Problem 18 - Beginning and Intermediate Algebra

Question

$$ 15-(-33) $$

Step-by-Step Solution

Answer

48

Step 1: Understand the problem

We need to subtract a negative number, which in some cases might appear deceiving. We will transform this problem by simplifying the subtraction of a negative number into an addition.

Step 2: Simplify the expression

Use the rule of subtracting a negative number, which states that this is equivalent to addition. Therefore, transform the expression \(15 - (-33)\) into \(15 + 33\). This step is crucial for simplification.

Step 3: Perform the addition

Now that our expression is simplified, add the two numbers together: \(15 + 33\). First, add the tens (10 + 30 = 40) and then the units (5 + 3 = 8), finally combine for the total: \(40 + 8 = 48\).

Key Concepts

Subtracting Negative Numbers

Subtracting negative numbers can be a bit tricky initially, but understanding a simple rule makes it easy. When you encounter a subtraction problem with a negative number, you can transform it into an addition problem. This might seem counterintuitive at first, but follows a basic principle: subtracting a negative is the same as adding a positive.

Think of it like this: if you remove a negative situation, you're actually doing something positive. Therefore, in mathematics:

• Subtracting a negative number is the same as adding its positive counterpart.

In our example, the problem starts as \(15 - (-33)\). By applying this rule, it becomes \(15 + 33\). This approach helps in simplifying and understanding not only this expression but is a key concept in arithmetic operations.

Simplifying Expressions

Simplifying an expression is all about making calculations easier by dealing with numbers in a straightforward way. By identifying components that can be simplified, we can transform complex statements into simpler ones. In this context, simplifying involves:

• Rewriting expressions to make them easier to solve.
• Understanding the relationship between operations, such as positive and negative numbers.

In the exercise, we turned \(15 - (-33)\) into \(15 + 33\). This is a classic example of simplification by transforming subtraction of a negative into an operation we are more familiar with, addition. Once simplified, the expression is much easier to compute.

Basic Arithmetic Operations

Basic arithmetic operations are the foundation of all mathematics. They include addition, subtraction, multiplication, and division. These operations are used to manipulate numbers to solve equations and problems.

In our example, after simplifying the expression to \(15 + 33\), we perform addition. Here’s a simple rundown of how to properly add two numbers:

• First, add the respective place values: tens to tens and units to units.
• Adding the tens: \(10 + 30 = 40\).
• Adding the units: \(5 + 3 = 8\).
• Combine these sums: \(40 + 8 = 48\).

Through these straightforward steps, addition becomes a manageable task, demonstrating how basic arithmetic operations solve real-world mathematical problems.