Quick Revision Notes: Class 7 Mathematics

Chapter: Comparing Quantities

Definition: Ratios are used to compare two quantities of the same kind. Two ratios are equivalent if their simplest forms are equal.
Key Point: To compare two ratios, convert them to like fractions (having the same denominator) or convert them into percentages.

Definition: Per cent means 'per hundred'. It is a fraction with denominator 100 and is denoted by the symbol %.
Converting Fraction to Percentage: Multiply the fraction by 100.
- Formula: Percentage = (Part / Whole) * 100
Converting Percentage to Fraction/Ratio: Remove the % sign and divide by 100.
- Formula: Fraction = Percentage / 100
Converting Decimal to Percentage: Multiply the decimal by 100 and put the % sign.

Finding Percentage of a Quantity:
- Formula: x% of Quantity = (x / 100) * Quantity
Converting Percentages to "How Many":
- Used to divide a quantity into given percentages (e.g., spending, saving).
Ratios to Percentages:
- Convert the parts of a ratio into fractions, then multiply each by 100 to get percentages. (Sum of parts becomes the denominator).

Cost Price (CP): The buying price of an article.
Selling Price (SP): The selling price of an article.
Profit (Gain): When SP > CP.
- Formula: Profit = SP - CP
Loss: When CP > SP.
- Formula: Loss = CP - SP
Profit Percentage: Calculated on the Cost Price.
- Formula: Profit % = (Profit / CP) * 100
Loss Percentage: Calculated on the Cost Price.
- Formula: Loss % = (Loss / CP) * 100

Principal (P): The original sum of money borrowed or lent.
Interest (I): Extra money paid by the borrower for using the money.
Rate (R): Interest charged per 100 rupees per year (usually expressed as % p.a. - per annum).
Time (T): The duration for which the money is borrowed/lent (in years).
Amount (A): The total money paid back at the end of the time period.
- Formula: Amount (A) = Principal (P) + Interest (SI)
Simple Interest Formula:
- Formula: SI = (P * R * T) / 100