LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

RATIO - RATIO & PROPORTION

__RATIO & PROPORTION -__

**Ratio and proportion are related mathematical concepts used to compare quantities and establish relationships between them. While they are often used interchangeably, they have distinct meanings and applications:**

__Ratio:-__

**A ratio is a comparison of two quantities, often expressed as a fraction, division, or using the colon notation.****It is used to express the relative size or proportion of one quantity in relation to another.****Ratios can be used to compare quantities of the same type, like comparing the number of boys to the number of girls in a classroom.****Ratios do not necessarily require the quantities being compared to be in the same units.**

__Proportion:-__

**A proportion is an equation that states that two****ratios are equal.****It expresses a relationship between two or more ratios, indicating that they maintain the same relative size.****Proportions are used to solve problems involving unknown quantities when you have known ratios.****Proportions are often used in real-world scenarios to find missing values or verify whether a set of ratios is consistent.**

**For example, consider the following scenario:**

**Example.1) In a group of 20 people, 12 are men, and the rest are women. What is the proportion of men to women?**

**Ans.)**

**Using Ratios: The ratio of men to women is 12:8, or simplified to 3:2.**

**Using Proportions: We can set up a proportion to find the proportion of men to women:**

** 12 men x men**

** ------------ = -----------**

** 8 women y women**

**By Cross-multiplying:-**

** 12 * y = 8 * x**

**Now, if we know either the number of men (x) or women (y), we can solve for the other using this proportion.**

**In summary, ratios are used to compare quantities, while proportions are used to establish and solve equations that represent equal ratios. Both concepts are important in various mathematical and real-world applications, especially when dealing with relative quantities and unknown values.**