Problem 27 - Elementary Algebra

Question

For the following exercises, perform the indicated operations. $$ -4-4 $$

Step-by-Step Solution

Answer

Answer: -8

Step 1: Rewrite the subtraction as addition of the opposite number

To subtract a negative number, we can rewrite the subtraction as an addition of the opposite number. So, we rewrite \(-4 - 4\) as \(-4 + (-4)\).

Step 2: Perform the addition operation

Now we just need to add the two negative numbers \(-4\) and \(-4\). When adding two negative numbers, we can add their absolute values and keep the negative sign: \(|-4| + |-4| = 4 + 4 = 8\). Since both numbers are negative, the sum will also be negative: \(-8\). So, the result of the operation \(-4-4\) is \(-8\).

Key Concepts

Understanding Integer Subtraction

Integer subtraction involves taking one integer away from another. A key tip is to think of subtraction as "adding the opposite." This means subtracting a number is the same as adding its negative.
For example,

• When you see \( -4 - 4 \),consider it as \( -4 + (-4) \).

Now, you can focus on the easier task of addition instead of subtraction. This conversion is handy when solving problems involving negative numbers.

Basics of Addition of Integers

Adding integers is straightforward once you know the signs of the numbers involved. If both numbers are negative, like \( -4 + (-4) \),add their absolute values and keep the negative sign.

• If you're adding \(-4\) and \(-4\),think: \(|-4| + |-4| = 4 + 4 = 8\).
• Because both numbers are negative, the result is negative: \(-8\).

This works similarly when adding two positive numbers. They combine to become larger without changing signs.

Role of Absolute Value in Calculations

Absolute value measures how far a number is from zero, ignoring its sign. It helps simplify operations with negatives.
For example,

• The absolute value of both \(-4\) and \(+4\) is \(4\).
• When adding or subtracting, compute the absolute values first and apply the sign later, streamlining your calculations.

This approach allows you to focus on magnitude before worrying about whether the number is positive or negative.

Adding Negative Numbers Explained

Adding negative numbers might seem tricky, but it follows simple rules.

• When adding two negative numbers, their absolute values are summed, and the result retains the negative sign.
• In the expression \(-4 + (-4)\),compute \(8\)from the absolute values \(4 + 4\).
• The result of \(-8\)maintains the negative sign, as both addends were negative.

So, don't worry about direction—negative plus negative just makes a bigger negative number.