Problem 26 - Algebra A Combined Function

Question

Add. See Examples 1 through 12,18, and 19. $$ -18+(-26) $$

Step-by-Step Solution

Answer

The sum of -18 and -26 is -44.

Step 1: Identify the problem

We need to find the sum of two negative numbers: -18 and -26.

Step 2: Understand adding negative numbers

When we add two negative numbers, we are essentially adding their absolute values and then attaching a negative sign to the result.

Step 3: Calculate the absolute values

The absolute value of -18 is 18, and the absolute value of -26 is 26.

Step 4: Add the absolute values

Add the absolute values of the numbers: 18 + 26 = 44.

Step 5: Apply the negative sign

Since we are adding two negative numbers, we attach a negative sign to the result from Step 4. Thus, -18 + (-26) = -44.

Key Concepts

Absolute Value

When you see a number with a negative sign, like \(-18\) or \(-26\), you're looking at negative numbers. But what if we want to focus on just the size of that number, without worrying about whether it's positive or negative? This is where the concept of "absolute value" comes in.

• The absolute value of a number is simply its distance from zero on the number line, irrespective of direction.
• For any negative number \(x\), its absolute value is \(-x\), turning it into a positive figure.
• For example, the absolute value of \(-18\) is \(18\), and the absolute value of \(-26\) is \(26\).

Understanding absolute values helps us simplify calculations involving negative numbers by focusing only on their size.

Integer Arithmetic

Integer arithmetic involves performing basic math operations—like addition or subtraction—specifically on integers. It follows specific rules, especially when negative integers are a part of the equation.

• When adding two negative numbers, like \(-18\) and \(-26\), calculate the absolute values first: \(18\) and \(26\).
• Then, add these absolute values: \(18 + 26 = 44\).
• Finally, since both numbers we added were negative, we attach a negative sign to their sum: \(-44\).

These steps make it easier to handle complex problems by dealing with their components separately before combining them.
Never forget to reassess which operations you are performing based on whether the numbers involved are positive or negative.

Negative Numbers

Negative numbers represent values below zero and have unique properties in arithmetic operations.

• A negative number is one that sits left of zero on a number line, like \(-1, -2, -3,\) etc.
• Adding negative numbers requires attention to both size and sign.
• Consider \(-18 + (-26)\): Start by ignoring the negative signs and focus on their sizes \(18\) and \(26\) instead.
• When the negative signs are reapplied, it represents their cumulative effect, giving us \(-44\).

Think of combining negative numbers as combining debts. Each negative number shows a certain amount of 'debt' or 'loss', and adding them combines these deficits.Acknowledging this helps see them as a logical extension of the more familiar positive numbers.