GANITA PRAKASH · GRADE 8 · PART II · CHAPTER 1
CHANGE — Percentage increase and decrease
Think first. Use AI purposefully. Verify always.
DISCOVER
Begin with a prediction.
Attendance falls from 160 to 100. Should the decrease be measured against 160 or 100?
Sketch or write an independent attempt before reading on. Test your idea using the model.
Understand
Percentage change compares the difference with the original value. A reverse change has a different base.
Key Ideas
Using the new value as the denominator answers a different question. A rise of 20% followed by a fall of 20% does not cancel.
Visualise
Original → change → new
Predict first. Change the controls, then compare your reasoning.
160→Change
-60→New
100
Signed percentage change:
Signed percentage change ≈ -37.5%. The denominator stays 160, the original.
Method
Find new minus original. Divide by the positive original value and multiply by 100. A negative signed change means a decrease.
Worked Example
Given
Attendance falls from 160 to 100.
To Find
Percentage decrease in attendance
Reasoning
Decrease percentage = decrease ÷ original × 100.
Solution
- Decrease = 160 − 100 = 60.
- × 100 = 37.5%.
Result
Attendance decreased by 37.5%.
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 price rises from ₹60 to ₹100. Find the exact percentage 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 16