Problem 32 - Algebra 1

Question

Find the difference. $$ 6-|-2| $$

Step-by-Step Solution

Answer

The difference is 4.

Step 1: Calculate Absolute Value

The absolute value of a negative number transforms it into a positive value. Hence, the absolute value of -2, which is denoted as \( |-2| \), will become +2.

Step 2: Perform Subtraction

Now, subtract this absolute value from 6. So, the operation becomes \( 6 - 2 \), which equals 4.

Key Concepts

Subtraction

In mathematics, subtraction is a fundamental operation which involves taking away one number from another. In simpler terms, if you have a certain number of objects, and you remove some, subtraction tells you how many are left. This process is pretty straightforward with positive numbers: if you have 6 apples and you give away 2, you end up with 4 apples. However, things can get a bit tricky when negative numbers are involved, which is where absolute values come into play.

• Subtraction helps us find how much more or less one number is compared to another.
• It's useful in calculating differences, decreases, or deficits.

In the exercise above, we begin by identifying that we need to subtract the absolute value of a number from another number. This operation is simplified by first handling the absolute value part of the equation.

Negative Numbers

Negative numbers represent values less than zero and are used to denote a loss, decrease, or an inverse. They play a crucial role in mathematics, particularly in contexts where values dip below zero, such as temperatures or financial debts.

• Negative numbers are preceded by a minus (-) sign.
• When paired with positive numbers, they reflect opposition (e.g., gain vs. loss).

With the exercise at hand, we deal with the negative number -2. When figuring out the difference between values, it's essential to understand how negative numbers behave, such as becoming positive when calculating absolute values. This ensures clarity and accuracy in mathematical operations.

Positive Numbers

Positive numbers are all the numbers greater than zero. They signify gains, increases, or something that exists. In many real-world scenarios, they help quantify amounts, distances, or similar upward trends.

• Positive numbers do not have any sign in front of them; they stand on their own.
• They are straightforward and intuitive to handle in equations.

In the exercise, the absolute value process turns the negative number -2 into the positive number 2 before subtraction is carried out. Recognizing this transformation is crucial for the correct application of subtraction in the exercise.