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Chapter 7: Problem 36

9 is what percent of 15?

Short Answer

Expert verified
9 is 60% of 15.

Step by step solution

01

Understand the Formula

To find what percent one number is of another, use the formula \( \text{percent} = \left( \frac{\text{part}}{\text{whole}} \right) \times 100 \). Here, 9 is the 'part' and 15 is the 'whole'.
02

Substitute the Numbers

Plug in the numbers into the formula: \( \text{percent} = \left( \frac{9}{15} \right) \times 100 \).
03

Calculate the Fraction

First, calculate the fraction \( \frac{9}{15} \). Simplify it to get \( \frac{3}{5} \).
04

Convert Fraction to Decimal

Convert the simplified fraction \( \frac{3}{5} \) to a decimal by dividing 3 by 5 to get 0.6.
05

Convert Decimal to Percent

Multiply the decimal 0.6 by 100 to convert it to a percentage. Therefore, \( 0.6 \times 100 = 60 \).

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Key Concepts

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

Fraction Simplification
When working with fractions, simplification is a critical skill. This means you reduce the fraction to its simplest form. A fraction is simplified by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it.
Take the fraction \( \frac{9}{15} \) as an example. Both 9 and 15 can be divided by 3, which is their GCD. When you divide both by 3, you get \( \frac{3}{5} \). Now, \( \frac{3}{5} \) is in its simplest form since 3 and 5 share no common divisor other than 1.
Simplifying fractions
  • Makes them easier to work with.
  • Helps in further calculations like converting to decimals or percentages.
  • Aids in comparing fractions more conveniently.
Converting Fractions to Decimals
Converting fractions to decimals is a straightforward process. You simply need to divide the numerator by the denominator. This can be done using long division or a calculator.
For instance, to convert \( \frac{3}{5} \) to a decimal, divide 3 by 5. You will get 0.6 as the decimal representation of the fraction.
Why convert fractions to decimals?
  • Decimals are often easier to understand in everyday situations.
  • They make some calculations simpler, like adding and subtracting.
  • Decimals help compare values more intuitively, especially when dealing with percentages.
Converting Decimals to Percentages
The transition from decimals to percentages is a simple operation that involves moving two decimal places to the right or, equivalently, multiplying the decimal by 100. This conversion helps in expressing numbers in a way that's easy to comprehend, especially in financial and statistical terms.
Using our decimal 0.6 from the previous example:
  • To convert 0.6 to a percentage, multiply by 100: \( 0.6 \times 100 = 60 \).
  • This tells us that 9 is 60 percent of 15, making it easy to interpret and compare.
Why use percentages?
  • They are a common way to express parts of a whole.
  • Percentages simplify comparisons across different contexts because they standardize values for easy interpretation.
  • Understanding percentages is crucial in various real-life situations, from grades to financial interest rates.

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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.

The loss of Arctic sea ice will allow for an underwater fiber optic cable that will cut the time it takes to send a message from London to Tokyo from a current 140 milliseconds down to 88 milliseconds. Associated PressTimes- Standard 01/22/10 Global warming opens up Northwest Passage for underwater fiber optic cable. a) What is the estimated percent decrease in communication time? b) At a cost of \(\$ 1.2\) billion, what is the cost per millisecond of saving (rounded to the nearest dollar)?

A bartender is granted a \(4.6 \%\) salary increase. If the bartender's current salary is $$\$ 2,500$$ per month, find the bartender's new monthly salary, rounded to the nearest dollar.

In an election for class president, Kamili received \(21 \%\) of the votes, Bernardo received \(22 \%\), Fernando received \(30 \%\) of the votes, and \(27 \%\) 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 Kamili'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?
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