Problem 18 - Elementary Algebra

Question

For the following exercises, perform the indicated operations. $$ 5-6 $$

Step-by-Step Solution

Answer

Answer: -1

Step 1: Identify the numbers

The numbers given in this exercise are 5 and 6. We will subtract the second number (6) from the first number (5).

Step 2: Perform subtraction

Perform the subtraction as follows: $$ 5 - 6 = -1 $$ The result of the operation is -1.

Key Concepts

Negative Numbers

When venturing beyond the world of positive numbers, we encounter negative numbers, which are essential for expressing values less than zero. They're signified by a minus sign (–) preceding the number. In the case of the subtraction problem 5 - 6, we end up with a negative number because we're essentially trying to take away more than we have.

Negative numbers are used in a variety of real-world contexts, such as temperatures below freezing, which are below 0°C, or in finances to represent debt. Understanding negative numbers is crucial as they extend our number system to include values on either side of zero, forming what is known as the number line. In this context, 5 - 6 can be visualized as starting at positive 5 and moving one unit past zero to the negative side, arriving at -1.

Arithmetic Operations

Arithmetic operations are the building blocks of math, comprising addition, subtraction, multiplication, and division. These operations are elementary yet foundational, as they are used in more complex mathematical concepts and real-life calculations.

Subtraction, one of these basic operations, is essentially the process of finding the difference between two numbers. It can easily be seen as the inverse operation of addition. When we consider the subtraction of positive and negative numbers, we're navigating the integration of these arithmetic operations with the concept of negative numbers. This further highlights the interconnected nature of arithmetic, where understanding one operation can help in grasping another.

Subtraction Process

The subtraction process involves taking away a certain value from another, and it's symbolized by the minus sign (–). If we start with a smaller number and subtract a larger one, as in our original exercise 5 - 6, we end up with a negative result because we've 'borrowed' more than we had available.

This concept can sometimes be a bit tricky for those just getting familiar with negative numbers. It's helpful to consider a common scenario like financial transactions. If you have \(5 and spend \)6, you would owe $1, which is notated as -1 in mathematics, signifying a deficit. The subtraction process here teaches us how to properly interpret and calculate scenarios where we must operate with values crossing the threshold of zero, which is a fundamental skill in mathematics.