# Percent Increase vs. Percent of Whole

Hello, and welcome to this Mometrix video lesson on the difference between a percent increase and a percent of a whole number.

**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.

P=n(%)

**Now, let’s try a couple of examples.**

What is 40% of 30? To answer this question, let’s follow our formula.

P= 30(40)

P= 1200 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. 40% of 30 is 12

What is 60% of 55?

P= 55(60)

P= 3,300

Add the decimal point

P= 33. 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.

I=[[(N-O)/O](100%)]

Working through a couple of examples might help you understand.

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=[[(110-78)/78](100%)]

I=[(32/78)(100%)]

I=(.410)(100%)

I=41%

The percent increase from 78 to 110 is 41%.

What is the percent increase of 17 to 72? The Original number (O) is 17. The New number (N) is 72.

I=[[(72-17)/17](100%)]

I=[(55/17)(100%)]

I=(3.23)(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. Be sure to “like” this video and “subscribe” to our channel for more help with your math problems. Happy studying!

## Practice Questions

**Question #1:**

What is 60% of 30?

**Answer:**

\(60\%\) of \(30\) can be calculated using the formula \(P=n(\%)\). \(P\) 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 \(18\). \(18\) is \(60\%\) of \(30\).

**Question #2:**

What is 24% of 55?

**Answer:**

\(24\%\) of \(55\) can be calculated using the formula \(P=n(\%)\). \(P\) 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 \(13.2\). \(13.2\) is \(24\%\) of \(50\).

**Question #3:**

What is 12% of 400?

**Answer:**

\(12\%\) of \(400\) can be calculated using the formula \(P=n(\%)\). \(P\) 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 \(48\). \(48\) is \(12\%\) of \(400\).

**Question #4:**

What is the percent increase from 12 to 50?

**Answer:**

The percent increase from \(12\) to \(50\) can be calculated using the formula:

\(I=\frac{N-O}{O}\times100\%\)

\(I\) represents “increase”, \(N\) represents “new number”, and \(O\) represents “original number”.

The formula becomes \(I=\frac{50-12}{12}\times100\%\), which simplifies to \(I=\frac{38}{12}\times100\%\). \(\frac{38}{12}\) equals approximately \(3.167\). Multiply this by \(100\%\) to get \(316.7\%\).

The percent increase from \(12\) to \(50\) is \(316.7\%\).

**Question #5:**

What is the percent increase from 25 to 90?

**Answer:**

The percent increase from \(25\) to \(90\) can be calculated using the formula:

\(I=\frac{N-O}{O}\times100\%\)

\(I\) represents “increase”, \(N\) represents “new number”, and \(O\) represents “original number”.

The formula becomes \(I=\frac{90-25}{25}\times100\%\), which simplifies to \(I=\frac{65}{25}\times100\%\). \(\frac{65}{25}\) equals \(2.6\). Multiply this by \(100\%\) to get \(260\%\).

The percent increase from \(25\) to \(90\) is \(260\%\).

**Question #6:**

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?

**Answer:**

To find the amount Kaya will save, we will multiply the price of the jeans by the marked down percentage (20) and then move the decimal two places to the left to reflect the percent. Therefore, the discount amount, or the amount that will get subtracted from the price of the jeans, is \($5.60\).

**Question #7:**

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?

**Answer:**

Since Bruce pays \($600\) for rent and the increase is \(15\%\), we multiply \(600\) by \(15\), then move the decimal two places to the left to reflect the percent. Therefore, Bruce’s rent will increase by \($90\).

**Question #8:**

Sophia’s gym membership increased from \($83\) to \($102\) per month. What is the percent increase for Sophia’s gym membership?

**Answer:**

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 \(100\) and we get \(22.89\). Therefore, Sophia’s gym membership fee increased by \(22.89\%\).

**Question #9:**

Zola buys a house for \($230{,}000\) in 2016. The value of her house increases by \(45\%\) after five years. What is the value of Zola’s house in 2021?

**Answer:**

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 2021.

\(\frac{n-230{,}000}{230{,}000}·100=45\)

We will solve for *n* using our algebra skills, 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 2021 is \($333{,}500\).

**Question #10:**

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?

**Answer:**

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 \(100\) is \(3.32640\)…Therefore, the city’s population grew by \(3.3\%\) in ten years.