GANITA PRAKASH · GRADE 8 · PART II · CHAPTER 1
FIND — Percentage of a quantity
Think first. Use AI purposefully. Verify always.
DISCOVER
Begin with a prediction.
Which contains more sugar: 120 g at 25%, or 95 g at 35%? Does the larger percentage settle it?
Sketch or write an independent attempt before reading on. Test your idea using the model.
Understand
A percentage is a multiplier applied to a specified whole. A larger percentage of a smaller whole need not produce a larger amount.
Key Ideas
Do not compare percentage amounts without checking both wholes.
Visualise
A percentage of a whole
Predict first. Change the controls, then compare your reasoning.
Bar scale: 0% to 200%. The midpoint marks 100%, which corresponds to 120 units.
Method
Estimate the amount first. Convert the percentage to a fraction or decimal, multiply by the whole, and retain the unit.
Worked Example
Given
120 g biscuits contain 25% sugar; 95 g biscuits contain 35% sugar.
To Find
Sugar mass in each packet
Reasoning
Percentage amount = percentage ÷ 100 × whole.
Solution
- First packet: 0.25 × 120 = 30 g.
- Second packet: 0.35 × 95 = 33.25 g.
- 33.25 − 30 = 3.25 g.
Result
The second packet contains 3.25 g more sugar.
AIMS Method
- A — Attempt independently
Estimate and predict first. - I — Investigate the idea
Identify the whole and the percentage base. - M — Make connections
Connect fractions, decimals, bars and multipliers. - S — Scrutinise your reasoning
Check units, bases and the reasonableness of the result.
Think first. Use AI purposefully. Verify always.
Focused Practice
A test is marked out of 75. What mark represents 80%? Predict a sensible range first.
Check & Feedback
Name the whole, explain the method and give one check that would catch a wrong percentage base.
Textbook connection: Ganita Prakash · Grade 8 · Part II · Fractions in Disguise · printed page 6