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Percentage Increase and Decrease

Measuring Growth, Decline, and Change in the Real World

One of the most powerful applications of mathematics is measuring how things change over time. When a shop offers a discount, or when the population of a city grows, we describe that change using Percentage Increase and Decrease.

Using raw numbers can often be misleading. If a price goes up by $10, is that a lot? Well, if the item was $5, yes! If the item was $5,000, not really. Percentages allow us to standardize this change, giving us a true sense of scale.

1. The Concept of Change

Before we calculate the percentage, we must calculate the raw change. This is simply the difference between the new value and the old value.

  • Increase: New Value - Original Value.
  • Decrease: Original Value - New Value.

The key to all percentage change problems is the Original Value. We always compare the change to where we started.

2. The Universal Formula

Whether calculating an increase or a decrease, the logic remains the same.

Percentage Change = (Difference / Original Value) x 100

3. Calculating Percentage Increase

Percentage increase measures growth. It is used for markups, salary raises, and population growth.

Example: A ticket price rises from $40 to $50. What is the percentage increase?

  1. Find the Difference: $50 - $40 = $10.
  2. Identify the Original: The price started at $40.
  3. Divide: 10 / 40 = 0.25.
  4. Multiply by 100: 0.25 x 100 = 25%.

The price increased by 25%.

4. Calculating Percentage Decrease

Percentage decrease measures reduction. It is used for sales discounts, weight loss, and depreciation.

Example: A phone drops in price from $200 to $150. What is the percentage decrease?

  1. Find the Difference: $200 - $150 = $50.
  2. Identify the Original: The price started at $200.
  3. Divide: 50 / 200 = 0.25.
  4. Multiply by 100: 0.25 x 100 = 25%.

The price decreased by 25%.

5. The Multiplier Method (The Fast Way)

If you want to find the new price directly without finding the difference first, you can use "Multipliers." This is how professionals calculate change.

For Increase

If you increase a number by 20%, you end up with 100% + 20% = 120% of the original.

New Value = Original x 1.20

Example: Increase 50 by 20%.
50 x 1.20 = 60.

For Decrease

If you decrease a number by 20%, you are left with 100% - 20% = 80% of the original.

New Value = Original x 0.80

Example: Decrease 50 by 20%.
50 x 0.80 = 40.

6. Reverse Percentages (Working Backwards)

This is the trickiest part of percentage math. Sometimes you know the final price and the percentage change, but you need to find the Original Price.

Problem: A shirt is sold for $44 after a 10% increase. What was the original price?

Many students try to subtract 10% of $44, but that is wrong! The 10% was based on the old price, not the new one.

The Correct Method:

  • The new price ($44) represents 110% of the original price (100% + 10%).
  • So, Original x 1.10 = 44.
  • Divide by the multiplier: 44 / 1.10 = 40.

The original price was $40.

7. Conclusion

Percentage increase and decrease allows us to navigate a changing world. Whether you are calculating the interest on a loan, figuring out how much you saved on a sale, or analyzing stock market trends, mastering these calculations ensures you understand the true impact of the numbers changing around you.