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UCAT Quantitative Reasoning skill

Identify the base value before touching the calculator.

A practical method for percentage changes, reverse percentages and percentage-point comparisons.

UCAT candidatesMedical applicantsDental applicants

Name the original value

Percentage change compares the difference with the original value: change divided by original, multiplied by 100. The denominator is the value you started from, not automatically the smaller number. Mark the starting period or group before copying figures from a table.

  • Change = new minus original
  • Divide by original
  • Multiply by 100

Separate percentage points from percentage change

If a rate rises from 20% to 25%, the increase is 5 percentage points. Relative to the original 20%, it is a 25% increase. Both numbers can be correct, so the wording decides which one is required. Look for “percentage points” explicitly.

  • Point change: subtract the percentages
  • Percentage change: divide the difference by the original percentage

Worked example: keep the base visible

Appointments rise from 480 to 540. The change is 60 and the original is 480, so 60 ÷ 480 × 100 = 12.5%. Dividing by 540 would measure the increase as a share of the new value and answer a different question.

  • Original 480
  • Change 60
  • 60 ÷ 480 = 0.125
  • Answer 12.5%

Handle decrease signs and wording

For a decrease, calculate original minus new when the answer expects a positive decrease percentage. If a question asks for signed change, new minus original will be negative. Decide the required form before calculating so a correct magnitude is not paired with the wrong direction.

  • Increase and decrease need a direction
  • Read the answer units
  • Do not drop a minus sign accidentally

Use multipliers for reverse percentages

After a 20% increase, the new value equals original × 1.20. To recover the original, divide the new value by 1.20 rather than subtracting 20% of the new number. Increases and decreases are based on different starting values, so equal percentages do not simply cancel.

  • Increase multiplier: 1 + rate
  • Decrease multiplier: 1 - rate
  • Reverse by dividing by the multiplier

Estimate before selecting

Round the change and base enough to predict the scale. A rise of about 60 on a base near 500 is a little above 10%, so 1.25% or 125% should be rejected immediately. Estimation catches keypad errors and often eliminates options before exact calculation.

  • Predict order of magnitude
  • Check denominator
  • Confirm whether the answer is a percent or points

Frequently asked questions

What is the formula for percentage change?

Change divided by the original value, multiplied by 100.

What is a percentage-point change?

It is the arithmetic difference between two percentages.

How do I reverse a percentage increase?

Divide the final value by one plus the percentage rate written as a decimal.

Which value is the denominator?

Use the original or baseline value identified by the question.

Editorial information

Prepared by LearnVello editorial team · Last reviewed · Read our editorial standards

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