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Simplifying fractions Percent to decimal Percent to fractionHere 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.

**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 percent | Percent 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.

Use this quiz to check your grade 6 to 7 studentsβ understanding of percents. 10+ questions with answers covering a range of 6th and 7th grade percent topics to identify areas of strength and support!

DOWNLOAD FREEUse this quiz to check your grade 6 to 7 studentsβ understanding of percents. 10+ questions with answers covering a range of 6th and 7th grade percent topics to identify areas of strength and support!

DOWNLOAD FREEHow 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.

In order to increase a value by a given percent:

**Calculate the given percent of the value.****Add the calculated percent to the original number.**

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?

**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.

2**Add 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.

Increase 400 by 60\%.

**Calculate the given percent of the value.**

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 the calculated percent to the original number.**

Add 240 on to the original value of 400.

400 + 240 = 640

The final answer is 640.

400 increased by 60\% is 640.

Increase 350 \, m by 30\%.

**Calculate the given percent of the value.**

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 the calculated percent to the original number.**

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.

The price of Katrinaβs train ticket last year was \$75. This year it has increased by 15\%. Find the price of Katrinaβs train ticket this year.

**Calculate the given percent of the value.**

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 the calculated percent to the original number.**

Add on \$11.25 to the original value.

\$ 75+\$ 11.25=\$ 86.25

The final answer is \$86.25.

Katrinaβs train ticket increased by 15\% is \$86.25.

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

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

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

**Add the percentage you are increasing by and ** \bf{100\%} **.**

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

100 \%+24 \%=124 \%

**Convert the percentage to a decimal.**

To do this, you divide the percentage by 100.

124 \% \div 100=1.24

124\% = 1.24

**Multiply the original amount by the decimal.**

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.

In 2015, Rachelβs monthly rent was \$620. Over the course of five years, Rachelβs monthly rent increased by 12.5\%. Find Rachelβs monthly rent at the end of the five years.

**Add the percentage you are increasing by and ** \bf{100\%} **.**

This is a 12.5 percent increase, so you add 12.5\% onto 100\%.

100 \%+12.5 \%=112.5 \%

**Convert the percentage to a decimal.**

112.5 \div 100=1.125

112.5\% = 1.125

**Multiply the original amount by the decimal.**

Multiply \$620 by 1.125.

620\times 1.125=\$697.50

Remember to always write money using two decimal places.

Rachelβs rent increased from \$620 to \$697.50 over 5 years.

In order to calculate the percent increase after a percent change:

**Find the amount of change by subtracting the original number from the new number.****Plug numbers into the percent change formula.**

\text { Percentage change }=\cfrac{\text { Change }}{\text { Original }} \times 100**Simplify the fraction, if necessary, using equivalent fractions.****Convert the fraction to a decimal.****Calculate percent change.**

The weight of a lamb has increased from 7 \, kg to 13 \, kg. Find the percent increase in the lambβs weight.

**Find the amount of change by subtracting the original number from the new number.**

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}

**Plug numbers into the percent change formula.**

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}

**Simplify the fraction, if necessary, using equivalent fractions.**

\cfrac{6}{7} \, does not need to be simplified.

\text { Percent change }=\cfrac{6}{7} \times 100

**Convert the fraction to a decimal.**

\cfrac{6}{7}=85.71

\text{Percent change } =0.86 \times 100

You can round this decimal to 0.86 to solve.

**Calculate percent change.**

0.86 \times 100=86

\text{Percent change } = 86\%

The lambβs weight has increased by 86\%.

Lucy buys an antique table for \$150 and sells it for \$185. Calculate Lucyβs percent profit.

**Find the amount of change by subtracting the original number from the new number.**

Work out the change in value by subtracting the original price from the new price:

\$ 185-\$ 150=\$ 35

**Plug numbers into the percent change formula.**

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

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

**Simplify the fraction, if necessary, using equivalent fractions.**

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

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

**Convert the fraction to a decimal.**

\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.

**Calculate percent change.**

0.23 \times 100=23

\text{Percent change }=23 \%

Lucyβs percentage profit is 23\%.

- 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.

**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.

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 \%

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.

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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