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Percent Increase and Decrease

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Percent Increase and Decrease

Study Guide

Key Definition

The percentage of increase or decrease is calculated by finding the difference between the new and original numbers, then dividing by the original number and multiplying by 100: $\frac{\text{New Number} - \text{Original Number}}{\text{Original Number}} \times 100$

Important Notes

Percent increase is used when the new number is greater than the original.
Percent decrease is used when the new number is less than the original.
The formula for percent increase is: $\frac{\text{Increase}}{\text{Original Number}} \times 100$
The formula for percent decrease is: $\frac{\text{Decrease}}{\text{Original Number}} \times 100$
Cross-multiplication can be used to solve the proportion.

Mathematical Notation

$\frac{a}{b}$ means division of a by b

$+$ represents addition

$-$ represents subtraction

$\times$ or $*$ represents multiplication

$\div$ or $/$ represents division

Remember to use proper notation when solving problems

Why It Works

Understanding percent changes helps in analyzing changes over time, such as in finance and economics, using proportions.

Remember

Always compare the change to the original value to find the percent increase or decrease.

Quick Reference

Percent Increase Formula:$\frac{\text{Increase}}{\text{Original Number}} \times 100$

Percent Decrease Formula:$\frac{\text{Decrease}}{\text{Original Number}} \times 100$

Understanding Percent Increase and Decrease

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Video explanation of this concept

Beginner

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Beginner Explanation

Percent increase is calculated by finding the difference between the new and original numbers, then dividing by the original number and multiplying by 100: $\frac{\text{New Number} - \text{Original Number}}{\text{Original Number}} \times 100$

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Celia's salary increased from $3000$ to $3750$. What is the percent increase?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

James bought a used car for $\$1500$ and sold it for $\$1200$. What is the percent decrease in the car's value?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

A store reduced the price of an item from $\$100$ to $\$85$. Calculate the percent decrease.

Challenge Quiz

Single Choice Quiz

Advanced

A population of bacteria grows from $200$ to $500$ in a day. What is the percent increase?

Recap

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Review key concepts and takeaways