Proportional Reasoning-1

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A ratio is a comparison of two quantities using division. It is written as a:b, where 'a' and 'b' are called the terms of the ratio. For example, if there are 60 mm width and 40 mm height, the ratio i

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The ratio 5:3 means that for every 5 units of the first quantity, there are 3 units of the second quantity. For example, if boys to girls ratio is 5:3, then for every 5 boys, there are 3 girls.

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To find the simplest form of a ratio, divide both terms by their HCF (Highest Common Factor). For example, 60:40 has HCF = 20, so dividing both terms: 60÷20 : 40÷20 = 3:2.

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Two ratios are proportional when they are equal in their simplest forms. We use the symbol '::' to show proportion. For example, 6:4 :: 9:6 because both simplify to 3:2.

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Cross multiplication is used to check if two ratios are proportional or to find missing terms. If a:b :: c:d, then a×d = b×c. For example, in 3:4 :: 6:8, we get 3×8 = 4×6 = 24.

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Using cross multiplication: 12 × ? = 15 × 8 12 × ? = 120 ? = 120 ÷ 12 = 10 Therefore, 12:15 :: 8:10

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The Rule of Three is an ancient method to solve proportion problems with four quantities where three are known and one is unknown. If a:b :: c:d, then d = (b×c)/a. This method was used by ancient Indi

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Set up proportion: 120:2 :: ?:5 Using cross multiplication: 2 × ? = 120 × 5 2 × ? = 600 ? = 300 km The car will travel 300 km in 5 hours.