Ratio

Welcome to Chapter 2 "Ratio" of the West Bengal Board Class 7 Mathematics syllabus. This chapter provides deep conceptual understanding of homogeneous ratio comparison, antecedents, consequents, ratios of greater and lesser inequalities, compound ratios, and proportionate division.

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🍵 The Purity of Ratios: Why Ratios Have No Units

Why do ratios have no units?

A ratio is a comparative measure expressing how many times one homogeneous quantity is contained within another. When two quantities of the exact same unit are divided, their measurement units cancel out completely, yielding a dimensionless, pure numerical relationship.

Why This Chapter Matters

Before You Begin (Prerequisites)

Simplification of fractions to lowest terms.
Unit conversions (e.g., years to months, rupees to paise).

What You Will Learn (Core Objectives)

Define a ratio and justify why it has no measurement unit.
Distinguish between antecedent and consequent, ratio of equality, greater inequality, and less inequality.
Compute inverse ratios and compound (mixed) ratios accurately.
Divide quantities proportionally in real-world arithmetic problems.

Chapter Roadmap & Progression

1 1. Fundamental Concept of Ratio

2 2. Classification of Ratios

Complete Concept Guide (100% Curriculum Coverage)

1. Fundamental Concept of Ratio

A ratio is a fraction that compares two quantities of the same kind measured in the same units.
Represented as $a : b = \frac{a}{b}$, where $a$ is the Antecedent (পূর্বপদ) and $b$ is the Consequent (উত্তরপদ).

2. Classification of Ratios

Ratio of Equality: Antecedent = Consequent ($a = b$, e.g. $1:1$).
Ratio of Less Inequality: Antecedent < Consequent ($a < b$, e.g. $3:5$). Value is $< 1$.
Ratio of Greater Inequality: Antecedent > Consequent ($a > b$, e.g. $7:2$). Value is $> 1$.
Inverse Ratio: Inverse of $a:b$ is $b:a$.
Compound (Mixed) Ratio: Product of antecedents : Product of consequents. For $a:b$ and $c:d$, it is $(a \times c) : (b \times d)$.

Key Formulas, Identities & Theorems

Ratio Form

$$a : b = \frac{a}{b}$$

Dimensionless pure number

Inverse Ratio

$$a : b \rightarrow b : a$$

Antecedent and consequent swap

Compound Ratio

$$(a \times c) : (b \times d)$$

Multiplication of antecedents : consequents

Conceptual Solved Examples & Case Studies

Example 1

Find the ratio of $3$ months to $1$ year $6$ months.

Step-by-Step Solution:

Convert both quantities to months:
$1$ year $6$ months = $12 + 6 = 18$ months.
Ratio = $3 : 18 = 1 : 6$.
Since $1 < 6$, this is a Ratio of Less Inequality.

Example 2

Find the compound ratio of $2:3$, $5:7$, and $9:4$.

Step-by-Step Solution:

Product of antecedents = $2 \times 5 \times 9 = 90$
Product of consequents = $3 \times 7 \times 4 = 84$
Compound ratio = $90 : 84 = 15 : 14$ (Ratio of Greater Inequality).

Common Misconceptions & Examiner Traps

Common Misconception

Writing units after a ratio result.

Scientific Reality & Correction

Ratios are dimensionless comparison numbers and must never carry unit suffixes.

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