Problem 83 - Prealgebra

Question

The problems below review addition, subtraction, multiplication, and division of positive and negative numbers, as covered in this chapter. Perform the indicated operations. $$-8+(-4)$$

Step-by-Step Solution

Answer

The result is \(-12\).

Step 1: Identify the Operation

The problem presents the expression \(-8 + (-4)\). Let's identify the operation: we are dealing with addition here.

Step 2: Understand Adding Negative Numbers

When adding a negative number to another number, you are essentially subtracting that number. So, \(-8 + (-4)\) is the same as \(-8 - 4\).

Step 3: Perform the Addition/Subtraction

Now perform the operation: subtract 4 from -8. This gives you the answer \(-8 - 4 = -12\). The result of \(-8 + (-4)\) is therefore \(-12\).

Key Concepts

Addition of Integers

When we talk about the addition of integers, we simply mean adding two whole numbers that could be either positive or negative. This operation is fundamental in mathematics and lays the groundwork for more complex concepts. Let's dive into the details to make this clear and easy to understand.

• If both integers are positive, you just add them as usual. For instance, 3 + 2 gives you 5.
• If you're adding a negative and a positive number, you essentially perform a subtraction between the absolute values of the numbers, and use the sign of the number with the larger absolute value.
• When both numbers are negative, the result is negative, and you add the absolute values together. For example, (-2) + (-3) results in -5. This is because the numbers are both pointing in the same negative direction.

Every situation with integer addition builds on these basic principles. Remember, with practice, these operations become second nature. Breaking it down into parts always helps make the process smoother and more intuitive.

Negative Numbers

Negative numbers can initially seem daunting, but they are simply numbers that are less than zero. Understanding negative numbers will help you solve many math problems involving situations like temperatures below zero or financial debt.

• Visualize negative numbers as positions to the left of zero on the number line. This visualization aids comprehension greatly.
• Think of negative numbers as owing something, like being in debt.
• Negative numbers play an essential role in many mathematical operations, especially in subtraction and addition when they alter the outcome compared to positive numbers.

It's important to become comfortable with these values because they frequently appear in equations and scenarios requiring calculations. Once you grasp negative numbers, you'll find many math problems easier to manage.

Subtraction of Integers

Subtraction of integers involves finding the difference between two numbers, which might be positive or negative. When working with integers, understanding subtraction helps solve a variety of problems.

• To subtract a positive number, you move to the left on the number line. This reduces the number’s value.
• When subtracting a negative number, it's similar to adding the absolute value of the negative number. For example, subtracting -3 is like adding 3.
• Using mental math techniques and number lines aids in simplifying subtraction.

Additionally, converting problems to an addition of the opposite number often makes operations more straightforward, as highlighted in the original solution where -8 + (-4) was translated to -8 - 4. Practice and visualization can transform these processes into second nature, allowing you to tackle more advanced arithmetic with ease.