Problem 37 - Elementary and Intermediate Algebra

Question

Subtract. $$ 6-8 $$

Step-by-Step Solution

Answer

-2

Step 1: Understand the Operation

Identify that the operation required here is subtraction.

Step 2: Analyze the Numbers

Notice that you need to subtract a larger number (8) from a smaller number (6).

Step 3: Apply the Rule for Subtracting Larger Number from Smaller Number

When subtracting a larger number from a smaller number, the result will be negative. Calculate as follows: 6 - 8 = -(8 - 6).

Step 4: Perform the Calculation

Subtract 6 from 8 to find the difference: 8 - 6 = 2Since we're subtracting the larger number from the smaller number, the answer is negative: 6 - 8 = -2

Step 5: Verify the Result

Make sure the result makes sense. Subtracting 8 from 6 indeed gives -2.

Key Concepts

basic arithmetic

Arithmetic is the foundation of mathematics and involves basic operations like addition, subtraction, multiplication, and division. In this exercise, we focus on one of these basic operations: subtraction.

negative numbers

Negative numbers represent values less than zero. They are useful for describing scenarios like temperature below freezing or oweing money. We use the minus sign (-) to denote negative numbers. In this exercise, we end up with a negative result because when we subtract a larger number from a smaller one, the result falls below zero.

subtraction rules

Subtraction might seem complicated, but it follows simple rules. If you subtract a larger number from a smaller number, the answer is negative. Here's how the rule works:
If you have to solve a problem like 6 - 8, you're essentially finding how much less 6 is than 8. You can rearrange the subtraction as follows:

• 6 - 8 becomes -(8 - 6)
• Calculate the subtraction inside the parentheses: 8 - 6 = 2
• Then, apply the negative sign, resulting in -2.

The final answer is -2. This method helps you correctly figure out whether your result should be positive or negative.

elementary algebra

Algebra involves using letters and symbols to represent numbers and operations. The problem we solved involves an elementary step in algebra called simplification.
To simplify 6 - 8, you need to understand the relationship between the numbers. Since subtracting a larger number from a smaller one gives a negative result, you apply this rule to find the answer.
In more advanced algebra, this concept helps you understand equations and solve for unknowns. But for now, grasping the negative result in such a subtraction problem sets the stage for more complex topics.