Important Properties of Proportion Video Lecture | CSAT Preparation - UPSC

Ans. The important properties of proportion include the following: 1. The product of the extremes is equal to the product of the means. For example, if we have a/b = c/d, then ad = bc. 2. If the product of the extremes is equal to the product of the means, the numbers are said to be in proportion. 3. Proportions can be solved using cross-multiplication, where the product of the means is equated to the product of the extremes. 4. Proportions can be used to solve various real-life problems, such as finding unknown quantities or comparing different items. 5. Proportions are widely used in various fields, including mathematics, economics, and science, to establish relationships and make predictions.

Ans. To solve proportions using cross-multiplication, follow these steps: 1. Write the given proportions in the form of a/b = c/d. 2. Multiply the means (b and c) and equate them to the product of the extremes (a and d). This can be represented as ad = bc. 3. Solve the equation for the unknown quantity by isolating it on one side of the equation. 4. Simplify the equation if necessary and find the value of the unknown quantity.

Ans. Proportions can be used to solve various real-life problems, such as: 1. Recipe scaling: If you want to make a larger or smaller batch of a recipe, proportions can be used to adjust the ingredient quantities accordingly. 2. Similar shapes: Proportions can be used to determine the corresponding sides of similar shapes, such as finding the height of a tree by measuring its shadow and using the shadow's proportion to the tree's height. 3. Currency exchange: Proportions can be used to convert one currency to another by establishing the exchange rate. 4. Speed and distance: Proportions can be used to calculate the time taken to travel a certain distance at a given speed or to determine the speed based on the distance and time taken. 5. Scale models: Proportions can be used to create scale models of buildings, vehicles, or other objects by reducing or enlarging the dimensions proportionally.

Ans. Proportions play a crucial role in mathematics, economics, and science in the following ways: 1. Mathematics: Proportions are used to establish relationships between different quantities, solve equations, and make predictions. They are fundamental in various branches of mathematics, including algebra, geometry, and statistics. 2. Economics: Proportions are used to analyze and compare economic data, such as calculating percentage changes, determining price elasticity, and measuring income distribution. 3. Science: Proportions are used to establish and describe relationships between different variables in scientific experiments and observations. They help scientists understand the cause-and-effect relationships and make predictions based on the observed proportions.

Ans. Proportions can be used to compare different items by establishing a relationship between their respective quantities. For example, if you want to compare the prices of two items, you can set up a proportion using their prices and quantities. By solving the proportion, you can determine which item offers a better value or is more cost-effective. Similarly, proportions can be used to compare the sizes, weights, or any other measurable attributes of different items. By setting up and solving proportions, you can make informed decisions and choose the option that best suits your needs or preferences.