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Simplifying fractions Percent to decimal Percent to fractionHere you will learn about percent change, including how to calculate the percentage by which a value has increased or decreased.
Students will first learn about percent change as part of ratios and proportional relationships in 7th grade.
Percent change equals the change in value divided by the absolute value of the original value, multiplied by It is when the percentage of its original value has changed to either increase or decrease the value.
When you calculate percent change, you are calculating by what percentage of its original value something has changed.
To calculate percent change, you can use the percentage change formula:
Percent change can refer to many different types of scenarios. This can include percentage increase, percentage decrease, percentage profit, percentage gain, markups and markdowns, or percentage loss.
Use this quiz to check your grade 6 to 7 students’ 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 students’ 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 FREEPercentage increase, or 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 in your savings account and by the end of the month you had you may want to find the percentage increase of the money you saved over the period of time.
Percentage decrease, or percent loss, is when the percent decreases, or gets smaller, between a starting percent and the final percent.
For example, buying a tank of gas last year was cheaper than it is now. You could calculate the percent decrease in the amount of a gallon of gas.
Percentage profit refers to when a store or person is selling a good or a service, and they want 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 a piece, but sells them to the students for The school store would make profit, or
Markups are the increased price of a good, and markdowns are the decreased price of a good.
Markdowns are more commonly known as discounts or sales in a retail store.
A company may markup an item that is in high demand, and people are willing to pay more money for it.
How does this relate to 7th grade math?
In order to calculate percent change, you need to:
The weight of a baby has increased from to Find the percentage difference in the baby’s weight.
The baby’s weight has increased from to Calculate the percent change:
2Plug numbers into the percent change formula.
The change is and the original number is Apply the percent change formula:
3Simplify the fraction, if necessary, using equivalent fractions.
does not need to be simplified.
4Convert the fraction to a decimal.
5Calculate percent change.
The final answer is percent change. The baby’s weight increased by
Anna bought a computer for years later, Anna sold the computer for
Calculate Anna’s percent loss.
Find the amount of change by subtracting the original number from the new number.
The initial price is and the new price is Calculate the change:
Plug numbers into the percent change formula.
The change is and the original price is Apply the percentage change formula:
Simplify the fraction, if necessary, using equivalent fractions.
can be simplified to
Convert the fraction to a decimal.
This is a repeating decimal, but you can round to to solve.
Calculate the percent change.
After selling the computer, Anna had a percent loss in the money she earned.
Matthew bought an antique for He sold it for Calculate Mattew’s percentage profit.
Find the amount of change by subtracting the original number from the new number.
The initial price is and the new price is Calculate the change:
Plug numbers into the percent change formula.
Simplify the fraction, if necessary, using equivalent fractions.
can be simplified to
Convert the fraction to a decimal.
Calculate the percent change.
Matthew earned a profit when selling the antique.
A clothing shop reduced the price of a jacket from to Find the percentage decrease.
Find the amount of change by subtracting the original number from the new number.
The starting value is and the new value is Calculate the change:
Plug numbers into the percent change formula.
Simplify the fraction, if necessary, using equivalent fractions.
can be simplified to
Convert the fraction to a decimal.
Calculate the percent change.
The price of the jacket was decreased by
Sometimes, a product in a shop may be discounted twice, or the value of something may increase and then decrease. It is common to think that you can just add the percentage changes together, but this does not work.
For example, if something is reduced by in a sale and the sale price is then reduced by this does not mean a total reduction of This is because of the sale price is not the same as of the original price.
To calculate the total percent change after two percentage changes:
A television was priced at and was reduced by in a sale. weeks later, the sale price was reduced by Find the overall percentage reduction in price.
Apply the first percent change.
of
Apply the second percent change.
of
Calculate the percent change between the final value and the original value and plug numbers into the percent change formula.
The old value is and the new value is
Change:
Simplify the fraction, if necessary, using equivalent fractions.
can be simplified to
Convert the fraction to a decimal.
Calculate the percent change.
The television price has decreased by over the two weeks.
Holly bought a diamond ring for in By the value of the ring had decreased by By the value of the ring had increased by from its value in
Find the overall percentage change in the value of the diamond ring.
Apply the first percent change.
of
Apply the second percent change.
of
Calculate the percent change between the final value and the original value and plug numbers into the percent change formula.
Change:
Simplify the fraction, if necessary, using equivalent fractions.
can be simplified to
Convert the fraction to a decimal.
Calculate the percent change.
The value of Holly’s diamond ring increased by .
Calculate the percent change that has occurred in each of these questions.
1. increased to
First, you will calculate the change from to
The change is so you can now plug the numbers into the percent change formula.
After simplifying the fraction to you would convert it to the decimal
2. reduced to
First, you will calculate the change from to
The change is so you can now plug the numbers into the percent change formula.
is in simplest terms, you would convert it to the decimal rounded to two decimal places.
3. increased to
First, you will calculate the change from to
The change is so you can now plug the numbers into the percent change formula.
After simplifying the fraction to you would convert it to the decimal
4. reduced to
First, you will calculate the change from to
The change is so you can now plug the numbers into the percent change formula.
After simplifying the fraction to you would convert it to the decimal
5. increased by and then increased again by a further
First, you will apply the first percent change, a increase to
of
Next, apply the second percent change, a increase to
of
The overall change is so you can now plug the numbers into the percent change formula.
After simplifying the fraction to you would convert it to the decimal
6. increased by and then decreased by
decrease
increase
decrease
increase
First, you will apply the first percent change, a increase from
of
Next, apply the second percent change, a decrease from
of
The overall change is so you can now plug the numbers into the percent change formula.
After simplifying the fraction to you would convert it to the decimal
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.
You use the same formula whether you are finding the percentage increase or decrease. With both, you are calculating the percentage to which the measure either increases or decreases.
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