of the 4-month loan period, how much interest is owed?

In an election for class president, Juanita received \(30 \%\) of the votes, Ali received \(24 \%\), Estevan received \(24 \%\) of the votes, and \(22 \%\) of the votes were received by other candidates. If a pie chart is created for this data, what will be the degree measure of the central angle of the sector representing Juanita's share of the vote? Round your answer to the nearest degree.

A business owner borrows $3,600 for 3 months at a 8% per year simple interest rate. At the end of the 3-month loan period, how much interest is owed?

A business owner takes out a 6-month loan at a 2% per year simple interest rate. At the end of the 6-month loan period, the interest owed is $40. What was the principal amount borrowed?
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