Curriculum Core Rules & Strategy
Always write out given values and the relevant formula before substituting numbers.
Substitute your final answer back into the original problem to verify correctness.
Double-check negative signs, common denominators, and arithmetic order of operations.
Mastering Percentage Increase & Decrease with SolveCalc
Percentage change always uses the ORIGINAL value as the base: Change% = (New − Old)/Old × 100. This is different from finding what percentage a number is of another — the denominator is always the starting point.
Percentage Increase — The Formula and Intuition
Percentage increase measures how much a quantity has grown relative to its starting value.
Formula: % Increase = (Increase ÷ Original) × 100 = ((New − Old) ÷ Old) × 100
Increase = £25,000. % Increase = (25,000 ÷ 250,000) × 100 = 10%
The multiplier method is faster for applying increases: multiply the original by (1 + rate). A 10% increase → multiply by 1.10. A 25% increase → multiply by 1.25.
Percentage Decrease and Reverse Percentage
% Decrease = (Decrease ÷ Original) × 100 = ((Old − New) ÷ Old) × 100
Reverse percentage — finding the original price when you know the final price and the % change:
£39,000 represents 130% of original.
Original = 39,000 ÷ 1.30 = £30,000
Successive Percentage Changes
When percentage changes are applied one after another, use the multiplier method — multiply all multipliers together:
Multiplier: 1.20 × 0.80 = 0.96
Net change: −4% (not 0%!)
This shows why successive equal increases and decreases don't cancel out — the base changes after each step. A 20% increase raises the base, so the same 20% decrease removes a larger absolute amount.
Percentage Change — Three Exam-Style Problems
(96,600−84,000)/84,000 × 100 = 12,600/84,000 × 100 = 15%
£89.60 ÷ 1.12 = £80
0.90 × 1.20 = 1.08 → +8% net gain
% Change Errors That Cost Exam Marks
- Using new value as the base: % change always uses the ORIGINAL as denominator, not the new value. Using new value gives a different (wrong) percentage.
- Assuming successive changes add: A 20% increase then 20% decrease ≠ 0% change. Use multipliers.
- Reverse percentage error: If price after 25% increase is £75, original ≠ £75 − 25% = £56.25. Correct: £75 ÷ 1.25 = £60.
Percentage Change — Fast Recall Under Pressure
- Multiplier table to memorise: 10% increase → ×1.10; 15% → ×1.15; 25% → ×1.25; 20% decrease → ×0.80; 5% decrease → ×0.95.
- "Divide the multiplier" for reverse: Post-increase price ÷ multiplier = original. Always divide, never subtract the percentage.
- "Multiply multipliers for successive changes" — chain multiple % changes by multiplying their individual multipliers together.
SolveCalc's Percentage Calculator handles all types including reverse percentage.
Common Student Pitfalls & Exam Traps
- Skipping steps: Even experienced mathematicians write every step. Skipping creates opportunities for errors.
- Not checking answers: Always substitute your answer back to verify correctness.
- Confusing similar concepts: Small differences in definitions can require completely different approaches.
- Unit errors: Always keep track of units and convert consistently when working with real-world problems.
SolveCalc Insight
DEEP DIVESolveCalc provides free, browser-based math tools for students and educators at every level. Use our interactive calculators alongside this curriculum guide to verify your calculations and explore concepts hands-on — no sign-up, no downloads, no limits.
Explore with SolveCalc's Math Tools Library→Frequently Asked Questions
What is the percentage increase from 50 to 75? +
((75-50)/50) × 100 = 50%.
How do you reverse a percentage? +
To find original after a 20% increase that gives $60: 60 ÷ 1.20 = $50.