GANITA PRAKASH · GRADE 8 · PART II · CHAPTER 1
Visual Lessons
Think first. Use AI purposefully. Verify always.
UNMASK — What percentage means: per hundred
A hundred equal parts
Predict first. Change the controls, then compare your reasoning.
Fractions on a bar
Predict first. Change the controls, then compare your reasoning.
Decimal ≈ 0.75; percentage ≈ 75%. Display rounded to at most four decimal places. Each outlined piece is of a whole; 4 pieces make one whole.
CONVERT — Fractions, decimals and percentages
One value, three representations
Predict first. Change the controls, then compare your reasoning.
Decimal ≈ 0.75; percentage ≈ 75%. Display rounded to at most four decimal places. Each outlined piece is of a whole; 4 pieces make one whole.
FIND — Percentage of a quantity
A percentage of a whole
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Bar scale: 0% to 200%. The midpoint marks 100%, which corresponds to 120 units.
ESTIMATE — Mental strategies and reverse percentage
Build a mental percentage
Predict first. Change the controls, then compare your reasoning.
Bar scale: 0% to 200%. The midpoint marks 100%, which corresponds to 120 units.
10% is 12. Build 25% as 2 lots of 10% plus 5% (6). All pieces refer to the same whole.
Recover the whole
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Whole ≈ 230 units. The entire bar is 100%, not 92 units.
BEYOND — Percentages greater than 100
Beyond one whole
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150% is 1.5 wholes. That is 50% above one whole.
COMPARE — Compare proportions using percentages
Compare on a scale of 100
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First share ≈ 84%; second share = 87.5%. Compare proportions, not raw scores.
CHANGE — Percentage increase and decrease
Original → change → new
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160→Change
-60→New
100
Signed percentage change:
Signed percentage change ≈ -37.5%. The denominator stays 160, the original.
TRADE — Cost, selling price, discount and tax
Cost → marked price → selling price
Predict first. Change the controls, then compare your reasoning.
₹100→MP
₹150→SP
₹75
Loss on cost: 25%. Markup uses ₹100; discount uses ₹150.
A discount uses the marked price
Predict first. Change the controls, then compare your reasoning.
On a marked price of ₹1800, discount = ₹450; selling price = ₹1,350. Discount base: ₹1800.
Tax on the stated amount
Predict first. Change the controls, then compare your reasoning.
₹8250+Tax
₹1,485
Total = ₹9,735. Tax base is ₹8250. These are given educational rates, not advice about current tax rates.
GROW — Interest, decline and successive changes
Simple and compound growth
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| Period | Simple | Compound |
|---|---|---|
| 0 | 1000.00 | 1000.00 |
| 1 | 1100.00 | 1100.00 |
| 2 | 1200.00 | 1210.00 |
| 3 | 1300.00 | 1331.00 |
Each compound period multiplies the current amount by 1.1. Calculations retain full precision between periods.
A shrinking base
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| Period | Remaining |
|---|---|
| 0 | 1000.00 |
| 1 | 900.00 |
| 2 | 810.00 |
| 3 | 729.00 |
Each period retains 90% (factor 0.9). Calculations retain full precision between periods.
Successive changes multiply
Predict first. Change the controls, then compare your reasoning.
Overall discount = 44%. Multiply (0.7) × (0.8); the second discount uses 70 as its base.