Last updated on August 5th, 2025
Relative change is a measure in mathematics that describes the change in a quantity relative to its original value. It is often expressed as a percentage. In this topic, we will learn the formula for calculating relative change.
Relative change helps to understand the proportional change in a quantity. Let’s learn the formula to calculate relative change.
The relative change is calculated using the formula: [ text{Relative Change} = frac{text{New Value} - text{Original Value}}{text{Original Value}} times 100\% ]
This formula calculates the change between the new and original values as a percentage of the original value.
In mathematics and real life, the relative change formula is crucial for analyzing data. Here are some important aspects of relative change:
- It helps compare changes in different datasets, even if they have different scales.
- Understanding relative change is vital in fields like finance, economics, and science, where percentage changes are more meaningful than absolute changes.
- By learning this formula, students can better understand concepts like growth rates, inflation rates, and percentage increases or decreases.
Students often find math formulas tricky and confusing. Here are some tips and tricks to master the relative change formula:
- Remember the sequence: subtract the original from the new, divide by the original, then multiply by 100.
- Connect the use of the relative change formula with real-life data, such as changes in stock prices, temperature differences, or population growth
- Use flashcards to memorize the formula and rewrite it for quick recall, and create a formula chart for quick reference.
In real life, the relative change formula plays a significant role in understanding data. Here are some applications:
- In finance, to calculate the percentage change in stock prices or investment returns.
- In economics, to determine inflation rates by comparing current and previous price levels.
- In environmental science, to assess changes in climate data, like temperature or sea level variations over time.
Students make errors when calculating relative change. Here are some mistakes and ways to avoid them:
If a stock price increases from $50 to $60, what is the relative change?
The relative change is 20%
To find the relative change, subtract the original price from the new price: $60 - $50 = $10 Then divide by the original price: $10/$50 = 0.2 Finally, multiply by 100 to convert to a percentage: 0.2 × 100 = 20%
A town's population decreased from 10,000 to 9,500. What is the relative change?
The relative change is -5%
First, subtract the new population from the original population: 9,500 - 10,000 = -500 Then divide by the original population: -500/10,000 = -0.05 Lastly, multiply by 100 for the percentage: -0.05 × 100 = -5%
A car's value depreciates from $20,000 to $18,000. Calculate the relative change.
The relative change is -10%
Subtract the new value from the original value: $18,000 - $20,000 = -$2,000 Divide by the original value: -$2,000/$20,000 = -0.1 Multiply by 100 for the percentage: -0.1 × 100 = -10%
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