## Exploring the Equation: (a - b) - c = a - (b - c)

This equation, at first glance, might seem confusing, but it holds a powerful truth about the way we manipulate numbers. Let's break down why it works and delve into its implications.

### The Essence of the Equation

The equation (a - b) - c = a - (b - c) demonstrates the **associative property of subtraction**. This property essentially states that the order in which we perform multiple subtractions doesn't affect the final result.

### Illustrative Example

Imagine you have $10 and need to pay for a $2 item, followed by a $3 item.

**Method 1: (a - b) - c**- You initially have $10 (a = 10) and buy the $2 item (b = 2), leaving you with $8 (a - b = 8).
- Then, you purchase the $3 item (c = 3), leaving you with $5 ((a - b) - c = 5).

**Method 2: a - (b - c)**- You have $10 (a = 10) and consider the total cost of the two items, which is $5 (b - c = 5).
- Subtracting the $5 total from your initial $10 leaves you with $5 (a - (b - c) = 5).

As you can see, both methods lead to the same final amount, $5.

### Practical Applications

The associative property of subtraction finds applications in various mathematical contexts, such as:

**Simplifying expressions:**It helps us reorder operations within an expression, making it easier to manipulate.**Solving equations:**This property allows us to rearrange terms in an equation to isolate the unknown variable.**Algebraic manipulations:**It is crucial in algebra for combining like terms and simplifying complex expressions.

### Key Takeaway

The equation (a - b) - c = a - (b - c) highlights a fundamental property of subtraction – the order in which we subtract multiple values doesn't influence the outcome. This understanding empowers us to simplify calculations, solve equations, and perform various mathematical operations with ease.