Problem 16 - Prealgebra and Introductory Algebra

Question

Add. $$8+(-12)$$

Step-by-Step Solution

Answer

The result of adding \(8+(-12)\) is \(-4\).

Step 1: Understand the concept

When you are given a problem where you need to add a positive and a negative number, remember that adding a negative number is the same as subtracting that number.

Step 2: Remove the parentheses

So, in \(8+(-12)\) it can also be written as \(8 - 12\).

Step 3: Perform the subtraction

When you subtract 12 from 8, you get \(-4\).

Key Concepts

Negative Numbers

Negative numbers can seem a bit tricky at first, but with some practice, they become easy to understand. A negative number is less than zero and is represented with a minus sign (-). For instance, in a number line:

• Numbers to the right of zero are positive (e.g., 1, 2, 3).
• Numbers to the left of zero are negative (e.g., -1, -2, -3).

To visualize negative numbers, think about temperatures below freezing or a bank account overdrawn.
They play a crucial role in math, especially when you perform operations like addition and subtraction. When you see an expression like \(8 + (-12)\), the \(-12\) signals a step into the negative realm. Understanding this helps in mastering the operations involving integers.

Subtraction

Subtraction of numbers can also be looked at as adding a negative. This may sound confusing, but once you get the hang of it, it's not too difficult. For instance:

• The expression \(8 + (-12)\) simplifies to \(8 - 12\).
• This means you're removing 12 units from 8.

Let's break this down:- Begin with 8 and imagine moving 12 steps to the left on a number line.- Each step backward takes you closer to negative numbers.By understanding subtraction in this way, it's easier to manage problems involving negative integers.
Remember, subtracting a larger number from a smaller one lands you in negative numbers.

Integer Operations

Integer operations combine various arithmetic actions involving whole numbers, both positive and negative.
Let's explore these operations with examples to make sense of the process:**Addition and Subtraction of Integers**

• When adding, if the signs are the same, add the numbers and keep the sign.
• If the signs are different, subtract the smaller number from the larger and use the sign of the larger number.

Consider the exercise \(8 + (-12)\):- Since 8 is positive and -12 is negative, we subtract.- Subtract 12 from 8, yielding \(-4\), because 8 is smaller.- The result is negative because the larger number, -12, dominates.By following these steps for integer operations, you can solve mathematical expressions with clarity and confidence.
Practicing these techniques will improve your understanding and ability to handle more complex problems successfully.