Problem 2 - Beginning and Intermediate Algebra

Question

Subtract. See Examples 1 through 5 $$ -12-8 $$

Step-by-Step Solution

Answer

-20

Step 1: Identify the Terms

The expression given is \(-12 - 8\).This consists of two numbers: a negative number \(-12\) and a positive number \(8\) being subtracted.

Step 2: Simplify the Expression

The subtraction of a positive number is the same as adding its negative. Therefore,\(-12 - 8\) can be rewritten as:\(-12 + (-8)\).

Step 3: Add Negative Numbers

Now, add the two negative numbers:\(-12 + (-8) = -(12 + 8) = -20\).The result is -20 because adding two negative numbers results in a more negative number.

Key Concepts

Negative Numbers

Negative numbers are simply numbers with a minus sign in front of them. They represent values less than zero. This can be thought of as owing something rather than having it. For example, if you have \(-5\), think of it as being 5 units below zero.
When working with negative numbers, it's important to remember:

• Negative numbers are less than positive numbers.
• A negative number on a number line is always to the left of zero.
• Multiplying or dividing two negative numbers yields a positive result.

Knowing how to work with negative numbers is essential for tackling various math problems, especially those involving subtraction or addition of negative values.

Adding Negative Numbers

Adding negative numbers might seem tricky at first, but it's quite straightforward once you get the hang of it. When we talk about adding negative numbers, what we're really doing is strengthening the negative value.
Consider the following concepts when adding negative numbers:

• Think of adding a negative as moving left on a number line.
• Two negative numbers added together make the sum even more negative.
• For instance, \(-12 + (-8)\) results in \(-(12+8) = -20\) because both numbers are negative and their combination results in an increase in the negative value.

Breaking down the addition into simpler steps, such as combining the absolute values and attaching a negative sign, can help make the process easier to understand.

Simplifying Expressions

Simplifying expressions involves reducing them to their simplest form to make calculations easier. This process becomes crucial when dealing with complex numbers, especially those with negative terms.
To simplify expressions effectively:

• Identify the terms in the expression. For example, in \(-12 - 8\), the terms are \(-12\) and \(-8\).
• Remember that subtracting a number is the same as adding its negative. So, \(-12 - 8\) can be transformed into \(-12 + (-8)\).
• Finally, combine the like terms. In this case, both terms are negative. Adding them gives you \(-20\).

The key takeaway is transforming subtraction problems into addition can often simplify the process, making it easier to arrive at the correct answer.