Problem 76 - Elementary and Intermediate Algebra

Question

Perform the operations. $$ 1-2-3 $$

Step-by-Step Solution

Answer

The result is -4.

Step 1: Identify the operation types

The exercise involves basic arithmetic operations, specifically subtraction. We have the equation: \[ 1 - 2 - 3 \]

Step 2: Simplify Left to Right

According to the order of operations, we perform subtraction from left to right. First, subtract 2 from 1:\[ 1 - 2 = -1 \]

Step 3: Continue the Subtraction

Now we subtract 3 from the result of the first operation:\[ -1 - 3 \] Subtracting 3 from -1 gives:\[ -1 - 3 = -4 \]

Key Concepts

Arithmetic Operations

Arithmetic operations are the foundation of elementary algebra and involve four primary actions: addition, subtraction, multiplication, and division. Each of these operations helps us process numbers in different ways to achieve specific results or solve equations. Here, we are focusing on subtraction, one of the basic arithmetic operations.

• Addition: Combining numbers to get a sum.
• Subtraction: Removing a number from another to get the difference.
• Multiplication: Increasing a number by a factor of another.
• Division: Splitting a number into equal parts by another.

Understanding these operations is key to solving more complex mathematical problems. Simple equations, like \(1 - 2 - 3\), may only involve subtraction, yet they require careful handling to prevent mistakes.

Order of Operations

In mathematics, the order of operations is essential in ensuring that expressions are solved correctly and consistently. While dealing with multiple arithmetic operations, knowing which to perform first can make a difference in the outcome.

The standard rule in mathematics for this order is the acronym PEMDAS:

• Parentheses
• Exponents (or indices)
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

For the problem \(1 - 2 - 3\), subtraction is the only operation, which implies that we work from left to right per the PEMDAS guide. This approach prevents errors that occur if operations were executed randomly.

Subtraction

Subtraction is an arithmetic operation used for calculating the difference between two numbers. It involves removing the value of one number (the subtrahend) from another (the minuend). This operation can result in negative numbers, especially when the subtrahend is greater than the minuend.

In the example \(1 - 2 - 3\), we perform subtraction twice:

• First, subtract 2 from 1, resulting in a negative number: \(-1\).
• Next, continue by subtracting 3 from \(-1\), further decreasing the value to \(-4\).

Understanding how to handle negative numbers during subtraction is vital. Each subtraction moves further left on the number line, demonstrating the importance of correctly following arithmetic operations.