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Mathematics · Class 10 · Chapter 24: Ratio and Proportion

8 min

Key points

Ratio is the comparison of two quantities of the same kind expressed as a:b or a/b
Proportion exists when two ratios are equal, written as a:b = c:d or a:b :: c:d
In proportion a:b :: c:d, terms a and d are called extremes, b and c are called means
Product of means equals product of extremes: b × c = a × d
Fourth proportional to a, b, c is d where a:b :: c:d
Third proportional to a, b is c where a:b :: b:c
Mean proportional between a and c is b where a:b :: b:c, so b = √(ac)
Direct proportion: when one quantity increases, other also increases proportionally
Inverse proportion: when one quantity increases, other decreases proportionally

Definitions

Ratio: Ratio is the comparison between two quantities of the same kind. It is expressed as a:b or a/b where b ≠ 0.
Proportion: An equality of two ratios is called proportion. If a:b = c:d, then a, b, c, d are said to be in proportion.
Fourth Proportional: If three quantities a, b, c are given, then fourth proportional d is such that a:b :: c:d.
Mean Proportional: Mean proportional between two quantities a and c is b such that a:b :: b:c, where b = √(ac).
Direct Proportion: Two quantities are in direct proportion if increase in one quantity causes proportional increase in the other quantity.

Worked example

If a:b = 3:4 and b:c = 2:5, find a:b:c. Also find the fourth proportional to 6, 9, and 8. (6 marks)

a:b:c = 3:4:10 and fourth proportional = 12

Common mistakes

Students confuse mean proportional formula: it's √(ac), not (a+c)/2
In proportion problems, always check units are same before comparing ratios
When finding fourth proportional, maintain correct order: a:b :: c:d
Students forget to simplify ratios to lowest terms
In word problems, students don't clearly define what x represents

Quick recap

Ratio compares two quantities of same kind using division (a:b). Proportion states equality of two ratios (a:b = c:d). Fourth proportional to a,b,c is d where a:b = c:d. Mean proportional between a and c is b where a:b = b:c.

Generated by AI from Sindh Textbook Board material; review state: ai_unreviewed. MCQs, past-paper references and examiner notes are held back until a teacher has checked them.