How to use this guide
This guide will teach you how to calculate percentages, increases, and decreases. Work through each section and apply the formulas to practice problems.
Big idea: Percentages are a way of expressing a number as a fraction of 100. Increases and decreases are adjustments based on percentages.
Calculating a Percentage of a Number
To find a percentage of a number:
\[
\text{Percentage Value} = \frac{\text{Percentage}}{100} \times \text{Original Number}
\]
Examples:
- 20% of 350: \( \frac{20}{100} \times 350 = 70 \)
- 15% of $480: \( \frac{15}{100} \times 480 = 72 \)
Percentage Increase
To calculate a percentage increase:
\[
\text{New Value} = \text{Original Value} \times \left(1 + \frac{\text{Percentage Increase}}{100}\right)
\]
Example: A price increased by 25%. Original price = $200
\[
\text{New Price} = 200 \times \left(1 + \frac{25}{100}\right) = 200 \times 1.25 = 250
\]
Percentage Decrease
To calculate a percentage decrease:
\[
\text{New Value} = \text{Original Value} \times \left(1 - \frac{\text{Percentage Decrease}}{100}\right)
\]
Example: A price decreased by 10%. Original price = $150
\[
\text{New Price} = 150 \times \left(1 - \frac{10}{100}\right) = 150 \times 0.9 = 135
\]
Example Problems
Problem: Calculate the percentage increase from 80 to 100.
Step 1: Find the difference:
\[
\text{Increase} = 100 - 80 = 20
\]
Step 2: Calculate the percentage increase:
\[
\text{Percentage Increase} = \frac{20}{80} \times 100 = 25\%
\]
Answer: The percentage increase is 25%.
Mixed Practice
Problem 1: Find 30% of 250.
\[
\text{Percentage Value} = \frac{30}{100} \times 250 = 75
\]
Problem 2: A product costs $400 and its price rises by 12%. Find the new price.
\[
\text{New Price} = 400 \times \left(1 + \frac{12}{100}\right) = 400 \times 1.12 = 448
\]
Problem 3: A subscription decreases from $60 to $54. Find the percentage decrease.
\[
\text{Decrease} = 60 - 54 = 6
\]
\[
\text{Percentage Decrease} = \frac{6}{60} \times 100 = 10\%
\]
Test