Problem 55 - Intermediate Algebra

Question

Simplify each numerical expression. $$ 9-12-8+5-6 $$

Step-by-Step Solution

Answer

The simplified expression is -12.

Step 1: Address Subtraction Sequentially

Start by addressing the expression from left to right, focusing on subtraction first.First, compute: \[ 9 - 12 = -3 \]The expression becomes: \[ -3 - 8 + 5 - 6 \]

Step 2: Continue with Subtraction

Continue with the next subtraction in the expression:\[ -3 - 8 = -11 \]The expression now is:\[ -11 + 5 - 6 \]

Step 3: Address Addition

Proceed with the addition in the expression:\[ -11 + 5 = -6 \]Now, the expression is:\[ -6 - 6 \]

Step 4: Complete Final Subtraction

Finish simplifying by performing the final subtraction:\[ -6 - 6 = -12 \]The expression is now fully simplified.

Key Concepts

Understanding Numerical Expressions

Numerical expressions can be thought of as a combination of numbers and operations that together form an expression to be solved. In essence, each part of the expression contributes to a solution, guiding you to the final simplified result. Working with numerical expressions often requires:

• Breaking down the complex expressions into smaller, more manageable parts
• Applying basic arithmetic operations like addition and subtraction
• Clearly following the order of operations to ensure each part of the expression is simplified correctly

By carefully solving each part of the expression while following these principles, you can simplify any numerical expression accurately.

Mastering Sequential Subtraction

Sequential subtraction occurs when you have multiple subtraction operations in a row within an expression. Tackling these subtractions in the correct order is crucial for arriving at the right answer. Here's how to manage sequential subtraction:

• Start from the leftmost subtraction and move step by step to the right
• Resolve each subtraction individually to help keep track of your progress through the expression
• Be particularly attentive to negative results, as these can impact subsequent calculations

By proceeding methodically through sequential subtractions, you maintain clarity and control over the simplification process, ultimately ensuring you do not miss any necessary computations.

Navigating Addition and Subtraction

Once you understand how to handle sequential subtraction and when to perform each operation, it's key to balance between addition and subtraction for complete accuracy. You can do this by:

• Identifying each operation clearly in the expression
• Solving any subtractions before moving to additions, particularly if they appear first in sequence
• Observing any changes in sign and keeping your workspace organized to minimize errors

Integrating these steps will make addition and subtraction a simple, routine part of solving any arithmetic expression. With practice, you'll gain a smoother, more intuitive grasp of how to navigate both operations seamlessly.