Problem 23 - Introductory and Intermediate Algebra for College Students 4th

Question

Perform the indicated subtraction. $$0-13$$

Step-by-Step Solution

Answer

-13

Step 1: Identify the Numbers

Identify the two numbers involved in the subtraction. In this case, those numbers are 0 and 13.

Step 2: Perform the Subtraction

Subtract the second number (13) from the first number (0). This can be done by writing it as \(0 - 13\) and performing the simple arithmetic.

Key Concepts

Negative Numbers

When working with subtraction, it's essential to grasp the concept of negative numbers. A negative number is simply a number less than zero. Think of them as a shift to the left on the number line.
For instance, if you start at zero and subtract a positive number, you move left into the negative territory. In our exercise, subtracting 13 from 0 (\(0 - 13\)) results in the negative number -13 because you are moving 13 steps to the left from zero.

• Negative numbers are indicated by the minus sign (-).
• They are crucial in solving problems involving deficits or losses.

Negative numbers play a key role in many real-life situations, such as temperatures below freezing or depths below sea level.

Basic Arithmetic

Basic arithmetic involves four fundamental operations: addition, subtraction, multiplication, and division. Subtraction, in particular, is the operation of finding the difference between numbers. It involves taking one value away from another.
In our example, we perform subtraction by removing 13 from 0 to reach a solution.

• Start by identifying the values involved, which are the minuend (first number: 0) and subtrahend (second number: 13).
• Write the expression (\(0 - 13\)) aligning the numbers appropriately if needed.
• Solve by subtracting directly or adding the inverse of the subtrahend, turning subtraction into addition of a negative.

This helps in transforming the problem into a simpler form, often making subtraction easier to understand.

Integer Operations

Integers include all whole numbers and their negative counterparts. When dealing with subtraction involving integers, the rules differ slightly from positive numbers.
Our task (\(0-13\)) illustrates how operations with integers can lead to negative results.

• Integers encompass zero; thus 0 is neither negative nor positive.
• When subtracting, treating the operation as addition of the negative integer (\(0 + (-13)\)) can simplify calculations.
• Knowing that subtraction of a positive number turns into adding a negative number is crucial.

Understanding these operations is fundamental in mathematics, showing both the flexibility and the challenges integers provide in arithmetic tasks.