Percentages are an integral part of our daily lives, woven into the fabric of our financial decisions, academic pursuits, and even casual conversations. Understanding percentages empowers us to decipher discounts, calculate tips, and analyze data effectively. One common scenario where percentages come into play is when we encounter questions like “36 is 30 percent of what number?” This seemingly simple question unlocks a fundamental concept in mathematics: proportions.
Solving this type of problem not only strengthens our mathematical skills but also equips us with a valuable tool for real-world problem-solving. Whether we’re figuring out the original price of an item after a discount or determining the total amount earned from a percentage-based bonus, grasping the concept of proportions is essential.
In this comprehensive guide, we’ll delve into the world of percentages, explore the concept of proportions, and walk you through the step-by-step process of solving the problem “36 is 30 percent of what number?” We’ll also touch upon related concepts and real-world applications to solidify your understanding.
Understanding Percentages
A percentage is a fraction out of one hundred. The symbol “%” represents “out of one hundred.” For example, 50% means 50 out of every 100, which can be expressed as the fraction 50/100 or the decimal 0.50. Percentages are widely used to express proportions, ratios, and parts of a whole.
Calculating Percentages
To calculate a percentage of a number, follow these steps:
- Convert the percentage to a decimal by dividing it by 100.
- Multiply the decimal by the number.
For instance, to find 25% of 80:
- 25% divided by 100 = 0.25
- 0.25 multiplied by 80 = 20
Therefore, 25% of 80 is 20.
The Concept of Proportions
A proportion is a statement that two ratios are equal. It can be written in several ways, including:
- a/b = c/d
- a : b = c : d
In the context of percentages, a proportion can be used to express a relationship between a part and a whole. For example, if 36 is 30% of a certain number, we can set up a proportion:
36 / x = 30 / 100 (See Also: How Does Stone Measurement Work? Unveiled)
where ‘x’ represents the unknown number.
Solving the Problem: 36 is 30 Percent of What Number?
Now that we understand the concept of proportions, let’s solve the problem step-by-step:
Setting up the Proportion
As mentioned earlier, we can express the relationship between 36, 30%, and the unknown number ‘x’ as a proportion:
36 / x = 30 / 100
Cross-Multiplication
To solve for ‘x’, we can use cross-multiplication. This involves multiplying the numerator of the first fraction by the denominator of the second fraction, and vice versa:
36 * 100 = 30 * x
Simplifying the Equation
Perform the multiplication on both sides of the equation:
3600 = 30x
Isolating ‘x’
To isolate ‘x’, divide both sides of the equation by 30:
3600 / 30 = x (See Also: How Much Does a Sun Room Addition Cost? Unveiled)
Solution
Simplify the expression to find the value of ‘x’:
120 = x
Therefore, 36 is 30 percent of 120.
Real-World Applications of Percentages and Proportions
Percentages and proportions are ubiquitous in our daily lives. Here are a few examples:
Sales and Discounts
When shopping, we often encounter sales and discounts expressed as percentages. For example, a 20% discount on a $50 item means we save 20% of $50, which is $10. The final price would be $40.
Tip Calculation
In restaurants, we typically calculate tips as a percentage of the bill amount. A 15% tip on a $50 bill would be $7.50.
Interest Rates
Interest rates on loans and savings accounts are expressed as percentages. A 5% interest rate on a $1000 loan means we would pay $50 in interest over a year.
Population Growth
Population growth rates are often expressed as percentages. A 2% annual population growth rate means the population increases by 2% each year.
Conclusion
Understanding percentages and proportions is essential for navigating the complexities of our world. From everyday transactions to complex financial calculations, these concepts empower us to make informed decisions and analyze data effectively. The problem “36 is 30 percent of what number?” serves as a stepping stone to mastering these fundamental mathematical tools. By grasping the relationship between parts and wholes, we unlock a deeper understanding of the world around us. (See Also: How Is Boolean Algebra Used in Computers? Unlocking Digital Secrets)
Throughout this guide, we’ve explored the definition of percentages, the concept of proportions, and the step-by-step process of solving the given problem. We’ve also highlighted real-world applications of percentages and proportions, demonstrating their relevance in various aspects of life. By mastering these concepts, we equip ourselves with a valuable toolkit for success in both academic and professional pursuits.
FAQs
What is a percentage?
A percentage is a fraction out of one hundred. It is represented by the symbol “%” and is used to express proportions, ratios, and parts of a whole.
How do you calculate a percentage of a number?
To calculate a percentage of a number, convert the percentage to a decimal by dividing it by 100, and then multiply the decimal by the number.
What is a proportion?
A proportion is a statement that two ratios are equal. It can be written in several ways, including a/b = c/d or a : b = c : d.
How do you solve a proportion?
To solve a proportion, you can use cross-multiplication. This involves multiplying the numerator of the first fraction by the denominator of the second fraction, and vice versa. Then, solve for the unknown variable.
What is the difference between a percentage and a proportion?
A percentage is a specific type of proportion where one of the ratios is out of one hundred. A proportion is a more general term that encompasses any two equal ratios.