Solve multi-step percent problems in context using proportional reasoning, including simple interest, tax, gratuities,
commissions, fees, markups and markdowns, percent increase, and percent decrease.
Arkansas Academic Standards:
7.RP.A.3
Use proportional relationships to solve multi-step ratio and percent problems
Note: Examples include but are not limited to simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease.
Arizona - K-12 Academic Standards:
7.RP.A.3
Use proportional relationships to solve multi-step ratio and percent problems (e.g., simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error).
Common Core State Standards:
Math.7.RP.3 or 7.RP.A.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.
Georgia Standards of Excellence (GSE):
MGSE7.RP.3
Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, and fees.
Louisiana Academic Standards:
7.RP.A.3
Use proportional relationships to solve multi-step ratio and percent problems of simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, and percent error.
North Carolina - Standard Course of Study:
7.RP.3
Use scale factors and unit rates in proportional relationships to solve ratio and percent problems.
New York State Next Generation Learning Standards:
7.RP.3
Use proportional relationships to solve multi-step ratio and percent problems. Note: Examples of percent problems include: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, and percent error.
Wisconsin Academic Standards:
7.RP.A.3
Use proportional relationships to solve multi-step ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
Pennsylvania Core Standards:
CC.2.1.7.D.1
Analyze proportional relationships and use them to model and solve real-world and mathematical problems.
Pennsylvania Core Standards:
M07.A-R.1.1.6
Use proportional relationships to solve multi-step ratio and percent problems.
7th Grade Math - Ratio & Percent Problems Lesson
A percent can be used to represent the ratio between two quantities. A percent of a number can be found by multiplying the percent by the number.
Percents can be used to find:
Simple interest
Tax
Markups
Discounts
Gratuities
Commissions
Fees
Percent increase and decrease
Percent error
Example:
The sales tax is 7.5% of $55.60. First, multiply 7.5% by $55.60 to find the sales tax.
7.5% × $55.60
=
0.075 × $55.60
=
$4.17
Then, add the sales tax to the cost of the clothes.
$55.60 + $4.17 = $59.77
So, Summer spent $59.77 with tax included.
Example:
First, find the decrease in the number of employees.
125 - 105 = 20
Then, find the percent decrease by dividing the decrease by the original number of employees.
20 ÷ 125
=
0.16
=
16%
So, the number of employees at the company decreased by 16%.
Percent error is used to show how far an experimental value is from an actual or expected value.
Percent error can be found using the formula below.
Example:
Substitute the experimental and expected, or actual, values into the percent error formula.
So, the percent error is 14%.
The simple interest earned from an investment can be calculated by multiplying the amount invested, interest rate, and time.
interest
=
amount invested
×
interest rate
×
time
Example:
Multiply the amount invested, interest rate, and time to find the interest.
interest
=
amount invested
×
interest rate
×
time
=
$350
×
0.04
×
6 years
=
$84
So, the interest is $84.
A proportion can be used to solve a problem with two equal ratios.
Example:
Set up a proportion to represent the situation. Let p represent the unknown number of passengers.
Cross multiply, then solve.
So, 40 passengers can be on the track at one time.
7th Grade Math - Ratio & Percent Problems Lesson