Percentage Increase & Decrease | How to Calculate Percentage Change – Video & Lesson Transcript | camilledimaio.com

Finding the Increase and Decrease

Continuing to consider Company A and Company B, Company A stock has increased from $125 to $150 in the last twelve months while Company B stock has increased from $1250 to $1350.

Since both values have risen over the time period in question, the percentage change calculation will be a percentage increase or percentage growth calculation.

The steps to calculate percentage change are:

1. Find the difference between the original and new values.
2. Divide the difference by the original value.
3. Multiply the resulting quotient by 100.
4. If the result is positive, format the result as a percentage increase. If it is negative, format it as a positive percentage and identify it as a percentage decrease.

Here is how to calculate percentage increase for both Company A and Company B:

• Company A: find the difference between the current stock value and the past stock find then divide by the original value. Finally, multiply by 100 to format the answer as a percent. So, we have eqdfrac150-125125 times 100 = 20text% /eq

• Company B: find the percentage growth in the same manner to get, eqdfrac1350-12501250 times 100 = 8text% /eq

Notice that Company A had a percentage growth of 20%, while Company B, which had a larger absolute difference between values, actually had a much smaller percentage growth of only 8%. Company A would be seen as the stronger investment because its percentage growth is higher than that of Company B.

Finding percentage decrease entails finding the difference between the original price and the new price, then dividing by the original price and multiplying the result by 100.

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Percentage Increase and Decrease Formula

Essentially, the formulas for percentage increase and percentage decrease are the same. The general formula is:

Percentage change formula.

If the percent change value is positive, the answer represents a percentage increase. If the value is negative, it can be written as a positive and identified as a percentage reduction.

For example, if the value of a single share in a company dropped from $2.00 to $1.90, this would represent a -5% percentage change or a 5% percentage reduction.

The direct percentage decrease formula is:

The percentage decrease formula is similar to the percentage change formula.

Notice that this formula is basically the same formula with the only change being that the difference is calculated in such a way as to end with a positive number; it is still the difference divided by the original value with that quotient multiplied by 100.

Examples of Percentage Increase and Decrease

The best way to learn a new mathematical concept is to practice. Percentage change problems are best approached using real-world examples. Here are some examples to help you practice how to do percentage change problems.

Example 1

The housing market has seen a drastic decline in recent years. Five years ago, houses in Neighborhood C averaged $1,350,000. Today, the average property value in the same neighborhood is $1,150,000. What is the percentage reduction in property value for this neighborhood?

Example 1: Answer

This is a percentage reduction problem so the formula can be formatted like this:

eqbeginalign textPercentage reduction &= dfrac1,350,000-1,150,0001,350,000 times 100 \ &\ &= dfrac200,0001,350,000 times 100 \ &\ &= 0.1481 times 100 \ &\ &approx 14.8text% endalign /eq

The percentage reduction for the area is approximately 14.8%

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Example 2

Scientists are concerned about the population growth rate of an invasive species of mushrooms in Forest M. If the population growth rate is higher than 55% the scientists must start an eradication program in the area. The original sample found 1125 mushrooms and the most recent sample found 1800 mushrooms. Will an eradication program be needed?

Example 2: Answer

This is a percentage increase problem since the new number is higher than the original number. Set up the problem like this:

eqbeginalign textPercentage increase &= dfrac1800-11251125 times 100 \ &\ &= dfrac6751125 times 100 \ &\ &= 0.6 times 100 \ &\ & = 60text% endalign /eq

The percentage growth amount is 60%, which is higher than the maximum allowed 55% growth; thus, an eradication program must begin.

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How to Reverse Percentage Increase and Decrease

Sometimes it is necessary to work backward to find the original value from the new value and the percentage increase or decrease. This might happen when trying to calculate the original cost of a car prior to a discount deducted from the price. For instance, assume a car is being sold for $15,000 and the salesman states this represents a 25% discount (percentage decrease) on the original price.

It is tempting to just reverse the previous steps, but that will not work.

To find the original price follow these steps:

1. Subtract the percentage from 100 (since it is a decrease in price. An increase in price would need to be added to 100).
2. Convert the resulting percentage into a decimal (by dividing by 100).
3. Divide the given price (new value) by the percentage in decimal form to arrive at the original price.

For the car example:

1. 25% discount means 100-25 = 75%
2. 75% = 0.75
3. 15,000/0.75= $20,000.

The car originally cost $20,000 before the discount.

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Lesson Summary

Percentage change is a measure of the degree to which a value has changed, either increased or decreased, over time presented in percent form. In the case of percentage increase the change represents an increase in the overall value of the measured item and can be said to represent its percentage growth. Alternatively, percentage decrease represents percentage reduction, or the amount a measured item decreases in overall value over time.

To find percentage change, follow these steps:

1. Find the difference between the original and new values.
2. Divide the difference by the original value.
3. Convert the resulting decimal into percent form.

Reversing percentages requires altering 100% either up or down depending on the direction of the reversal, converting the new percentage into a decimal, and then dividing the given value by the decimal version of the percent.

To find our percentage increase then, we divide our 100 by our month one total. We get 100/1400 = 0.0714. Multiply this by 100, we get a percentage of 7.1%. So our sales increased by 7.1%. And we are done!

Example 2

This time, we have a teacher looking at her attendance charts. She wants to know if the attendance this week is better than the attendance last week. She wants to know because this week, she changed her teaching approach to a more humorous one. The previous week, she was very serious and didn’t allow any fooling around. Looking at her records, she sees that the previous week, she had an attendance record of 95%. This week, her attendance record is 90%. Do we have an increase or decrease?

We have a decrease since the second total is lower. How much is our decrease? We have 95 – 90 = 5. We decreased by five percent. How much of a percentage decrease is this? We divide our 5 / 95 * 100. We get approximately 5.3%. So, we have a percentage decrease of 5.3%. And we are done.

Notice here that in this problem we are already dealing with percentages. But our process is still the same. So, as long as we have the same format of our totals, then we use the same process regardless if the numbers are already percentages or not.

Lesson Summary

Let’s review what we’ve learned. A percentage increase or decrease is the amount of increase or decrease expressed as a percentage. To calculate it, we first calculate the first total and then the second total. If we are comparing two consecutive years, the first year gives us the first total, and the second year gives us the second total. Then we determine if there is an increase or decrease happening. Then we calculate the amount of this increase or decrease. To find the percentage, we divide the amount of increase or decrease by the first total and multiply by 100.

Learning Outcomes

By the end of this lesson you should be able to:

• State the formula for determining percent increase or decrease
• Calculate the percentage of increase of decrease

To find our percentage increase then, we divide our 100 by our month one total. We get 100/1400 = 0.0714. Multiply this by 100, we get a percentage of 7.1%. So our sales increased by 7.1%. And we are done!

Example 2

This time, we have a teacher looking at her attendance charts. She wants to know if the attendance this week is better than the attendance last week. She wants to know because this week, she changed her teaching approach to a more humorous one. The previous week, she was very serious and didn’t allow any fooling around. Looking at her records, she sees that the previous week, she had an attendance record of 95%. This week, her attendance record is 90%. Do we have an increase or decrease?

We have a decrease since the second total is lower. How much is our decrease? We have 95 – 90 = 5. We decreased by five percent. How much of a percentage decrease is this? We divide our 5 / 95 * 100. We get approximately 5.3%. So, we have a percentage decrease of 5.3%. And we are done.

Notice here that in this problem we are already dealing with percentages. But our process is still the same. So, as long as we have the same format of our totals, then we use the same process regardless if the numbers are already percentages or not.

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Lesson Summary

Let’s review what we’ve learned. A percentage increase or decrease is the amount of increase or decrease expressed as a percentage. To calculate it, we first calculate the first total and then the second total. If we are comparing two consecutive years, the first year gives us the first total, and the second year gives us the second total. Then we determine if there is an increase or decrease happening. Then we calculate the amount of this increase or decrease. To find the percentage, we divide the amount of increase or decrease by the first total and multiply by 100.

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Learning Outcomes

By the end of this lesson you should be able to:

• State the formula for determining percent increase or decrease
• Calculate the percentage of increase of decrease