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Math5-10 minutesStep-by-step guide

How to calculate a percentage change

Calculating percentage change involves finding the difference between a starting and ending value, then expressing this difference as a percent of the starting value. This is useful for measuring increases or decreases in quantities such as prices or populations.

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What you need

  • Original value (e.g., old price)
  • New value (e.g., new price)
  • Calculator (for quick computation)
  • Paper or digital note to record answer

Every step

  1. 1

    Write down original and new values

    Record the starting and ending values. For example, the price of a shirt was $40 and is now $50. Clearly mark which is the original and which is the new value.

    CHECKPOINT · Original and new values clearly identified.
  2. 2

    Calculate the absolute difference

    Subtract the original value from the new value: $50 - $40 = $10. This is the change in value. Negative results indicate a decrease.

    CHECKPOINT · Difference (positive or negative) calculated (e.g., $10).
  3. 3

    Divide the difference by the original value

    Take the difference and divide by the original value: $10 / $40 = 0.25. This ratio represents the proportional change before converting to a percentage.

    CHECKPOINT · Resulting decimal found (e.g., 0.25).
  4. 4

    Multiply by 100 to get the percentage

    Convert the result to a percentage: 0.25 * 100 = 25%. The percentage change from $40 to $50 is +25%.

    CHECKPOINT · Percentage change calculated (e.g., 25%).
  5. 5

    Label as increase or decrease

    If the difference was negative, label the percent change as a decrease. For example, if price drops from $50 to $40: $40-$50 = -$10; -$10/$50 = -0.20; -0.20 x 100 = -20%, or 20% decrease.

    CHECKPOINT · Change correctly labeled as increase or decrease.

Common mistakes

  • Always divide by the original value, not the new value.
  • Ignoring the sign may lead to misunderstanding direction of change.

Finished when

Percentage change clearly marked as an increase or decrease with supporting calculation.

Questions about this task

What if the original value is zero?

Percentage change can't be computed if the original value is zero since you can’t divide by zero. Consider showing an absolute change instead.

Can percentage change exceed 100%?

Yes, if the increase is greater than the original value, percentage change exceeds 100%. For example, from $40 to $90: (90-40)/40 = 1.25, or 125% increase.

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