Problem 20 - Introductory and Intermediate Algebra for College Students 4th

Question

Perform the indicated subtraction. $$26-26$$

Step-by-Step Solution

Answer

The answer is 0.

Step 1: Understand the Problem

We are given:
Perform the indicated subtraction.
$$26-26$$

Step 2: Apply Relevant Concepts

We apply mathematical definitions, properties, and theorems.

Step 3: Solution

The answer is 0.

Key Concepts

Arithmetic Operations

Arithmetic operations are the foundation of basic mathematics and include processes such as addition, subtraction, multiplication, and division. These operations are part of everyday calculations and are essential for solving a range of more complex mathematical problems. Subtraction is one of the primary arithmetic operations and involves determining the difference between two numbers, where one number is decreased by the value of another.

When we look at the example \(26 - 26\), we're performing a straightforward subtraction operation where the same number is subtracted from itself. In arithmetic terms, any whole number subtracted by itself will always result in zero. This concept is fundamental to mathematics, and understanding it paves the way to further explore arithmetic operations within the realm of numbers.

Elementary Algebra

Elementary algebra is the branch of mathematics that introduces algebraic concepts using numbers and variables. It extends the arithmetic operation of subtraction to include unknowns, which can be represented as letters (such as \(x\), \(y\), or \(z\)). This foundational knowledge is vital for solving equations and understanding how to manipulate expressions involving variables.

In the context of the exercise \(26 - 26\), we don't deal directly with variables or algebraic expressions. However, the principle that any number minus itself equals zero is also applicable in algebra. For instance, \(x - x = 0\) regardless of the value of \(x\). Recognizing these fundamental rules within elementary algebra helps students build a strong mathematical foundation and prepares them for more complex algebraic operations.

Solving Subtraction Problems

Solving subtraction problems is a skill that requires understanding the concept of 'taking away' or 'finding the difference.' In subtraction, we start with a minuend (the number from which another number is to be subtracted) and subtract a subtrahend (the number to be subtracted) from it to get the difference.

In our exercise, the minuend and the subtrahend are the same; hence, the difference is zero. To build on this example, let's consider another subtraction problem: \(53 - 27\). Here, the goal is to take away 27 from 53.

• Start at the ones place: \(3 - 7\) cannot be performed without borrowing because 3 is less than 7.
• Borrow 1 from the tens place, turning the 5 into 4 and the 3 into 13.
• Subtract the ones place: \(13 - 7 = 6\).
• Subtract the tens place: \(4 - 2 = 2\).
• Combine the results to get \(26\).

Through practice and understanding the basic steps, solving subtraction problems becomes a straightforward task, preparing students for more advanced mathematical challenges.