Problem 70 - Algebra 1

Question

Find the sum. $$6+(-8)-4$$

Step-by-Step Solution

Answer

-6

Step 1: Understanding the Negative Numbers

We have to remember that the negative numbers get subtracted when added. So, \(6 + (-8)\) is equivalent to \(6 - 8\). Thus, the operation turns into \(6 - 8 - 4\).

Step 2: Execution of Subtraction

Perform the first subtraction: \(6 - 8 = -2\). So, the equation becomes \(-2 - 4\).

Step 3: Final Subtraction

Perform the final subtraction: \(-2 - 4 = -6\).

Key Concepts

Negative Numbers

Negative numbers can seem a bit tricky at first, but with a little understanding, they become simple. Negative numbers are those less than zero and are represented with a minus sign (-). They show amounts that are less than nothing, like depths below sea level or temperatures below freezing.
When you add a negative number to a positive one, it's similar to subtraction. For example, the expression \(6 + (-8)\) is the same as \(6 - 8\). You see, adding a negative is like taking away from the original number. So, instead of thinking of it as an addition, think of it as subtracting the absolute value of the negative number. Here, \(6 + (-8)\) means you're reducing 6 by 8.

Order of Operations

When solving math problems, the order in which you do operations matters a lot. This is known as the "order of operations." If you've ever heard of PEMDAS, it's a helpful way to remember the order: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right) are the steps.
In our example, the expression is \(6 + (-8) - 4\). There are no parentheses or exponents, and no multiplication or division. So, we move directly to addition and subtraction from left to right.

• First, handle the addition: transform \(6 + (-8)\) into \(6 - 8\).
• Then, subtract 8 from 6 to get \(-2\).
• Lastly, subtract 4 from \(-2\), resulting in \(-6\).

Subtraction of Integers

Subtraction can be thought of as "taking away" when dealing with numbers. However, with integers (which include negative numbers), there's a twist. The rule is: subtracting an integer is the same as adding its negative counterpart.
For instance, subtracting 8 from 6 as in \(6 - 8\) is straightforward and results in \(-2\). When you have a negative number, like after the first operation, subtracting a positive number becomes a bit like diving deeper into the negatives.
Consider \(-2 - 4\), which starts at \(-2\) and further decreases by 4. When working through the steps:

• Start at \(-2\), which means 2 units below zero.
• Subtracting 4 from it takes you 4 more units below zero.
• Thus, you land at \(-6\), verifying the final result of this subtraction series.

By understanding this flow, you'll find subtracting integers much less daunting.