Ratio and Proportion

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A ratio is the comparison of two quantities of the same kind. If a and b are two quantities of the same kind with b ≠ 0, then the ratio of a to b is written as a:b or a/b. Example: If a man is 40 year

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In the ratio a:b, 'a' is called the antecedent (the first term) and 'b' is called the consequent (the second term). For example, in the ratio 3:5, 3 is the antecedent and 5 is the consequent.

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1. Ratios can only be found between quantities of the same kind/unit 2. Ratios have no units 3. Order of terms matters: a:b ≠ b:a (unless a = b) 4. Usually expressed in lowest terms 5. Second term can

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When two or more ratios are multiplied termwise, the resultant ratio is called compound ratio. If a:b and c:d are two ratios, their compound ratio is ac:bd. Example: Compound ratio of 3:4 and 2:5 is (

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Duplicate ratio is the compound ratio of two equal ratios. The duplicate ratio of a:b is a²:b². Example: Duplicate ratio of 3:4 is 3²:4² = 9:16. Duplicate ratio of 1:2 is 1²:2² = 1:4.

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Triplicate ratio is the compound ratio of three equal ratios. The triplicate ratio of a:b is a³:b³. Example: Triplicate ratio of 3:4 is 3³:4³ = 27:64. Triplicate ratio of x:2y is x³:8y³.

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Sub-duplicate ratio of a:b is √a:√b. Example: Sub-duplicate ratio of 49:36 is √49:√36 = 7:6. Sub-duplicate ratio of 9x²:4y² is 3x:2y.

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Sub-triplicate ratio of a:b is ∛a:∛b. Example: Sub-triplicate ratio of 125:64 is ∛125:∛64 = 5:4. Sub-triplicate ratio of (a-b)³:(a+b)³ is (a-b):(a+b).