# How to Find the Percentage Increase

Finding percent increase is similar to finding the decrease, but the formula is a little different. This video demonstrates this using three examples. To find the percent increase in the numbers 1.8 and 3.0, use the equation 3.0 – 1.8 ÷ 1.8 = 1.2/1.8, which can be simplified to 2/3. The decimal equivalent to 2/3 is 66.7%.

In this example problem we have three different types of number pairs. **We have decimals, fractions, and dollar amounts.** What the question asks us to do is to find the percentage increase for each of these pairs. Now the formula for finding the percentage increase is going to be the same for all three pairs, but the process will be a little bit different depending on the type of number.

**I’ll demonstrate all three.** The first one we have 3.0 minus 1.8, divided by 1.8. **The formula is the second minus the first, over the first.** That’s going to be consistent throughout. Now to solve this we can take 3 minus 1.8, which is 1.2. We have 1.2 over 1.8, which is equivalent to 2 over 3, and the percentage form of 2 over 3 is 66.7 percent. The second example we have 1 over 4 and 2 over 5.

**We’re going to use the same formulas here.** We’re going to have 2 over 5, minus 1 over 4, divided by 1 over 4. Now we have to get a common denominator here, so we’re going to multiply this first number by 4 over 4 to get 8 over 20. The second number we’re going to multiply by 5 over 5 to get 5 over 20. What we have here is 8 over 20, minus 5 over 20, which is equal to 3 over 20.

Then we have to divide it by 1 over 4, or equivalently what we have here is 3 over 20, times 4 over 1. Now the 4 and the 20 cancels, dividing each by 4 we get a 1 and a 5. **What we have here is 3 over 5.** Now the percentage equivalent of 3 over 5 is 60 percent. In this final example we have dollar amounts. We have 225 and 405. We’ll take the final amount 405, subtract the initial amount, 225 and divide by the additional 225.

Now 405 minus 225 is a 180. What we have 180 divided by 225. Now we can reduce this by dividing top and bottom by 45. 45 goes into 180 4 times and 45 goes into 225 5 times. What we have is 4 over 5, or the percentage equivalent which is 80 percent.

## Practice Questions

**Question #1:**

What is the percent increase from 4 to 27?

25%

75%

575%

625%

**Answer:**

The correct answer is 575%. To find percent increase, use the following formula:

\(\text{% increase}=\frac{\text{new}-\text{original}}{\text{original}}\times100\)

The new value is 27 and the original value is 4.

\(\text{% increase}=\frac{27-4}{4}\times100=\frac{23}{4}\times100=575\text{%}\)

**Question #2:**

What is the percent increase from 17 to 39?

129.4%

29.6%

229.4%

89.6%

**Answer:**

The correct answer is 129.4%. To find percent increase, use the following formula:

\(\text{% increase}=\frac{\text{new}-\text{original}}{\text{original}}\times100\)

The new value is 39 and the original value is 17.

\(\text{% increase}=\frac{39-17}{17}\times100=\frac{22}{17}\times100=129.4\text{%}\)

**Question #3:**

The 2020 version of a car costs $24,000. The 2021 version of the same car costs $27,000. What is the percent increase in the price of the car from 2020 to 2021?

211.5%

42.5%

12.5%

112.5%

**Answer:**

The correct answer is 12.5%. To find percent increase, use the following formula:

\(\text{% increase}=\frac{\text{new}-\text{original}}{\text{original}}\times100\)

The new price is $27,000 and the original price is $24,000.

\(\text{5 increase}=\frac{27,000-24,000}{24,000}\times100=\frac{3,000}{24,000}\times100=12.5\text{%}\)

**Question #4:**

A family moves from a $232,000 house to a $312,000 house. What is the percent increase from the price of their original house to their new house?

27.9%

34.5%

127.9%

134.5%

**Answer:**

The correct answer is 34.5%. %. To find percent increase, use the following formula:

\(\text{% increase}=\frac{\text{new}-\text{original}}{\text{original}}\times100\)

The new price is $312,000 and the original price is $232,000.

\(\text{% increase}=\frac{312,000-232,000}{232,000}\times100=\frac{80,000}{232,000}\times100=34.5\text{%}\)

**Question #5:**

Savannah pays $527 per month for health insurance for health insurance for her and her family. She upgrades to a more inclusive plan that is $576 per month. What is the percent increase from her original plan cost to the upgraded plan cost?

9.3%

86.7%

186.7%

109.3%

**Answer:**

The correct answer is 9.3%. To find percent increase, use the following formula:

\(\text{% increase}=\frac{\text{new}-\text{original}}{\text{original}}\times100\)

The new cost is $576 and the original cost is $527.

\(\text{% increase}=\frac{576-527}{527}\times100=\frac{49}{527}\times100=9.3\text{%}\)