Problem 51 - Prealgebra

Question

Translate each of the following and simplify the result. Subtract \(-4\) from the sum of \(-8\) and 12

Step-by-Step Solution

Answer

The result is 8.

Step 1: Identify the Operation

The problem requires us to first find the sum of two numbers: -8 and 12. Then, we need to subtract -4 from that sum.

Step 2: Calculate the Sum

Add -8 and 12 together: \(-8 + 12 = 4\). This is the sum of the two numbers.

Step 3: Perform the Subtraction

Now subtract -4 from the previously calculated sum (4): \(4 - (-4)\). Subtracting a negative number is the same as adding its positive, so this becomes: \(4 + 4 = 8\).

Step 4: Simplify the Expression

After performing all operations, the simplified result of the expression is 8.

Key Concepts

Addition and Subtraction of Integers

When working with integers, a key skill is to grasp how to effectively add and subtract them. Integers are whole numbers that include positive numbers, negative numbers, and zero.
To make things simple:

• Adding a positive number moves the sum to the right on the number line, increasing the total.
• Adding a negative number is equivalent to subtracting a positive number, which moves the sum to the left on the number line, decreasing the total.
• Subtracting a negative number can be tricky. It is the same as adding its absolute positive value, because double negatives cancel each other out.

Let's use these principles in the specific exercise. We start with the sum of -8 and 12. The process is straightforward: \[-8 + 12 = 4\] Moving forward, we subtract -4 from this sum, but since subtracting a negative is the same as adding a positive, we perform this operation as: \[4 - (-4) = 4 + 4 = 8\] Mastering these operations makes solving integer problems much easier!

Negative Numbers

Negative numbers are integral to understanding integer operations. They represent values less than zero and are important in prealgebra.
When dealing with negative numbers:

• Adding a negative number decreases the value of the total.
• Subtracting a negative number increases the value of the total.

Negative numbers appear in various mathematical concepts, including temperature scales, depth measurements, and even financial transactions (like debts). While they are initially less intuitive, practicing with them helps build confidence.
For example, in our original problem, we encountered the need to subtract a negative number: \[4 - (-4)\] This simplifies to adding a positive, due to the nature of negative signs: \[4 + 4\]Understanding this enables students to solve similar problems with ease and to apply this knowledge to diverse real-world scenarios.

Prealgebra

Prealgebra lays the foundation for understanding more complex math concepts by introducing basic operations and number types such as integers. It's crucial for students to become comfortable with these concepts to move on to higher-level math studies.
In prealgebra:

• Students learn about the importance of operations like addition, subtraction, multiplication, and division.
• They explore different categories of numbers, including whole numbers, negative numbers, and fractions.
• Using number lines may help to visualize the operations with integers.

In the context of our exercise, recognizing that -8 is a negative number, while 12 is positive, and then effectively performing the subtraction \[4 - (-4)\] as an addition \[4 + 4\]is part of developing these fundamental skills in prealgebra.
These basic skills act as building blocks essential for tackling the complexities of algebra and beyond.