GANITA PRAKASH · GRADE 8 · PART II · CHAPTER 1
Study Materials
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UNMASK — What percentage means: per hundred
A percentage expresses a share relative to a whole of 100 equal parts. Always identify what counts as the whole.
Name the whole. Write part ÷ whole. Scale the fraction to a denominator of 100 when possible, or multiply it by 100 to find the percentage.
Textbook connection: Ganita Prakash · Grade 8 · Part II · Fractions in Disguise · printed page 1
Worked example →CONVERT — Fractions, decimals and percentages
Fractions, decimals and percentages are different representations of a number. A recurring decimal may need an approximation; a fraction can preserve the exact value.
Fraction to decimal: divide numerator by denominator. Decimal to percentage: multiply by 100 and attach %. Percentage to decimal: divide by 100.
Textbook connection: Ganita Prakash · Grade 8 · Part II · Fractions in Disguise · printed page 8
Worked example →FIND — Percentage of a quantity
A percentage is a multiplier applied to a specified whole. A larger percentage of a smaller whole need not produce a larger amount.
Estimate the amount first. Convert the percentage to a fraction or decimal, multiply by the whole, and retain the unit.
Textbook connection: Ganita Prakash · Grade 8 · Part II · Fractions in Disguise · printed page 6
Worked example →ESTIMATE — Mental strategies and reverse percentage
Known percentages can be combined when they refer to the same whole. Reverse percentage recovers the whole from a known part and its percentage.
Build 15% as 10% + 5%, or 75% as three quarters. For a reverse problem, find 1% or divide the part by its decimal share.
Textbook connection: Ganita Prakash · Grade 8 · Part II · Fractions in Disguise · printed page 10
Worked example →BEYOND — Percentages greater than 100
100% is one whole. A percentage above 100 describes more than one copy of the reference whole; it is not automatically an error.
Divide the compared quantity by the reference whole, then multiply by 100. Distinguish percentage of the original from percentage increase.
Textbook connection: Ganita Prakash · Grade 8 · Part II · Fractions in Disguise · printed page 11
Worked example →COMPARE — Compare proportions using percentages
Normalising to a common whole of 100 compares proportions with different denominators. It does not make the actual totals equal.
Identify each denominator separately. Convert each share to a percentage. State whether the question asks about proportion or absolute quantity.
Textbook connection: Ganita Prakash · Grade 8 · Part II · Fractions in Disguise · printed page 14
Worked example →CHANGE — Percentage increase and decrease
Percentage change compares the difference with the original value. A reverse change has a different base.
Find new minus original. Divide by the positive original value and multiply by 100. A negative signed change means a decrease.
Textbook connection: Ganita Prakash · Grade 8 · Part II · Fractions in Disguise · printed page 16
Worked example →TRADE — Cost, selling price, discount and tax
CP is cost price, MP is marked price, and SP is selling price. Discount uses MP as base; trading profit or loss percentage uses CP. A stated tax rate applies to its specified taxable amount.
Follow the price journey in order. Identify the base at each arrow. Subtract other expenses to move from gross profit to net profit; a net-profit-on-revenue margin uses revenue, not CP.
Textbook connection: Ganita Prakash · Grade 8 · Part II · Fractions in Disguise · printed page 17
Worked example →GROW — Interest, decline and successive changes
Simple interest adds interest calculated on the original principal. Compounding applies each new rate to the updated amount. Repeated decline also changes the base.
p = original principal; t = whole years; r = annual rate as a decimal (10% → 0.10).
Annual compounding:
For a decline at decimal rate d, replace the factor by (1 − d). These models assume a constant stated rate and no additional deposits or withdrawals.
Convert the annual percentage rate to decimal r. Simple amount: p(1 + rt). Annual compound amount: p(1 + r) raised to t. For decline use a factor below 1; multiply factors for successive changes.
Textbook connection: Ganita Prakash · Grade 8 · Part II · Fractions in Disguise · printed page 22
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