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CLASS VIII • FRACTIONS IN DISGUISESmart Lab: Percentages, FDP Trio & Change

Fractions in Disguise: Percentage Lab

Explore percentages as “out of 100”, convert between fractions-decimals-percentages, calculate percentages of quantities, compare proportions, and model percentage increase/decrease.

Fact Sheet: What is a Percentage?

Per cent means per hundred. So, 25% means 25 out of every 100.

Fraction to Percentage: Multiply the fraction by 100. Example: 3/4 × 100 = 75%.
Percentage of a Quantity: y% of z = (y/100) × z. Example: 35% of 95 = 33.25.
FDP Trio: 50% = 50/100 = 1/2 = 0.5. Fractions, decimals and percentages are three forms of the same idea.
More than 100%: 120% means 1.2 times the original value, or 20% more than the whole.
75% = 3/4

Formula Hub

Percent as Fraction

z% = z/100

24% = 24/100 = 6/25

Fraction to Percent

a/b = (a ÷ b) × 100%

2/5 = 40%

Percent of Quantity

y% of z = y/100 × z

25% of 120 = 30

Find Whole

If p% is value v, whole = v × 100 / p

40% is 92 → whole = 230

Percentage Change

Change% = change/original × 100

30 to 42: increase = 40%

Compare Proportions

Convert both to percentages.

42/50 = 84%; 70/80 = 87.5%

percentage = part ÷ whole × 100

Interactive Lab: Percentage Solver

Score: 0Current Streak: 🔥 0Badge: Percentage Explorer


Activity Zone

🔁 FDP Converter

Enter a fraction and convert it into percentage and decimal form.

75%

🧮 Percentage of a Quantity

Find y% of z and view it on a bar model.

25%

🚴 Journey Bar Model

If p% of a journey is covered and equals d km, find total and remaining distance.

92 km

📈 Percentage Increase / Decrease

Compare original and new values.

🎯 Target Achievement > 100%

Useful for sales targets, goals, and harvest comparisons.

120%

⚖️ Compare Two Scores

Convert both to percentages before comparing.

Worksheet Generator

Generate practice on fraction-to-percent conversion, percent of a quantity, percentage change, and comparing proportions.



Real-World Use

Shopping: Discounts like “50% off” mean half of the marked price is reduced.
Food Labels: Percentages help compare ingredients across different packet sizes.
School Marks: Scores from tests with different maximum marks can be compared by converting to percentages.
Targets: 120% of a target means the goal was exceeded by 20%.

🌍 Real-Life Case Generator

Teacher Tools

Learning Outcomes

  • Explain that percent means out of 100.
  • Convert among fractions, decimals, and percentages.
  • Find percentage of a quantity using bar models, fractions, decimals, or proportional reasoning.
  • Compare proportions by converting to percentages.
  • Interpret percentages greater than 100 and percentage increase/decrease.

Exit Ticket Prompts

  • Why is 25% the same as one-fourth?
  • Find 40% of 230 mentally and explain your method.
  • A score is 42/50 and another is 70/80. Which is better and why?
  • Give an example where comparing only percentages is misleading.

Common Misconceptions

  • Comparing percentages without checking the whole quantity.
  • Thinking percentages cannot exceed 100.
  • Using the new value instead of original value as the base in percentage change.