Problem 66 - Elementary and Intermediate Algebra

Question

Perform the operations. Subtract 30.3 from \(0 .\)

Step-by-Step Solution

Answer

The result is -30.3.

Step 1: Identify the Numbers

The numbers in the exercise are 0 and 30.3. We need to subtract 30.3 from 0.

Step 2: Set Up the Subtraction Problem

We perform the subtraction by writing it as:\[ 0 - 30.3 \]

Step 3: Perform the Subtraction

Subtract 30.3 from 0. Since subtracting a positive number from zero results in a negative number, the operation yields:\[ 0 - 30.3 = -30.3 \]

Step 4: Conclusion: Write the Result

The result of subtracting 30.3 from 0 is -30.3.

Key Concepts

Subtraction

Subtraction is one of the basic operations in arithmetic, allowing us to find the difference between numbers. It involves taking one number away from another. In this exercise, when you subtract 30.3 from 0, you are looking to see how much remains after removing 30.3. Often, the terms are organized as:

• Minuend: the number you subtract from (here it is 0).
• Subtrahend: the number you subtract (here it is 30.3).

The result of subtraction is referred to as the difference. Subtraction is essentially the inverse of addition, where you undo the process of adding by finding what needs to be taken away. Remember, when dealing with decimals, align them carefully to get the right difference.

Negative Numbers

Negative numbers are an integral part of mathematics, used to represent values less than zero. These numbers are denoted with a minus sign (-). In our exercise, when you subtract 30.3 from 0, the result is -30.3, a negative number.
Understanding negative values can be visualized using a number line. Imagine a line where 0 is in the middle, positive numbers extend to the right, and negative numbers extend to the left. Subtracting a positive number from zero moves you to the left on the number line.
Handling negative numbers requires some important rules:

• Subtracting a positive number moves you left on the number line.
• The farther left you go, the more negative the number becomes.

Recognizing patterns in subtraction helps make understanding negative results easy.

Basic Arithmetic Operations

Arithmetic operations form the foundation of mathematics. They include addition, subtraction, multiplication, and division. These operations allow us to manipulate numbers to solve real-world problems.
Each operation has its unique characteristics:

• **Addition** combines two numbers to form a total.
• **Subtraction** finds the difference between numbers, as explained in previous sections.
• **Multiplication** repeatedly adds a number to itself a specified number of times.
• **Division** breaks a number into equal parts.

When solving problems that involve any of these operations, always pay attention to the order of operations (PEMDAS/BODMAS) to calculate correctly. Subtraction is used when you need to determine how much is left, identify shortages, or compare two quantities, emphasizing its practical applications in daily life. Understanding these concepts deeply can boost confidence when working with numbers.