Problem 55 - Elementary Algebra

Question

Simplify. (Assume all denominators are nonzero.) $$ 1+11+12 $$

Step-by-Step Solution

Answer

The simplified result is 24.

Step 1: Identify the Problem Type

The exercise asks us to simplify a simple arithmetic expression composed only of addition.

Step 2: Understand the Expression Structure

The expression is a straightforward addition: \(1 + 11 + 12\). All operations are addition.

Step 3: Perform the Addition Sequentially

First, add the first two numbers: \(1 + 11 = 12\). Next, add the result to the third number: \(12 + 12 = 24\).

Step 4: Confirm the Simplified Result

Verify that the operations were carried out correctly. By checking: \(1 + 11 + 12 = 24\), we can confirm each step of addition was accurate.

Key Concepts

Addition

Addition is one of the fundamental operations in arithmetic. It involves combining two or more numbers to find their total, or sum. In the context of this exercise, we are simply adding three numbers together.

• The numbers to be added are 1, 11, and 12.
• Each of these numbers is known as an addend.
• The process of addition is commutative, meaning the order of numbers does not affect the sum.

Understanding how to perform addition is crucial for not only this exercise but also for handling more complex mathematics problems later.

Simplification

Simplification means breaking down or reforming an arithmetic expression to make it easier to understand or evaluate. For this particular exercise, the term simplification refers to combining all numbers in the expression into a single result.

• Initial expression: \( 1 + 11 + 12 \).
• The goal is to find a single number that represents the same value.
• This task is achieved by adding the numbers in sequence.

No parentheses or complex operations exist in the expression, which makes simplification straightforward. Simplification ensures expressions are in their simplest form, making it easier for us to work with them, especially in equations or formulas.

Step-by-Step Solution

A step-by-step solution breaks down a problem into smaller, more manageable parts. This approach not only guides us through the process but enhances understanding. Let's explore the step-by-step solution for this addition problem:

• Identify the problem: Recognize that the task is to add three numbers.
• Understand the structure: Realize all numbers are connected by addition signs, indicating a simple addition process.
• Perform the addition: First, add the first two numbers: \( 1 + 11 = 12 \).
• Add sequentially: Take the result (12) and add the third number: \( 12 + 12 = 24 \).
• Confirm the result: Verify each calculation step to ensure accuracy.

This structured methodical approach not only solves the problem but instills confidence in solving similar problems.