# Percent increase

Here you will learn about percent increase, including how to increase a value by a given percentage, use multipliers to calculate percentage increase and work out percentage change.

Students will first learn about percent increase as part of ratios and proportions in the 7th grade.

## What is percent increase?

Percent increase means adding a given percentage of a value onto the original value. To do this, you can either calculate the given percentage of the value and then add it on to the original value or use a percent as a decimal.

For example,

Increase \30 by 20\%. Add on the percentPercent as a decimal \begin{aligned} & 10 \%=\ 3 \\\\ & 20 \%=\6 \end{aligned} So \30 increased by

20\% = \$30+\$ 6=\36. \begin{aligned} & 100 \%+20 \%=120 \% \\\\ & 120 \%=\frac{120}{100}=1.2 \\\\ & \ 30 \times 1.2=\36 \end{aligned} When given two values, you can calculate the percentage difference or percentage change. When the value goes up, this may also be called percent gain, percent profit, or a markup. You can calculate percent change using the percentage change formula: \text { Percentage change }=\frac{\text {amount of change }}{\text { original }} \times 100 • Percent gain Percent gain is when the percent increases or gets bigger, between a starting percent and the final percent. For example, At the beginning of the month, you had \50 in your savings account, and by the end of the month, you had \$75. Work out the percent increase. \text { Percent increase }=\cfrac{75-50}{50} \times 100=50 \% • Percent Profit Percent profit is when a store or person selling a good or a service wants to calculate the difference between the cost price and the selling price and represent it as a percent. For example, A school store buys pencils for \$0.80 and sells them to the students for \$1.00. Work out the percent profit. \text { Percent profit }=\cfrac{1-0.80}{0.80} \times 100=25 \% • Markups Markups are the increased price of a good. A company may markup an item that is in high demand and people are willing to pay more money for it. For example, if a new makeup item is in high demand, a store may markup the price by a given percent due to the shortage of the item, or overall high demand. ### What is percent increase? ## Common Core State Standards How does this relate to 7th grade math? • Grade 7: Ratios and Proportional Relationships (7.RP.3) Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. ## How to increase a value by a percent In order to increase a value by a given percent: 1. Calculate the given percent of the value. 2. Add the calculated percent to the original number. ## Percent increase examples ### Example 1: percent increase in value Kalli purchased a collector’s baseball card for \$50 in 2021. In 2022, the value increased by 40\%. What is the value of the baseball card now?

1. Calculate the given percent of the value.

You will first need to solve for 40\% of \$50. The easiest way is to calculate 10\% (by dividing by 10 ) and then multiply by 4 to get 40\%. 10\% of \$50 = \$5. 5 \times 4=20 40\% of \$50 = \$20. 2Add the calculated percent to the original number. Add \$20 on to the original value of \$50. \$ 50+\$20=\$ 70

The final answer is \$70. The value of the baseball card increased to \$70.

### Example 2: percent increase

Increase 400 by 60\%.

You will first calculate 60\% of 400.

The easiest way is to calculate 10\% (by dividing by 10 ) and then multiply by 6 to get 60\%.

10\% of 400 = 40.

40 \times 6=240

60\% of 400 = 240.

Add 240 on to the original value of 400.

400 + 240 = 640

400 increased by 60\% is 640.

### Example 3: percent increase

Increase 350 \, m by 30\%.

You will first calculate 30\% of 350.

The easiest way to calculate 30\% is to calculate 10\% (by dividing by 10 ) and then multiply by 3 to get 30\%.

10\% of 350 = 35.

35 \times 3=105

30\% of 350 = 105.

Add 105 \, m on to the original value.

350 \, m+105 \, m=455 \, m

The final answer is 455 \, m.

350 \, m increased by 30\% is 455 \, m.

### Example 4: percent increase in value

The price of Katrina’s train ticket last year was \$75. This year it has increased by 15\%. Find the price of Katrina’s train ticket this year. You will first need to find 15\% of \$75.

10\% of \$75 = \$7.50.

7.50 \div 2=3.75

5\% of \$75 = \$3.75.

\$7.50+3.75=\$ 11.25

15\% of \$75 is \$11.25.

Add on \$11.25 to the original value. \$ 75+\$11.25=\$ 86.25

The final answer is \$86.25. Katrina’s train ticket increased by 15\% is \$86.25.

## Percent increase using a percent as a decimal

In order to increase a value by using a percent as a decimal:

1. Add the percent you are increasing by and \bf{100\%} .
2. Convert the percent to a decimal.
3. Multiply the original amount by the decimal.

### Example 5: percent as a decimal

Increase 3,200 \, ml by 24\%.

Here you are calculating a 24 percent increase, so add 24\% on to 100\%.

100 \%+24 \%=124 \%

To do this, you divide the percentage by 100.

124 \% \div 100=1.24

124\% = 1.24

Multiply 3,200 by 1.24.

3,200\times 1.24=3,968 \, ml

The final answer is 3,968 \, ml.

3,200 \, ml increased by 24\% is 3,968 \, ml.

### Example 6: percent as a decimal

In 2015, Rachel’s monthly rent was \$620. Over the course of five years, Rachel’s monthly rent increased by 12.5\%. Find Rachel’s monthly rent at the end of the five years. This is a 12.5 percent increase, so you add 12.5\% onto 100\%. 100 \%+12.5 \%=112.5 \% 112.5 \div 100=1.125 112.5\% = 1.125 Multiply \$620 by 1.125.

620\times 1.125=\$697.50 Remember to always write money using two decimal places. Rachel’s rent increased from \$620 to \697.50 over 5 years. ## Calculating percent increase In order to calculate the percent increase after a percent change: 1. Find the amount of change by subtracting the original number from the new number. 2. Plug numbers into the percent change formula. \text { Percentage change }=\cfrac{\text { Change }}{\text { Original }} \times 100 3. Simplify the fraction, if necessary, using equivalent fractions. 4. Convert the fraction to a decimal. 5. Calculate percent change. ### Example 7: calculating percent change The weight of a lamb has increased from 7 \, kg to 13 \, kg. Find the percent increase in the lamb’s weight. The weight of the lamb has changed from 7 \, kg to 13 \, kg. You will subtract the original weight from the new weight. 13-7=6 \mathrm{~kg} Apply the percent change formula. The change is 6 \, kg and the original amount is 7 \, kg. \begin{aligned} & \text { Percent change }=\cfrac{\text { Change }}{\text { Original }} \times 100 \\\\ & \text { Percent change }=\cfrac{6}{7} \times 100 \end{aligned} \cfrac{6}{7} \, does not need to be simplified. \text { Percent change }=\cfrac{6}{7} \times 100 \cfrac{6}{7}=85.71 \text{Percent change } =0.86 \times 100 You can round this decimal to 0.86 to solve. 0.86 \times 100=86 \text{Percent change } = 86\% The lamb’s weight has increased by 86\%. ### Example 8: calculating percentage profit Lucy buys an antique table for \150 and sells it for \$185. Calculate Lucy’s percent profit. Work out the change in value by subtracting the original price from the new price: \$ 185-\$150=\$ 35

Apply the percent change formula. The change is \$35 and the original price is \$150.

\text { Percent change }=\cfrac{35}{150} \times 100

\cfrac{35}{150} \, can be simplified to \, \cfrac{7}{30}.

\text { Percent change }=\cfrac{7}{30} \times 100

\cfrac{7}{30}=23.333\ldots

\text { Percent change }=0.23 \times 100

This is a repeating decimal, but you can round this decimal to 0.23 to solve.

0.23 \times 100=23

\text{Percent change }=23 \%

Lucy’s percentage profit is 23\%.

### Teaching tips for percent increase

• When calculating percent change, sometimes the numbers can be quite large. Students may use a calculator, or a percentage change calculator, to assist them with solving these problems.

• Percent change can be calculated using Microsoft Excel. For students who are proficient using Excel, this could be an additional teaching point while discussing percent change.

### Easy mistakes to make

• Believing that percentages cannot be greater than \bf{100\%}
For percent increase using a percent as a decimal, you encounter a lot of percentages greater than 100\% as you are adding on to the original 100\%.

• Incorrectly converting percentages to decimals
The most common mistakes are with single digit percentages (for example, 5\% ), multiples of 10 (for example, 40\% ), and decimal percentages (for example, 3.2\% ).
Remember to divide the percentage by 100 to find the decimal.
For example, 5\%=0.05, \, 40\%=0.4, \, 3.2\%=0.032, \, 106.5\%=1.065

• Using an incorrect value for the denominator in the percentage increase formula
Using the new value instead of the original value for the denominator when calculating percentage change.

### Percent increase practice questions

Calculate the percent increase that has occurred in each of these questions.

1. Increase \$520 by 20\%. \$540 \$104 \$624 \$640 You will first calculate 20\% of \$520.

10\% of \$520 = \$52.

52 \times 2=104

20\% of \$520 = \$104.

20\% of 520 is 104.

This can be added to the original amount to find the quantity after the increase.

\$104+\$ 520=\$624 2. Increase 3,400 \, m by 40\%. 3,463 \, m 4,760 \, m 1,470.6 \, m 3,563 \, m You will first calculate 40\% of 3,400. 10\% of 3,400 = 340. 340 \times 4=1,360 40\% of 3,400 = 1,360 40\% of 3,400 is 1,360. This can be added to the original amount to find the quantity after the increase. 3,400+1,360=4,760 3,400 \, m increased by 40\% is 4,760. 3. Use a percent as a decimal to increase 38 by 14\%. 5.32 43.32 42 33.3 Add the percentage you are increasing by, 14\%, and 100. 100+14 =114 Next, you will convert the percentage to a decimal by dividing. 114 \div 100=1.14 Then multiply the original amount by the decimal. 38 \times 1.14=43.32 38 increased by 14\% is 43.32. 4. Use a percent as a decimal to increase 650 \, kg by 26\%. 172.25 \, kg 819 \, kg 513.83 \, kg 676 \, kg Add the percentage you are increasing by, 26\%, and 100. 100+26 =126 Next, you will convert the percentage to a decimal by dividing. 126 \div 100=1.26 Then multiply the original amount by the decimal. 650 \times 1.26=819 650 \, kg increased by 26\% is 819 \, kg. 5. Find the percent increase when 400 \, ml is increased to 620 \, ml. 55\% 155 \% 220\% 110\% First, you will calculate the change from 400 \, ml to 620 \, ml. 620-400=220 The change is 220 \, ml, so you can now plug the numbers into the percent change formula. \text {Percent change }=\cfrac{220}{400} \times 100 After simplifying the fraction to \, \cfrac{55}{100} \, , you would convert it to the decimal 0.55. 0.55 \times 100=55 \text {Percentage increase }=55 \% 6. Find the percentage profit when Karam buys a house for \$124,000 and sells the house for \$137,640. 111\% 89 \% 11\% 136.4\% First, you will calculate the change from \$124,000 to \$137,640. 137,640-124,000=13,640 The change is \$13,640, so you can now plug the numbers into the percent change formula.

\text {Percent change }=\cfrac{13,640}{124,000} \times 100

After simplifying the fraction to \, \cfrac{11}{100} \, , you would convert it to the decimal 0.11.

0.11 \times 100=11

\text {Percentage increase }=11 \%

## Percent increase FAQs

Can finding the percent change give you a negative number for a percent?

If you are finding a percent decrease, or any percentage where the value is decreasing, the initial percent change calculation will result in a negative number. However, you will use the absolute value of the difference to calculate the overall percent change, which will result in a positive number.

What is a percent increase calculator?

It is an automated way for you to calculate the percentage increase of a given value. It is recommended that you use the calculator when dealing with large numbers and decimals.

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