Chapter 7 - Ratio and Proportion Revision Notes - Class 7 Mathematics

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📌 Key Points

Ratio is a comparison of two quantities of the same kind. Written as a:b or a/b.
Ratio has no units. Example: 5 boys to 3 girls is 5:3 (not 5:3 boys:girls).
Order matters in ratio. 3:5 ≠ 5:3
Simplify ratio by dividing both terms by their HCF.
Equivalent ratios: multiply or divide both terms by same non-zero number. 2:3 = 4:6 = 6:9
Proportion: statement that two ratios are equal. a:b = c:d or a/b = c/d
Cross-multiplication property: If a:b = c:d, then ad = bc (product of extremes = product of means).
Unitary method: find value of one unit, then multiply by required quantity.
Direct variation: y = kx. As one increases, other increases proportionally. k is constant.
Indirect (inverse) variation: xy = k or y = k/x. As one increases, other decreases.
To compare ratios, convert to decimals or same denominator.
To divide a quantity in given ratio: find total parts, calculate each share.
In direct variation, ratio y/x is constant.
In inverse variation, product xy is constant.
Quantities must be in same units before making ratio.

📘 Important Definitions

Ratio

Comparison of two quantities of same kind, expressed as a:b or a/b. No units.

Antecedent

First term in a ratio. In ratio 5:8, antecedent is 5.

Consequent

Second term in a ratio. In ratio 5:8, consequent is 8.

Simplest form

Ratio where both terms have no common factor except 1. Example: 3:5 is simplest form of 6:10.

Proportion

A statement that two ratios are equal. a:b = c:d means a/b = c/d.

Extremes

In proportion a:b = c:d, extremes are a and d (first and last terms).

Means

In proportion a:b = c:d, means are b and c (middle terms).

Unitary Method

Method of finding value of one unit first, then calculating the required quantity.

🔢 Formulas & Laws

Simplifying Ratio

Divide both terms by their HCF

Example: 24:36 ÷ 12 = 2:3

Cross-Multiplication

If a:b = c:d, then ad = bc

Used to check if ratios form proportion or find unknown term

Direct Variation

y = kx (where k = constant)

Ratio y/x remains constant. y/x = k

Indirect Variation

xy = k or y = k/x (where k = constant)

Product xy remains constant as one increases, other decreases

Dividing in Ratio

Each part = (Part ratio / Total parts) × Total quantity

To divide Q in ratio a:b:c: First = (a/(a+b+c))×Q

⚠️ Common Mistakes

✗ Wrong: Forgetting to simplify ratios. Writing 12:8 without simplifying to 3:2.

✓ Correct: Always express ratio in simplest form by dividing by HCF.

✗ Wrong: Changing order of ratio. 5:8 is different from 8:5.

✓ Correct: Order matters. 5:8 means first is 5 and second is 8.

✗ Wrong: Not converting to same units. Ratio of 1 hour to 30 minutes written as 1:30.

✓ Correct: Convert to same units: 1 hour = 60 minutes, so ratio = 60:30 = 2:1

✗ Wrong: Confusing direct and indirect variation. 'More workers = more time'.

✓ Correct: 'More workers = less time' (inverse). 'More speed = more distance' (direct).

✗ Wrong: Cross-multiplication error in proportions. Multiplying wrong terms.

✓ Correct: In a:b = c:d, cross-multiply: ad = bc (extremes = means).

✗ Wrong: In unitary method, calculating wrong unit value.

✓ Correct: Always: Find value of 1 unit first, then multiply by required quantity.

📝 Exam Focus

These questions are frequently asked in CBSE exams:

Simplifying and comparing ratios

1m★★★

Finding unknown term using proportion/cross-multiplication

2m★★★

Unitary method word problems (cost, distance, time)

2m★★★

Dividing quantities in given ratio

3m★★

Identifying and solving direct/indirect variation

2m★★

Scale and map-related problems

🎯 Last-Minute Recall