Problem 47 - College Algebra

Question

Exercises will help you prepare for the material covered in the next section. In cach exercise, perform the indicated operation or operations. $$-6-(-5)$$

Step-by-Step Solution

Answer

-1

Step 1: Understand the operation

The given operation is \(-6-(-5)\). This is a case of subtracting a negative number or removing a negative.

Step 2: Apply the rules for subtracting negatives

In terms of subtraction, two negatives make a positive. Hence, the operation \(-6-(-5)\) becomes \(-6+5\).

Step 3: Perform Addition

Now, you just add the numbers \(-6+5\) which equals \(-1\).

Key Concepts

Subtracting Negatives

Subtracting a negative number might initially seem confusing, but it's simpler than it appears. When you see an expression like -6 - (-5), it means you're taking away a negative number. In mathematics, subtracting a negative is the same as adding its positive opposite. So, -6 - (-5) becomes -6 + 5.

The rule to remember is:

• Subtracting a negative is equivalent to adding.

It's the same idea as removing an unwanted burden, which makes things lighter or more positive. This transformation from subtracting negative to simple addition is an essential building block in arithmetic operations, providing a deeper understanding of how numbers relate to each other.

Integer Addition

Adding integers involves combining numbers, which could be positive or negative, along a number line. When we perform the operation -6 + 5, we're essentially moving negatively and then positively along the number line.

Here are key points to consider:

• If you add a positive number, move to the right.
• If you add a negative number, move to the left.

In our example of -6 + 5, we begin at -6 and move 5 steps to the right, ending at -1.

Understanding integer addition prepares you for handling more complex expressions and calculations. It's like basic navigation on the number landscape, showing where you "land" after combining different values.

Mathematical Expressions

Mathematical expressions involve numbers and operations represented in a structured format. The expression -6 - (-5) illustrates several important concepts, from operations with integers to transforming expressions.

Here’s how to approach them:

• Recognize the operations involved - here, subtraction and addition.
• Apply mathematical rules, like converting a double negative into a positive.
• Solve step-by-step, leading from the complex to the simple.

These expressions are like mathematical sentences, and understanding them lets you know exactly what to do with numbers. It's a crucial skill in maximising mathematical fluency and leading towards solving even more advanced equations with ease.