## Understanding the Expression (a+b)/(c+d)

The expression (a+b)/(c+d) represents a **fraction** where:

**(a+b)**is the**numerator**, representing the**top part**of the fraction.**(c+d)**is the**denominator**, representing the**bottom part**of the fraction.

This expression represents a **division operation**. It tells us to **divide the sum of 'a' and 'b' by the sum of 'c' and 'd'**.

### Simplifying the Expression

In some cases, you might be able to simplify this expression. Here are some scenarios:

**Factoring:**If you can factor out common factors from the numerator and denominator, you can cancel them out to simplify the expression. For example, if (a+b) = 2(x+y) and (c+d) = 4(x+y), then the expression simplifies to 1/2.**Combining like terms:**If the numerator and denominator have like terms, you can combine them to simplify the expression. For example, if a = 2x, b = 3x, c = y, and d = 2y, then the expression becomes (5x)/(3y).

### Real-world Applications

The expression (a+b)/(c+d) finds its way into various applications, including:

**Calculating averages:**If 'a' and 'b' represent two quantities, and 'c' and 'd' represent their respective weights, then (a+b)/(c+d) gives the**weighted average**of the two quantities.**Calculating proportions:**In some scenarios, this expression can represent a**ratio**or a**proportion**. For example, if 'a' and 'b' represent the number of successes and failures in a trial, and 'c' and 'd' represent the total number of trials, then the expression gives the**proportion of successes**.**Solving equations:**This expression can appear in equations that need to be solved for a specific variable.

### Important Note:

It's crucial to remember that the denominator (c+d) **cannot be zero**. Division by zero is undefined. Therefore, when working with this expression, always make sure the denominator is not equal to zero.