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# Percentage Increase and Decrease

The increase and decrease of values and quantities are constant in our everyday lives. One way to measure this change is in form of a percentage.

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## What is a percentage?

A percentage is a fraction of a number. It is popularly defined as “parts per 100”.

The percentage of a number is found by dividing the number by 100.

The percentage is denoted by the symbol %.

$3%$ is $\frac{3}{100}$ which is equal to $0.03$.

With this knowledge, we are now ready to define the percentage increase and decrease of a number.

## Percentage Increase and Decrease definition

Percentage increase is the increase of a number, amount, or quantity expressed in percentage.

Percentage decrease is the decrease of a number, amount, or quantity expressed in percentage.

The difference between percentage increase and percentage decrease is that one has to do with increase and the other has to do with decrease. What to note here is that whether increase or decrease, there is a change in value.

## Percentage Increase and Decrease formula

Let's take a look at different percentage increase and decrease formulas and how we can use them in our calculations.

### Percentage Increase calculation

To find the percentage increase, we find the difference between the numbers that are being compared and then change the result to a percentage by dividing the result by the original number and multiplying by $100$.

The following steps will guide you on how to calculate a percentage increase.

1. First, find the increase by subtracting the original number from the new number.
2. Divide the result by the original number and multiply by $100$ to get the percentage increase.

The formulae of the increase and the percentage increase are as follows,

$Increase=Newnumber-Originalnumber\phantom{\rule{0ex}{0ex}}%Increase=\frac{Increase}{Originalnumber}×100$

### Percentage Decrease calculation

To find the percentage decrease, you will first find the difference between the numbers or quantities to be compared and then divide the result by the original number and multiply by $100$. Below are the steps to follow.

1. Find the decrease by subtracting the new number from the original number
2. Then find the percentage decrease by dividing the decrease by the original number and multiplying by $100$.

The formula to use is below.

$Decrease=Originalnumber-Newnumber\phantom{\rule{0ex}{0ex}}%Decrease=\frac{Decrease}{Originalnumber}×100$

### Increasing and decreasing a number by a percentage

When increasing or decreasing a number by a percentage, you first find the percentage of the number and add or subtract it from the original number. We will see some examples hereafter.

### Percentage increase or decrease over time

You may come across questions where you will be asked to find the percentage change, either increase or decrease over time. These types of questions aim to analyze growth or reduction over time. In this case, you will use the following formula.

The same formula is used to calculate the percentage increase and decrease over time.

If you are using the formula to calculate the percentage decrease, you will get a negative answer. In this case, we remove the negative sign and say that the quantities being compared decreased by that number.

The formula looks a little complex and may not be easy to remember. So, let’s break it down in the following steps.

1. Divide the new number by the original number and subtract 1 from the result.
2. Multiply the result of the first step by 100
3. Divide the result by the time given.

The unit of percentage increase or decrease over time is percentage per time, that is, $%/time$. The time can be in seconds, minutes, years or in any other way the time can be measured.

## Percentage Increase and Decrease examples

We've looked at the various formulas that are associated with percentage increase and decrease. Now, let's take some percentage increase and decrease examples.

The first set of examples will show how to calculate a percentage increase.

The price of a bag of rice went up from £20 to £35. What is the percentage increase?

Solution

The formula to be used here is the following,

$Increase=Newnumber-Originalnumber\phantom{\rule{0ex}{0ex}}%Increase=\frac{Increase}{Originalnumber}×100$

The first thing is to identify the values that are given. The question says that the price went up from $£20$ to $£35$. This means that,

$Originalnumber=20\phantom{\rule{0ex}{0ex}}Newnumber=35$

We will first find the increase.

$Increase=Newnumber-Originalnumber\phantom{\rule{0ex}{0ex}}Increase=35-20\phantom{\rule{0ex}{0ex}}=15$

We will now find the percentage increase.

$%Increase=\frac{Increase}{Originalnumber}×100\phantom{\rule{0ex}{0ex}}=\frac{15}{20}×100\phantom{\rule{0ex}{0ex}}=75%$

This means the price increased by $75%$.

Let's take another example.

A bag contains 15 balls. After some time, the number of balls increased to 35. What is the percentage increase?

Solution

From the question, the original number is $15$ and the new number is $35$.

We will first find the increase as shown below.

$Increase=Newnumber-Originalnumber\phantom{\rule{0ex}{0ex}}=35-15\phantom{\rule{0ex}{0ex}}=20$

We will now find the percentage increase.

$%Increase=\frac{Increase}{Originalnumber}×100\phantom{\rule{0ex}{0ex}}%Increase=\frac{20}{15}×100\phantom{\rule{0ex}{0ex}}=133.33%$

This means the number of balls increased by $133.33%$.

The next set of percentage increase and decrease examples will show how to calculate percentage decrease.

Harry had £2000 in his bank account last week but now he has £800. What is the percentage decrease?

Solution

From the question, the original amount or number is $2000$ and the new amount or number is$800$.

We will first find the decrease using the formula below.

$Decrease=Originalnumber-Newnumber\phantom{\rule{0ex}{0ex}}=2000-800\phantom{\rule{0ex}{0ex}}=1200$

We will now use the decrease to find the percentage decrease using the formula below.

$%Decrease=\frac{Decrease}{Originalnumber}×100\phantom{\rule{0ex}{0ex}}=\frac{1200}{2000}×100\phantom{\rule{0ex}{0ex}}=60%$

This means the money in Harry’s bank account decreased by $60%$.

Let's take another example.

A factory went from producing 200 packs of its product to producing 180. What is the percentage decrease?

Solution

The formula to be used is the following,

$Decrease=Originalnumber-Newnumber\phantom{\rule{0ex}{0ex}}%Decrease=\frac{Decrease}{Originalnumber}×100$

From the question, the original number is $200$ and the new number is $180$. So we will first find the decrease and then find the percentage decrease as shown below.

$Decrease=Originalnumber-newnumber\phantom{\rule{0ex}{0ex}}=200-180\phantom{\rule{0ex}{0ex}}=20\phantom{\rule{0ex}{0ex}}%Decrease=\frac{Decrease}{Originalnumber}×100\phantom{\rule{0ex}{0ex}}=\frac{20}{200}×100\phantom{\rule{0ex}{0ex}}=10%$

The percentage decrease is $10%$.

The next set of examples shows how to increase and decrease a number by a percentage.

Increase £80 by 5%.

Solution

The first thing to do here is to find $5%$ of $£80$. We will do this by multiplying $5%$ by $£80$.

$5%×80=\frac{5}{100}×80=4$.

Now, we will add $4$ to $£80$ since we are looking for an increase. If it were to be a decrease, we would be subtracting.

$£80+4=£84$

Therefore, $£80$ increased by $5%$ is $£84$.

Let's take another example.

The length of a 70 cm wood was decreased by 3%. What is the new length?

Solution

We want to know the new length after $3%$decrease. To find this we will solve for $3%$ of the original wood length which is $3%of70$.

$3%×70=\frac{3}{100}×70\phantom{\rule{0ex}{0ex}}=2.1$

Since we are looking for the decreased length, we will subtract 2.1 from the original length of 70.

$70-2.1=67.9$

The new length of the wood is $67.9cm$.

These last set of examples show how to calculate percentage increase or decrease over time.

Over 2 years, it was noticed that the price of petrol went from £199 per liter to £215 per liter. What is the percentage increase over time?

Solution

We are asked to find the percentage increase over time. The time given is 2 years. Following the steps above, the first thing we would do is divide the new number by the original number and subtract 1.

$\frac{Newnumber}{Originalnumber}-1=\frac{215}{199}-1\phantom{\rule{0ex}{0ex}}=0.08$

We will now multiply by $100$.

$0.08×100=8$

The last step is to divide by the time given which is $2years$.

$\frac{8}{2}=4%/year$

Therefore, the percentage increase over time is $4%/year$.

Let's take another example.

Within 30 minutes, the amount of water in a drum went from level 30 to level 15. What is the percentage decrease over 30 minutes?

Solution

Let’s use the formula for this. The formula to be used is below.

All we need to do is to insert the values that are given to us. The values given to us are:

$Time=30minutes\phantom{\rule{0ex}{0ex}}Originalnumber=30\phantom{\rule{0ex}{0ex}}Newnumber=15$

We will now insert the values in the formula.

Therefore, the percentage decrease over time is $0.017%/min$

Notice that the negative sign is taken out. If you get a negative value when calculating, it means that there has been a decrease. You should take out the negative sign and say that the quantity or whatever is being measured has decreased by that value.

## Percentage Increase and Decrease - Key takeaways

• Percentage increase is the increase of a number, amount or quantity expressed in percentage.
• Percentage decrease is the decrease of a number, amount or quantity expressed in percentage.
• If you get a negative value when calculating, it means that there has been a decrease. You should take out the negative sign and say that the quantity or whatever is being measured has decreased by that value.
• The percentage is denoted by the symbol %.

#### Flashcards in Percentage Increase and Decrease 4

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How do you calculate percentage increase and decrease?

To find percentage increase, find the difference between the numbers that are being compared and then change the result to a percentage by dividing it by the original number and multiplying by 100. In other words, find the increase and then the percentage of the increase.

Increase = New number - Original number

% Increase = Increase/Original number

To find percentage decrease, find the difference between the numbers or quantities to be compared and then divide the result by the original number and multiply by 100. In other words, find the decrease and then the percentage of the decrease.

Decrease = Original number - New number

% Decrease Decrease/Original number x 100

What is the percentage increase and decrease formula?

The percentage increase formula is:

% Increase = Increase/Original number x 100

The percentage decrease formula is:

% Decrease = Decrease/Original number x 100

How do you increase and decrease percentages?

When increasing or decreasing a number by a percentage, you first find the percentage of the number and add or subtract it from the original number.

What is the percentage increase and decrease example?

If the price of an item was £20 and it increased to £35, this means that the price increased by 75%.

If the price of an item was £2000 and it decreased to £800, it means it decreased by 60%.

How to average percentage increase and decrease?

The average of two percentages can be calculated by adding the percentages and dividing them by the number of percentages. Finding the average of more than two percentages will require you taking other things into considerations like sample size.

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