In the realm of mathematics, percentages often serve as a fundamental tool for understanding proportions and relationships. The concept of “percent” signifies a fraction out of one hundred, allowing us to express parts of a whole in a standardized way. From calculating discounts and interest rates to determining the composition of mixtures, percentages permeate various aspects of our daily lives. One common scenario involves determining what number a given percentage represents. For instance, “12 is 15 percent of what number?” This seemingly simple question unveils a deeper understanding of how percentages work and their practical applications.
Understanding this concept not only enhances our mathematical literacy but also equips us with the ability to solve real-world problems involving proportions. Whether you’re analyzing financial data, comparing product prices, or simply trying to figure out the size of a discount, knowing how to calculate percentages is an invaluable skill.
Understanding Percentages
Before delving into the specific problem of finding the number represented by 12 as 15 percent, it’s crucial to establish a firm grasp of the concept of percentages. A percentage is essentially a fraction with a denominator of 100. The symbol “%” signifies “out of one hundred.” Therefore, 15 percent can be expressed as 15/100, which simplifies to 0.15 as a decimal.
Calculating Percentages
To calculate a percentage of a number, we can follow these steps:
1.
Convert the percentage to a decimal by dividing it by 100. In this case, 15 percent becomes 15/100 = 0.15.
2.
Multiply the decimal by the number. For example, to find 15 percent of 80, we would multiply 0.15 by 80, resulting in 12.
Representing Percentages
Percentages can be represented in various forms, including fractions, decimals, and words. Understanding these different representations is essential for working with percentages effectively.
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Fractions: A percentage is a fraction with a denominator of 100. For instance, 75 percent is equivalent to the fraction 75/100, which can be simplified to 3/4.
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Decimals: To convert a percentage to a decimal, divide it by 100. For example, 20 percent is equal to 20/100 = 0.20.
* (See Also: Difference Between Algebra 2 and Precalculus? Unlocking Math Secrets)
Words: Percentages can also be expressed in words, such as “twenty-five percent” or “one hundred percent.”
Solving the Problem: 12 is 15 Percent of What Number?
Now that we have a solid understanding of percentages, let’s tackle the specific problem: “12 is 15 percent of what number?” To solve this, we can use the concept of proportions. A proportion states that two ratios are equal. In this case, we can set up a proportion where 12 is to the unknown number as 15 percent is to 100 percent.
Setting Up the Proportion
We can represent this proportion mathematically as follows:
12 / x = 15 / 100
where “x” represents the unknown number.
Solving for x
To solve for “x,” we can use cross-multiplication:
12 * 100 = 15 * x
1200 = 15x
Divide both sides by 15 to isolate “x”:
x = 1200 / 15
x = 80
Therefore, 12 is 15 percent of 80. (See Also: How Is Percent Chance of Rain Calculated? Inside The Forecast)
Applications of Percentages
Understanding percentages has numerous applications in various fields and aspects of daily life. Here are a few examples:
Finance
Percentages are widely used in finance for calculating interest rates, discounts, and taxes. For example, a bank might offer a loan with an annual interest rate of 5 percent, meaning that borrowers will pay an additional 5 percent of the loan amount each year.
Shopping
When shopping, percentages are essential for understanding discounts and sales. A “20 percent off” sale means that the price of an item is reduced by 20 percent of its original price.
Statistics
In statistics, percentages are used to express proportions and frequencies. For instance, a survey might report that 75 percent of respondents support a particular policy.
Science
Percentages are used in science to express concentrations and ratios. For example, a solution might be 10 percent saline, meaning that it contains 10 grams of salt per 100 grams of solution.
Recap
In conclusion, understanding percentages is a fundamental mathematical skill with wide-ranging applications. We explored the concept of percentages, their representations, and how to calculate them. We also solved the specific problem of finding the number represented by 12 as 15 percent. By grasping the principles of percentages, we can effectively analyze data, make informed decisions, and navigate the complexities of our world.
Key takeaways from this discussion include:
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Percentages represent fractions out of one hundred.
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Percentages can be expressed as fractions, decimals, or words.
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To calculate a percentage of a number, convert the percentage to a decimal and multiply it by the number. (See Also: 50 To 62 Is What Percent Increase? Find Out)
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Proportions can be used to solve problems involving percentages.
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Percentages have numerous applications in finance, shopping, statistics, and science.
FAQs
What is 15 percent of 12?
15 percent of 12 is 1.8.
How do you calculate 15 percent?
To calculate 15 percent, divide 15 by 100, which equals 0.15. Then multiply that decimal by the number you want to find the percentage of.
What is a percentage?
A percentage is a way of representing a part of a whole as a fraction of 100. The symbol “%” means “out of one hundred.”
How do you find what number a percentage is of?
To find what number a percentage is of, you can use proportions. Set up a proportion where the percentage is equal to the part over the whole. Solve for the unknown whole number.
What are some real-world examples of percentages?
Real-world examples of percentages include sales tax, interest rates, discounts, and election results.