Mathematics
Grade 10
15 min
Percent of change
Percent of change
What you'll learn
- Calculate the percent increase or decrease between two given values using the formula and express the result as a percentage with correct rounding to the nearest tenth.
- Identify whether a given scenario represents a percent increase or a percent decrease based on the context provided in a word problem.
- Solve real-world problems involving percent of change, such as calculating discounts, markups, or inflation, and explain the meaning of the calculated percentage in the context of the problem.
- Explain the difference between percent of increase and percent of decrease using examples and compare and contrast their applications in everyday situations.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Calculate the percent of change (increase or decrease) between two values.
Solve for an original or new value when given the other value and the percent of change.
Apply the concept of percent change to geometric measurements, such as the side length, area, and volume of figures.
Analyze and solve problems involving multiple or sequential percent changes.
Critically interpret percent of change in real-world contexts, including financial data and geometric scaling.
Formulate and solve algebraic equations representing percent of change scenarios.
Ever see a stock price jump 15% in a day and wonder how much money was actually made? 📈 Let's explore the mathematics behind these dynamic changes.
This tutorial will teach you how to calculate and interpret...
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Key Concepts & Vocabulary
TermDefinitionExample
Percent of ChangeA measure of how much a quantity has changed relative to its original amount, expressed as a percentage.If a city's population grows from 50,000 to 55,000, the percent of change is a 10% increase.
Original Amount (Base)The starting value or base amount before any change occurs. This is the denominator in the percent of change formula.A video game console originally costs $500 before a sale.
New AmountThe value of a quantity after a change has occurred.During a sale, the $500 console now costs $450.
Amount of ChangeThe absolute difference between the new amount and the original amount.The amount of change for the console is |$450 - $500| = $50.
Percent IncreaseA percent of change where the new amount is greater than the original amount.A salary i...
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Core Formulas
General Formula for Percent of Change
P = \frac{\text{New Amount} - \text{Original Amount}}{\text{Original Amount}} \times 100
Use this to find the percent of change when you know the starting and ending values. A positive result indicates an increase, while a negative result indicates a decrease.
Formula for Finding the New Amount
\text{New Amount} = \text{Original Amount} \times (1 + \frac{P}{100})
Use this to calculate the final value after a percent change (P). Use a positive P for an increase and a negative P for a decrease.
Formula for Finding the Original Amount
\text{Original Amount} = \frac{\text{New Amount}}{1 + \frac{P}{100}}
Use this to work backward and find the starting value when you know the final value and the percent change (P).
4 more steps in this tutorial
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Challenging
The radius of a sphere is increased by 10%. By what percent does its volume increase? (Volume of a sphere = (4/3)πr³)
A.10%
B.30%
C.33.1%
D.21%
Challenging
The length of a rectangle is increased by p% and the width is decreased by p%. This causes the area of the rectangle to decrease by 16%. What is the value of p?
A.16
B.20
C.30
D.40
Challenging
An investment doubles in value. The new value is then decreased by X%. If the final value is 50% more than the original investment, what is the value of X?
A.25
B.33.3
C.50
D.75
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Frequently asked questions
What grade level is "Percent of change"?
Percent of change is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Percent of change?
You'll be able to: Calculate the percent increase or decrease between two given values using the formula and express the result as a percentage with correct rounding to the nearest tenth; Identify whether a given scenario represents a percent….
Is "Percent of change" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Percent of change?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.