GANITA PRAKASH · GRADE 8 · PART II · CHAPTER 1
BEYOND — Percentages greater than 100
Think first. Use AI purposefully. Verify always.
DISCOVER
Begin with a prediction.
A shop targets ₹5000 but sells ₹6000. Must its achievement stop at 100%?
Sketch or write an independent attempt before reading on. Test your idea using the model.
Understand
100% is one whole. A percentage above 100 describes more than one copy of the reference whole; it is not automatically an error.
Key Ideas
250% of an original amount means a 150% increase, not a 250% increase.
Visualise
Beyond one whole
Predict first. Change the controls, then compare your reasoning.
150% is 1.5 wholes. That is 50% above one whole.
Method
Divide the compared quantity by the reference whole, then multiply by 100. Distinguish percentage of the original from percentage increase.
Worked Example
Given
A sales target is ₹5000; sales are ₹6000.
To Find
Sales as a percentage of the target
Reasoning
Target is the reference whole.
Solution
- × 100 = 120%.
- The excess is 20% of the target.
Result
Sales reached 120% of the target.
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 harvest rises from 260 kg to 650 kg. Express the new harvest as a percentage of the old and state the increase.
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 11