Hello, and welcome to this Mometrix video lesson on the difference between a percent increase and a percent of a whole number.
Finding a Percent
The percent of a whole number means a part of a number. To determine the percent of a number, simply multiply the whole number by the percent. When you’ve reached an answer, move your decimal point two places to the left.
It’s important to note, you will NOT label your final number as a percent.
Here’s what the formula looks like written out. Let \(P\) stand for “part of,” and let \(n\) represent a given number.
Now, let’s try a couple of examples.
Example #1
What is 40% of 30? To answer this question, let’s follow our formula.
\(P= 1,200\)
Now that we have our number, what should we do next? That’s right, we need to add our decimal point.
Our final answer is \(P = 12\).
Example #2
What is 60% of 55?
\(P= 3,300\)
Add the decimal point
Our final answer is 60% of 55 is 33.
That’s just finding the regular percent of a number.
How to Calculate Percentage Increase
The percent increase of a number is just what it sounds like. It’s finding the percentage by which a number has increased to another number.
To find the percent increase of a number, you need to subtract the original number from your new number, divide that answer by the original number and then multiply the final answer by 100. You WILL label your final answer as a percent.
Let’s look at the formula written out, that might be a little easier to understand. Let \(I\) stand for “increase,” \(N\) for “new number,” and \(O\) for “original number.”
Working through a couple of examples might help you understand.
Example #1
What is the percent increase of 78 to 110? First, let’s identify our different parts for our equation! Our original number (\(O\)) is 78. The new number (\(N\)) is 110.
\(I=\frac{32}{78}\times 100\%\)
\(I=.410\times 100\%\)
\(I=41\%\)
The percent increase from 78 to 110 is 41%.
Example #2
What is the percent increase of 17 to 72? The original number (\(O\)) is 17. The new number (\(N\)) is 72.
\(I=\frac{55}{17}\times 100\%\)
\(I=3.23\times 100\%\)
\(I= 323\%\)
The percent increase from 17 to 72 is 323%.
Thank you for joining us on learning the differences between percent increase and percent of a whole number. Happy studying!
Practice Questions
What is 60% of 30?
60% of 30 can be calculated using the formula \(P=n(\%)\), where \(P\) represents “part of” and \(n\) represents the “given number.”
60% as a decimal is 0.60. The formula becomes \(P=30\times0.60\), which simplifies to 18. Therefore, 18 is 60% of 30.
What is 24% of 55?
24% of 55 can be calculated using the formula \(P=n(\%)\), where \(P\) represents “part of” and \(n\) represents the “given number.”
24% is equal to 0.24. Therefore, the formula becomes \(P=55\times0.24\), which simplifies to 13.2. Therefore, 13.2 is 24% of 50.
What is 12% of 400?
12% of 400 can be calculated using the formula \(P=n(\%)\), where \(P\) represents “part of” and \(n\) represents the “given number.”
12% is equal to 0.12 as a decimal, so the formula becomes \(P=400\times0.12\), which simplifies to 48. Therefore, 48 is 12% of 400.
What is the percent increase from 12 to 50?
The percent increase from 12 to 50 can be calculated using the formula:
\(I=\dfrac{N-O}{O}\times100\%\)
Here, \(I\) represents “increase,” \(N\) represents “new number,” and \(O\) represents “original number.”
The formula becomes:
\(I=\dfrac{50-12}{12}\times100\%\)
\(I=\dfrac{38}{12}\times100\%\)
The fraction \(\frac{38}{12}\) equals approximately 3.167. Multiply this by 100% to get 316.7%.
What is the percent increase from 25 to 90?
The percent increase from 25 to 90 can be calculated using the formula:
\(I=\dfrac{N-O}{O}\times100\%\)
Here, \(I\) represents “increase,” \(N\) represents “new number,” and \(O\) represents “original number.”
The formula becomes:
\(I=\dfrac{90-25}{25}\times100\%\)
\(I=\dfrac{65}{25}\times100\%\)
The fraction \(\frac{65}{25}\) equals 2.6. Multiply this by 100% to get 260%.
Kaya wants to buy a pair of jeans that are $28 and have been marked down 20%. How much money will Kaya save on the jeans?
To find the amount Kaya will save, we will multiply the price of the jeans by the marked down percentage. Convert the percentage to a decimal first by moving the decimal point two places to the left.
\(28 \times 0.20 = 5.60\)
Bruce pays $600 per month for rent. His landlord informs him that his rent will increase by 15% at the end of the month. How much will Bruce’s rent increase, in dollars, by the end of the month?
Since Bruce pays $600 for rent and the increase is 15%, we multiply 600 by 15. First convert the percentage to a decimal by moving the decimal point over two places to the left.
\(600 \times 0.15 = 90\)
Sophia’s gym membership increased from $83 to $102 per month. What is the percent increase for Sophia’s gym membership?
We will use the formula to calculate the percent increase, which is to take the difference between the new price and the old price, divide it by the old price then multiply by 100, since we are looking for the percent increase.
In this case, the difference between the new membership and old membership fee is 19. Divide that by 83 and multiply by 100 to get 22.89.
Zola buys a house for $230,000 in 2027. The value of her house increases by 45% after five years. What is the value of Zola’s house in 2032?
Since we know the old price of the house and the percent increase, we will substitute all the values we know into the formula for calculating percent increase. We will use the variable \(n\) to represent the new value of the house in 2032.
\(\dfrac{n-230{,}000}{230{,}000} \cdot 100=45\)
We will solve for \(n\) by dividing both sides by 100, eliminating the fraction, and then isolating the variable. The value of \(n\) is 333,500. Therefore, the value of Zola’s house in 2032 is $333,500.
A city’s population grows from 96,200 to 99,400 in ten years. How much did the city’s population grow, in percent, over the ten-year period?
The percent increase formula takes the difference between the new and old values, divides it by the old value, and then multiplies it by 100 to get the percent increase. The difference between the new and old city population is 3,200, divided by 96,200, then multiplied by 100, which is 3.32640
Therefore, the city’s population grew by 3.3% in ten years.
