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Ch-7 Ratio and Proportion

In ICSE (Indian Certificate of Secondary Education) mathematics, Chapter 7 often covers the topic of "Ratio and Proportion." Here are some important definitions and concepts related to ratio and proportion:

Ratio: A ratio is a comparison of two quantities by division. It is typically expressed in the form "a:b" or "a/b," where "a" and "b" are two numbers. For example, if there are 3 red balls and 5 blue balls, the ratio of red balls to blue balls is 3:5.

Proportion: A proportion is an equation that states that two ratios are equal. It is often written in the form "a:b = c:d." If a proportion is true, it means that the four quantities a, b, c, and d are in proportion to each other.

Means and Extremes: In a proportion a:b = c:d, "a" and "d" are called the "extremes," while "b" and "c" are called the "means." The product of the means is equal to the product of the extremes, i.e., a * d = b * c.

Continued Proportion: In a continued proportion, if a:b = b:c, then it is written as a:b:c. In this case, the middle term (b) is called the "mean proportion" between the first term (a) and the third term (c).

Properties of Proportions: Proportions have some important properties, such as the ability to cross-multiply to solve for unknown values and the fact that if the means are equal, or if the extremes are equal, then the proportion is true.

Direct Proportion: In a direct proportion, two quantities change in the same ratio. If one quantity doubles, the other also doubles, and if one quantity triples, the other also triples.

Inverse Proportion: In an inverse proportion, two quantities change in inverse ratio. If one quantity doubles, the other is halved, and if one quantity triples, the other is reduced to one-third.

Unitary Method: The unitary method is a technique used to solve problems involving ratios and proportions. It involves finding the value of one unit and then using it to find the value of other quantities.

Percentage: Percentage is a special kind of ratio where the denominator is 100. It is often used to express proportions as a percentage of the whole.

Understanding ratios and proportions is essential in various mathematical and real-world applications, including solving problems related to scaling, mixing ingredients, finance, and more. Mastery of these concepts is crucial for solving problems in mathematics and practical scenarios.

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