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 How to Calculate Percentage with SolveCalc
A percentage is a ratio expressed as parts per hundred. The master formula is: Percentage = (Part ÷ Whole) × 100. Every percentage problem is a variation of this one formula.
The Three Types of Percentage Problem
All percentage problems fall into exactly three types. Recognising which type you have determines the formula to use:
- Type 1 — Find the percentage: "What % of 80 is 20?" → (20 ÷ 80) × 100 = 25%
- Type 2 — Find the part: "What is 35% of 120?" → (35/100) × 120 = 42
- Type 3 — Find the whole: "18 is 30% of what number?" → 18 ÷ (30/100) = 60
All three use the same triangle relationship: Part = (Percentage/100) × Whole. Cover any one variable with your thumb — the remaining two give you the operation needed.
Fast Percentage Shortcuts Without a Calculator
These mental shortcuts let you estimate percentages instantly:
- 10% shortcut: Move the decimal point one place left. 10% of 350 = 35.
- 5% shortcut: Find 10%, then halve it. 5% of 240 → 10% = 24 → 5% = 12.
- 1% shortcut: Move decimal two places left. 1% of 4,500 = 45.
- Build complex percentages: 17.5% = 10% + 5% + 2.5%. Calculate each part and add.
- Commutative property: x% of y = y% of x. So 4% of 75 = 75% of 4 = 3. Use whichever is easier.
Solving Any Percentage Problem Systematically
- Identify which of the three values (Part, Whole, Percentage) is unknown
- Write the formula: Part = (Percentage ÷ 100) × Whole
- Substitute the two known values
- Solve for the unknown by algebraic rearrangement
- Check: verify all three values satisfy the triangle relationship
The £85 is 85% of the original (100% − 15% = 85%).
85 = (85/100) × Whole → Whole = 85 ÷ 0.85 = £100
Three Percentage Calculations — Solved in Full
(54 ÷ 72) × 100 = 0.75 × 100 = 75%
(22/100) × 360 = 0.22 × 360 = £79.20
36 = 20% of Whole → Whole = 36 ÷ 0.20 = £180
Percentage Calculation Errors to Eliminate
- Using the wrong whole: For "% increase," the whole is the ORIGINAL value, not the new one. Percentage increase = (increase ÷ original) × 100.
- Forgetting to convert % to decimal: 35% of 80 means 0.35 × 80 = 28, NOT 35 × 80.
- Successive percentage errors: A 20% increase followed by a 20% decrease does NOT return to the original. 100 → 120 → 96. Net change = −4%.
- Rounding too early: Keep full precision until the final step — early rounding compounds errors.
Never Forget Percentage Formulas
- "IS over OF times 100": "What % of 80 IS 20?" → 20/80 × 100 = 25%. The "IS" value goes on top; the "OF" value on the bottom.
- Multiplier method: A 30% increase → multiply by 1.30. A 15% decrease → multiply by 0.85. This handles combined discounts elegantly: 20% then 10% off = × 0.80 × 0.90 = × 0.72 = 28% total discount.
Use SolveCalc's Percentage Calculator to solve all three types instantly with full working.
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 basic percentage formula? +
Percentage = (Part ÷ Whole) × 100.
How do you find 30% of 250? +
250 × 0.30 = 75.