Problem 49 - Prealgebra and Introductory Algebra

Question

Find \(-138.72\) minus 510.64

Step-by-Step Solution

Answer

The result of \(-138.72 - 510.64\) is \(371.92\).

Step 1: Recognize the subtraction of a negative number

The problem is \(-138.72 - 510.64\). Here, it gets confusing for some because the first number is negative, and the second number is not. Recognize that subtracting a negative number is the same as adding a positive number. So, the equation would look like this: \(-138.72 + 510.64\).

Step 2: Add the amounts

Next, add \(-138.72\) and 510.64 together. This comes to 371.92.

Step 3: Add negative sign

The result is positive since it was a negative number being added to a more significant positive number. The final answer is \(371.92\)

Key Concepts

Prealgebra Concepts

Starting with the basics of prealgebra, it is crucial to understand numbers and their operations. Specifically, dealing with positive and negative numbers forms the foundation. When you encounter a problem that involves subtraction, such as

• negative numbers:
• understanding how to manipulate operations is key.

Through prealgebra, you learn simple rules that transform seemingly complex problems into manageable steps. This exercise takes us through subtracting a negative number from another, which can often appear more complicated than it is. By recognizing relationships such as "subtracting a negative is like adding a positive," you gain insight into structured problem-solving strategies. Remember, grasping these fundamental concepts sharpens your skills and builds a foundation for more advanced mathematics.

Integer Operations

Understanding integer operations is vital for mathematics. In this problem, you must manipulate negative and positive values to find solutions. Subtracting two numbers involves a few clear steps:

• Identify the numbers and their signs. Here, you subtract 510.64 from -138.72.
• Transform the operation by recognizing that subtracting a number can be seen as adding its negative. Thus, -138.72 - 510.64 becomes
• -138.72 + (-510.64).

This transformation simplifies calculations, allowing easier management of number signs. Applying this principle helps solve problems where signs can otherwise lead to mistakes. By honing your understanding of integer operations, you become adept at performing arithmetic with precision and efficiency.

Number Line Visualization

One way to visualize subtraction and addition clearly is by using a number line. Imagine stretching a line where numbers gradually increase to the right and decrease to the left. This exercise can illustrate subtracting negatives:

• Locate -138.72 on the number line.
• Consider moving 510.64 units towards the negative direction.
• Observe how it lands at -649.36.

This mental picture helps comprehend the positive and negative directions. It clarifies that moving left (subtracting) deepens the negative result. This visualization illustrates the calculation conceptually, guiding better understanding while handling numbers in practical scenarios. Employing number lines as a tool can significantly enhance your grasp of integer operations.