Fractions in Disguise
NCERT Class 8 Maths • Chapter 8
What is "Fractions in Disguise" about? (Class 8 Maths)
NCERT Class 8 Maths Chapter 8 (Ganita Prakash Part 2) explores percentages, discounts, profit and loss, and simple interest — all of which are applications of fractions. This CBSE chapter helps students recognise fractions hidden in everyday financial and commercial contexts, developing real-world problem-solving skills. Students learn to calculate percentages, compare quantities, and understand basic financial literacy.
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Fractions in Disguise: Key Terms & Definitions
- Percentage
- A fraction or ratio expressed as a part of 100; denoted by %; e.g., 25% means 25 out of 100, or 25/100 = 1/4.
- Profit and Loss
- In commerce, profit occurs when selling price > cost price; loss occurs when selling price < cost price. Profit/Loss % is calculated on the cost price.
- Discount
- A reduction in the marked price of an item; Discount % = (Discount/Marked Price) × 100. The price after discount is the selling price.
- Simple Interest
- Interest calculated only on the principal amount (not on accumulated interest): SI = (P × R × T) / 100, where P = principal, R = rate % per annum, T = time in years.
- Principal
- The initial sum of money borrowed or invested before interest is applied.
- Cost Price (CP)
- The price at which a seller purchases an item; profit or loss is calculated relative to the cost price.
- Selling Price (SP)
- The price at which a seller sells an item to the buyer; determines whether profit or loss is made.
Frequently Asked Questions
What is the formula for profit and loss percentage Class 8?
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Profit % = (Profit / Cost Price) × 100, where Profit = SP - CP. Loss % = (Loss / Cost Price) × 100, where Loss = CP - SP. Both profit and loss percentages are always calculated on the cost price (CP), not the selling price. Example: CP = ₹500, SP = ₹600; Profit = ₹100; Profit% = (100/500)×100 = 20%.
How do you calculate simple interest Class 8 Maths?
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Simple Interest (SI) = (P × R × T) / 100, where P = Principal (initial amount), R = Rate of interest per year (%), T = Time in years. Amount (A) = P + SI. Example: P = ₹1000, R = 5%, T = 3 years; SI = (1000 × 5 × 3)/100 = ₹150; Amount = ₹1150.
What is the difference between marked price and selling price Class 8 NCERT?
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Marked Price (MP) is the price printed on the item (list price). Selling Price (SP) is what the buyer actually pays after any discount. Selling Price = Marked Price - Discount. Discount % = (Discount / Marked Price) × 100. If there is no discount, SP = MP.
How do you convert fractions to percentages and back Class 8?
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To convert a fraction to a percentage: multiply by 100%. Example: 3/4 = (3/4) × 100% = 75%. To convert a percentage to a fraction: divide by 100 and simplify. Example: 35% = 35/100 = 7/20. To convert a percentage to a decimal: divide by 100. Example: 45% = 0.45. NCERT Class 8 Chapter 8 uses these conversions extensively.
How do you find the original price before discount Class 8?
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If an item costs ₹x after a y% discount, find the original (marked) price: SP = MP × (1 - y/100), so MP = SP / (1 - y/100). Example: A shirt costs ₹800 after a 20% discount. MP = 800 / (1 - 0.20) = 800 / 0.80 = ₹1000. So the original price was ₹1000.
What is the difference between simple and compound interest Class 8?
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Simple Interest (SI) is calculated only on the principal for the entire period: SI = PRT/100. Compound Interest (CI) is calculated on the principal plus accumulated interest (interest on interest). While Class 8 focuses mainly on simple interest, it introduces compound interest conceptually. CI grows faster than SI over time.
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