GCSE Maths Number - How to Solve: Percentage Increase and Decrease

How to Solve: Percentage Increase and Decrease

Complete Guide For GCSE/A-Level Physics, Chemistry, Biology

Introduction

"Mastering percentage increase and decrease lets you calculate drug dosages in medicine, energy efficiency in physics, and reaction yields in chemistry—worth up to 6 marks in a single GCSE exam question!"

WHAT YOU NEED TO KNOW FIRST

1. Basic percentages – How to find 10% of a number (divide by 10).
2. Decimal multiplication – Converting percentages to decimals (e.g., 25% = 0.25).
3. Rearranging equations – Solving for an unknown in simple formulas.

KEY TERMS & FORMULAS

Key Terms

• Original value – The starting number before any change.
• New value – The number after the increase or decrease.
• Percentage change – The amount of change expressed as a percentage of the original.

Formulas

1. Percentage Increase/Decrease Formula
   [
   \text{Percentage Change} = \left( \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \right) \times 100
   ]
2. MEMORISE THIS – Used in almost every question.

3. Variables:

   • New Value = Final amount after change.
   • Original Value = Starting amount.

4. Calculating New Value After Increase/Decrease
   [
   \text{New Value} = \text{Original Value} \times \left(1 + \frac{\text{Percentage Change}}{100}\right)
   ]

5. MEMORISE THIS – Use when given the original value and percentage change.

6. Example: A 20% increase on 50 → (50 \times (1 + 0.20) = 60).

7. Reverse Percentage (Finding Original Value)
   [
   \text{Original Value} = \frac{\text{New Value}}{1 + \frac{\text{Percentage Change}}{100}}
   ]

8. Given on exam sheet (but practice using it!).
9. Example: After a 25% increase, the new value is 125 → Original = ( \frac{125}{1.25} = 100 ).

STEP-BY-STEP METHOD

Step 1: Identify What You’re Given

• Are you given the original value and percentage change? → Use New Value formula.
• Are you given the new value and percentage change? → Use Reverse Percentage formula.
• Are you given both values and asked for the percentage change? → Use Percentage Change formula.

Step 2: Convert Percentage to Decimal (If Needed)

• Divide the percentage by 100.
• Example: 15% → 0.15.

Step 3: Plug Values into the Correct Formula

• Follow the formula exactly. No shortcuts!

Step 4: Calculate and Check Units

• If the question asks for a percentage, add the % sign.
• If it asks for a value, include units (e.g., grams, joules).

Step 5: Verify Your Answer

• Does it make sense?
• A 50% increase on 100 should give 150, not 50.
• A 20% decrease on 80 should give 64, not 100.

WORKED EXAMPLES

Example 1 – Basic (Percentage Increase)

Question: A plant grows from 30 cm to 36 cm. What is the percentage increase?

Step 1: Identify what’s given. - Original Value = 30 cm - New Value = 36 cm

Step 2: Use the Percentage Change formula. [ \text{Percentage Increase} = \left( \frac{36 - 30}{30} \right) \times 100 ]

Step 3: Calculate. [ = \left( \frac{6}{30} \right) \times 100 = 0.2 \times 100 = 20\% ]

What we did and why: - We used the Percentage Change formula because we had both the original and new values. - The answer is 20%, meaning the plant grew by 20% of its original height.

Example 2 – Medium (Reverse Percentage)

Question: After a 15% increase, a chemical’s mass is 230 g. What was its original mass?

Step 1: Identify what’s given. - New Value = 230 g - Percentage Increase = 15%

Step 2: Use the Reverse Percentage formula. [ \text{Original Value} = \frac{230}{1 + \frac{15}{100}} = \frac{230}{1.15} ]

Step 3: Calculate. [ = 200 \text{ g} ]

What we did and why: - We used reverse percentage because we knew the new value and the percentage change. - The original mass was 200 g before the 15% increase.

Example 3 – Exam-Style (Disguised Question)

Question: A battery’s voltage drops from 9V to 7.2V. What is the percentage decrease? (3 marks)

Step 1: Identify what’s given. - Original Value = 9V - New Value = 7.2V

Step 2: Use the Percentage Change formula. [ \text{Percentage Decrease} = \left( \frac{9 - 7.2}{9} \right) \times 100 ]

Step 3: Calculate. [ = \left( \frac{1.8}{9} \right) \times 100 = 0.2 \times 100 = 20\% ]

What we did and why: - The question disguised the percentage decrease by not explicitly asking for it. - We recognised it was a percentage change problem and applied the formula. - The answer is 20% decrease.

COMMON MISTAKES

EXAM TRAPS

1-MINUTE RECAP

"Right, listen up—this is your last-minute cheat sheet for percentage increase and decrease. First, memorise the two key formulas: 1. Percentage Change = (New - Original) / Original × 100 2. New Value = Original × (1 ± % change as a decimal)

If you’re given the new value and need the original, use reverse percentage—divide by (1 + % increase) or (1 - % decrease).

Common mistakes? Dividing by the wrong number, forgetting to convert % to decimal, or mixing up increase and decrease. Always check: Does your answer make sense? A 50% increase on 100 should be 150, not 50!

Exam traps? Watch for two-step changes (e.g., first increase, then decrease) and reverse percentage questions. Don’t assume they cancel out—calculate each step!

Now go smash those questions!"