# Percent decrease

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

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

## What is percent decrease?

Percent decrease means subtracting a given percentage of a value from the original value. To do this, you can either calculate the given percent of the value and subtract it from the original or use a percent as a decimal.

For example,

Decrease \$30 by 20\%. When given two values, you can calculate the percent difference or percentage change. When the value goes down this may also be called percent decrease, percent loss, or a markdown. You can calculate percent change using the percentage change formula: • Percent loss Percent loss is when the percent decreases or gets smaller between a starting percent and the final percent. For example, At the beginning of the month, you had \$150 in your savings account, and by the end of the month, you had \$75. Work out the percent decrease. \text { Percent decrease }=\cfrac{150-75}{150} \times 100=50 \% • Markdowns Markdowns are the decreased price of a good. Markdowns are more commonly known as discounts, or sales, in a retail store. For example, at the end of the summer, stores will place their summer clothing and swimsuits on markdown to make room for their fall and winter clothing. ### What is percent decrease? ## 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 decrease a value by a percent In order to decrease a value by a percent: 1. Calculate the given percent of the value. 2. Subtract the calculated percent from the original number. ## Percent decrease examples ### Example 1: percent decrease Decrease \$80 by 30\%.

1. Calculate the given percent of the value.

You will need to calculate 30\% of \$80. The easiest way to calculate 30\% is to calculate 10\% (by dividing by 10 ) and then multiply by 3 to get 30\%. 10\% of \$80 = \$8 8 \times 3=24 30\% of \$80 = \$24 2Subtract the calculated percent from the original number. You will subtract \$24 from the initial value of \$80. \$80-\$24 = \$56

A 30\% decrease of \$80 is \$56.

### Example 2: percent decrease

Decrease 250 \, km by 45\%.

You will calculate 45\% of 250 by first finding 40\%.

10\% of 250 \, km = 25 \, km

25 \times 4=100

40\% of 250 \, km = 100 \, km

You will then need to calculate 5\%. Find 10\% then divide by 2 to find 5\%.

10\% of 250 \, km = 25 \, km

25 \div 2=12.5

5\% of 250 \, km = 12.5 \, km

100 \mathrm{~km}+12.5 \mathrm{~km}=112.5 \mathrm{~km}

45\% of 250 \, km = 112.5 \, km

You will subtract 112.5 \, km from the original value.

250-112.5 = 137.5 \, km

A 45\% decrease of 250 \, km is 137.5 \, km.

### Example 3: percent decrease

Decrease 760 by 40\%.

You will calculate 40\% of 760.

10\% of 760 = 76

76 \times 4=304

40\% of 760 = 304

You will subtract 304 from the original number.

760-304=456

A 40\% decrease of 760 is 456.

### Example 4: a markdown

A jacket that costs \$35.00 is reduced by 15\% in a sale. Calculate the new price of the jacket. You will calculate 15\% of \$35.

You will calculate 15\% of \$35 by first finding 10\%. 10\% of \$35 = \$3.50 You will then need to calculate 5\%. Use 10\% then divide by 2 to find 5\%. 10\% of \$35 = \$3.50 3.50 \div 2=1.75 5\% of \$35 = \$1.75 \$ 3.50+1.75=\$5.25 15\% of \$35 is \$5.25. You will subtract \$5.25 from the original price.

\$35.00-\$ 5.25=\$29.75 The new price for the jacket is \$29.75.

## Percent decrease using a percent as a decimal

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

1. Subtract the percent you are decreasing from \bf{100\%} .
2. Convert the percent to a decimal.
3. Multiply the original amount by the decimal.

### Example 5: percent as a decimal

Decrease 84 \, m by 46\%.

Here you are calculating a 46 percent decrease so subtract 46\% from 100\%.

100 \%-46 \%=54 \%

To convert a percent to a decimal, you divide the percentage by 100.

54 \div 100=0.54

54\% = 0.54

You will multiply the starting value by the decimal.

84\times 0.54=45.36 \, m

84 \, m decreased by 54\% is 45.36 \, m.

### Example 6: percent as a decimal

Daniel has \$3,600. He spends 25\% of his money. How much does he have left? This is a 25 percent decrease so subtract 25\% from 100\%. 100\%-25\% = 75\% To convert a percent to a decimal, you divide the percent by 100. 75 \div 100=0.75 75\% = 0.75 You will multiply \$3,600 by 0.75.

3,600 \times 0.75=\$2,700 Daniel has \$2,700 left.

## Calculating percent decrease

In order to calculate the percent decrease 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

Ricky weighed 70 \, kg in March. By June his weight had decreased to 62 \, kg. Calculate the percent decrease in his weight.

Ricky’s weight has changed from 70 \, kg to 62 \, kg. You will subtract his original weight from his new weight.

70 \, kg-62 \, kg = 8 \, kg

The change is 8 \, kg and the original amount is 70 \, kg.

\begin{aligned} &\text { Percent change }=\cfrac{\text { Change }}{\text { Original }} \times 100\\\\ &\text { Percentage change }=\cfrac{8}{70} \times 100 \end{aligned}

\cfrac{8}{70} \, can be simplified to \, \cfrac{4}{35} \, .

\text { Percent change }=\cfrac{4}{35} \times 100

\cfrac{4}{35}=0.114

You can round this decimal to 0.11 to solve.

\text { Percent change }=0.11 \times 100

0.11\times 100=11

\text{Percent change } = 11\%

The percent decrease is about 11\%.

### Example 8: calculating percent loss

Louise buys a car for \$7,500 and sells it for \$6,150 two years later. Calculate Louise’s percent loss.

The value has changed from \$7,500 to \$6,150.

\$7,500-\$6,150 = \$1,350 The change is \$1,350 and the original amount is \$7,500. \text { Percent change }=\cfrac{\text { Change }}{\text { Original }} \times 100 \text { Percent change }=\cfrac{1350}{7500} \times 100 \cfrac{1,350}{7,500} \, can be simplified to \, \cfrac{18}{100} \, . \text { Percent change }=\cfrac{18}{100} \times 100 \cfrac{18}{100}=0.18 \text { Percent change }=0.18 \times 100 0.18 \times 100=18 \text{Percent change }=18 \% Louise’s percent loss is 18\%. ### Teaching tips for percent decrease • There are times when the figures used to calculate percent change can be rather big. To help them with these tasks, students can use calculators or percentage change calculators. • Microsoft Excel may be used to calculate percent change. This could serve as an additional teaching point when talking about percent change with students who are comfortable with Excel. ### Easy mistakes to make • Incorrectly converting percents to decimals The most common mistakes are with single digit percents (6\%), multiples of 10 \, (60\%) and decimal percentages (1.2\%). Remember to divide the percent by 100 to find the decimal. For example, 6\%=0.06, \, 50\%=0.5, \, 1.2\%=0.012, \, 206.5\%=2.065 • Using an incorrect value for the denominator in the percentage decrease formula Using the new value instead of the original value for the denominator when calculating percentage change. ### Practice percent decrease questions Calculate the percent decrease that has occurred in each of these questions. 1. Decrease 7,500 \, m by 20\%. 7,480 \, m 7,520 \, m 9,000 \, m 6,000 \, m First, you will need to calculate 20\% of 7,500. 10\% of 7,500 \, m = 750 \, m 750 \times 2=1,500 20\% of 7,500 \, m = 1,500 \, m Then you will subtract 1,500 \, m from the original value. 7,500-1,500=6,000 \mathrm{~m} A 20\% decrease of 7,500 \, m is 6,000 \, m. 2. Decrease 45 \, ml by 80\%. 9 \, ml 80 \, ml 36 \, ml 51 \, ml First, you will need to calculate 80\% of 45 \, ml. 10\% of 45 \, ml = 4.5 \, ml 4.5 \times 8=36 80\% of 45 \, ml = 36 \, ml Then you will subtract 36 \, ml from the original value. 45-36=9 \, ml An 80\% decrease of 45 \, ml is 9 \, ml. 3. Use a percent as a decimal to decrease \$750 by 25\%.

\$562.50 \$731 \$173 \$927.42 This is a 25 percent decrease so start by subtracting 25\% from 100 \%.

100 \%-25 \%=75 \%

Next, to convert a percent to a decimal, you divide the percent by 100.

75 \div 100=0.75

75\% = 0.75

Then, you will multiply the original number, \$750, by the decimal. 750 \times 0.75=\$ 562.50

\$750 decreased by 25\% is 562.50. 4. Use a percent as a decimal to decrease 250 \, g by 40\%. 215.8 \, g 6.65 \, g 97.028 \, g 150 \, g This is a 40 percent decrease so start by subtracting 40\% from 100\%. 100 \%-40 \%=60 \% Next, to convert a percent to a decimal, you divide the percent by 100. 60 \div 100=0.60 60\% = 0.60 Then, you will multiply the original number, 250 \, g, by the decimal. 250 \times 0.60=150 250 \, g decreased by 40\% is 150 \, g. 5. Find the percent decrease when 650 \, kg is decreased to 320 \, kg. 330\% 50.77 \% 49.23\% 203.125\% Start by finding the amount of change by subtracting the original number from the new number. The value has changed from 650 \, kg to 320 \, kg. 650-320=330 \, kg Next, plug numbers into the percent change formula. The change is 330 \, kg and the original amount is 650 \, kg. \text { Percent change }=\cfrac{\text { Change }}{\text { Original }} \times 100 \text { Percent change }=\cfrac{330}{650} \times 100 If the fraction can be simplified, do that next. \cfrac{330}{650} \, can be simplified to \, \cfrac{33}{65} \, . \text {Percent change }=\cfrac{33}{65} \times 100 Then you will convert the fraction to a decimal. \cfrac{33}{65}=0.51 \text {Percent change }=0.51 \times 100 Then you will calculate the percent change. 0.51 \times 100=51 \text {Percent change }=51 \% The percent change is a 51\% decrease. 6. Find the percent loss when Tristan buys a tractor for \$11,500 and sells the tractor for \$9,500 one year later. 18.25\% 85 \% 17.4\% 82.25\% Start by finding the amount of change by subtracting the original number from the new number. The value has changed from \$11,500 to \$9,500. 11,500-9,500=\$ 2,000

Next, plug numbers into the percent change formula.

The change is \$2,000 and the original amount is \$11,500.

\text { Percent change }=\cfrac{\text { Change }}{\text { Original }} \times 100

\text { Percent change }=\cfrac{2,000}{11,500} \times 100

If the fraction can be simplified, do that next.

\cfrac{2,000}{11,500} \, can be simplified to \, \cfrac{4}{23} \, .

\text {Percent change }=\cfrac{4}{23} \times 100

Then you will convert the fraction to a decimal.

\cfrac{4}{23}=0.174

\text {Percent change }=0.174 \times 100

Then you will calculate the percent change.

0.174 \times 100=17.4

\text {Percent change }=17.4 \%

The tractor decreased in value by 17\%.

## Percent decrease 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.

Is there a different formula to calculate percent increase and percent decrease?

You use the same formula whether you are finding the percent increase or decrease. With both, you are calculating the percent to which the measure either increases or decreases.

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