How to Find a Percentage of a Number: A Step-by-Step Guide and Real-Life Examples

I. Introduction

Whether in school, at work, or in our daily lives, knowing how to calculate percentages is essential. It allows us to make informed decisions, compare prices, track changes, and solve problems. In this article, we’ll explore three methods for finding a percentage of a number: multiplying by the percentage, dividing by the decimal equivalent, and using a calculator. We’ll also look at real-life examples of calculating percentages, such as sales tax and stock prices, and discuss some common mistakes or misconceptions. Finally, we’ll provide practice problems and exercises to help you apply what you’ve learned.

II. Step-by-Step Guide to Finding Percentages

A. Multiplying by the Percentage

This method involves multiplying the number by the percentage in decimal form (i.e., 50% = 0.5). Here’s an example:

What is 25% of 80?

To solve this problem, we can use the formula:

Percentage x Number = Result

In this case, we have:

25% x 80 = Result

To get the decimal equivalent of 25%, we divide it by 100:

25 ÷ 100 = 0.25

Now we can substitute and solve:

0.25 x 80 = 20

Therefore, 25% of 80 is 20.

Here’s a visual aid to help you remember:

B. Dividing by the Decimal Equivalent

This method involves dividing the number by the decimal equivalent of the percentage (i.e., 25% = 0.25). Here’s an example:

What is 40% of 125?

To use this method, we can use the formula:

Number ÷ Decimal Equivalent = Result

In this case, we have to find the decimal equivalent of 40%:

40 ÷ 100 = 0.4

Now we can substitute and solve:

125 ÷ 0.4 = 312.5

Therefore, 40% of 125 is 312.5.

Here’s a visual aid to help you remember:

C. Using a Calculator

This method is the easiest and most convenient, especially for larger or more complex problems. Most calculators have a percentage button (%) that simplifies the process. Here’s an example:

What is 75% of 240?

To use this method, we can simply enter the following on our calculator:

240 x 75% = Result

The calculator will automatically convert 75% to 0.75 and multiply it by 240:

240 x 0.75 = 180

Therefore, 75% of 240 is 180.

Here’s a visual aid to help you:

III. Real-Life Examples of Calculating Percentages

A. Sales Tax

One common example of calculating percentages is sales tax. Sales tax is a percentage of the cost of a product or service that is added to the total amount. The percentage varies depending on the state or country. Here’s an example:

You buy a book for $20 and the sales tax is 7%. How much do you pay in total?

To solve this problem, we can use the multiplying method:

7% x $20 = Result

First, we convert 7% to 0.07:

7 ÷ 100 = 0.07

Then we can multiply:

0.07 x $20 = $1.40

This means that the sales tax is $1.40. To find the total amount, we add the cost of the book and the sales tax:

$20 + $1.40 = $21.40

Therefore, the total amount you pay is $21.40.

Here’s an example of a receipt or invoice showing the breakdown:

B. Stock Price

Another example of calculating percentages is stock prices. Investors use percentages to track the increase or decrease in the value of a stock over time. The percentage represents the difference between the current price and the previous price. Here’s an example:

The price of a stock is $50 per share. Yesterday it was $40 per share. What is the percentage increase?

To solve this problem, we can use the dividing method:

(Price Now – Price Before) ÷ Price Before x 100 = Result

First, we subtract the previous price from the current price:

$50 – $40 = $10

Then we divide the difference by the previous price:

$10 ÷ $40 = 0.25

Finally, we multiply by 100 to get the percentage:

0.25 x 100 = 25%

This means that the stock price increased by 25%. Here’s a visual aid to help you understand:

IV. Different Scenarios Where Calculating Percentages is Important

A. Calculating Grades

Grades are often calculated using percentages, especially in school or university. The percentage represents the proportion of correct answers or tasks completed out of the total. Here’s an example:

Your final grade in a course is based on three exams, each worth 30%, 35%, and 35%. You got 90%, 85%, and 95% on each exam respectively. What is your final grade?

To solve this problem, we can use the following formula:

Exam Grade x Exam Weight = Exam Score

Then we can add up the exam scores and divide by the total weight to get the final grade:

((90% x 30%) + (85% x 35%) + (95% x 35%)) ÷ (30% + 35% + 35%) x 100% = Result

First, we multiply each exam grade by its weight:

(90% x 30%) = 27%

(85% x 35%) = 29.75%

(95% x 35%) = 33.25%

Then we add them up:

27% + 29.75% + 33.25% = 90%

Finally, we divide by the total weight (100%) and multiply by 100:

90% ÷ 100% x 100% = 90%

Therefore, your final grade is 90%. Here’s an example of a grading scale:

B. Wind Chill Factor

Wind chill factor is a measure of how cold it feels outside based on the combination of temperature and wind speed. The lower the temperature and the higher the wind speed, the lower the wind chill factor. Here’s an example:

The temperature is -5°C and the wind speed is 10 km/h. What is the wind chill factor?

To solve this problem, we can use a formula that takes into account the temperature and the wind speed:

13.12 + 0.6215T – 11.37V^(0.16) + 0.3965TV^(0.16) = Result

Where T is the temperature in Celsius and V is the wind speed in kilometers per hour.

First, we substitute the values:

13.12 + 0.6215(-5) – 11.37(10)^(0.16) + 0.3965(-5)(10)^(0.16) = Result

Then we solve using a scientific calculator or an online wind chill calculator:

-16.15°C

Therefore, the wind chill factor is -16.15°C.

Here’s a visual aid to help you:

V. Common Mistakes or Misconceptions

A. Forgetting to Divide by 100

One common mistake when calculating percentages is forgetting to divide by 100 to get the decimal form. This can lead to incorrect results or confusion. Here’s an example:

What is 15% of 200?

An incorrect way to solve it would be:

15 x 200 = 3000

However, 15 should be converted to 0.15 before multiplying:

0.15 x 200 = 30

Therefore, 15% of 200 is 30.

Here’s an example to illustrate the mistake:

B. Confusing Percentages and Decimals

Another common mistake when dealing with percentages is confusing them with decimals. While percentages are expressed as parts per hundred (i.e., 50% = 50/100 = 0.5), decimals are just fractions of a whole number (i.e., 0.5 = 1/2 = 50%). Here’s an example:

What is 60% of 80?

An incorrect way to solve it would be:

0.6 x 80 = 48

However, 60% should be converted to 0.6 first, and the result should be expressed as a percentage:

0.6 x 100% = 60%

60% of 80 = 48

Therefore, 60% of 80 is 48.

Here’s an example to illustrate the mistake:

VI. Practice Problems and Exercises

Here are 5 practice problems for you to try on your own:

1. What is 20% of 500?
2. What is 75% of 200?
3. What is the percentage increase from $80 to $100?
4. If a shirt costs $25 before tax and the sales tax rate is 8%, how much do you pay in total?
5. You got 85%, 90%, and 80% on three quizzes in a course where each quiz is worth 25%. What is your average quiz grade?

When you’re ready, check your answers with the answer key:

• 100
• 150
• 25%
• $27.00
• 83.75%

VII. Conclusion

In this article, we’ve covered three methods for finding a percentage of a number: multiplying by the percentage, dividing by the decimal equivalent, and using a calculator. We’ve also looked at real-life examples of calculating percentages, such as sales tax and stock prices, and discussed some common mistakes or misconceptions. Remember to double-check your calculations, convert percentages to decimals, and practice with the included exercises. Calculating percentages may seem daunting at first, but with a little practice, you’ll be able to master it and use it in various situations.