Problem 79 - Algebra A Combined Function

Question

Perform the indicated operation. \(7+(-12)\)

Step-by-Step Solution

Answer

The result of \(7 + (-12)\) is \(-5\).

Step 1: Recognize the operation

We need to perform the addition of 7 and -12, which involves adding a positive number to a negative number. In mathematical terms, this is expressed as \( 7 + (-12) \).

Step 2: Adjust the signs

Adding a negative number is the same as subtracting the positive value of that number. Thus, \( 7 + (-12) \) is equivalent to \( 7 - 12 \).

Step 3: Perform the subtraction

Subtract the larger number from the smaller one and retain the negative sign because the magnitude of 12 is larger than that of 7. This gives us \( 12 - 7 = 5 \), thus the expression evaluates to \(-5\).

Key Concepts

Addition with Negative Numbers

When you first encounter the addition of negative numbers, it might seem a bit tricky. Let's break it down so it's easy to digest! When you add a negative number to a positive number, think of it as a movement on a number line.

• A positive number moves you to the right.
• A negative number moves you to the left.

So, for the problem of adding 7 and -12, you start at 7 and move 12 units to the left. Rather than thinking of this as an additon, envision it as a backward movement. This movement will place you at -5 on the number line. The numerical value decreases as you're adding a negative value, essentially subtracting its magnitude from the initial positive number.

Sign Adjustment in Arithmetic

Adjusting signs in arithmetic is a crucial skill to master. Understanding how to work with positive and negative numbers can simplify many problems! When you see something like \( 7 + (-12) \), you can adjust the signs for an easier computation. Simply put, adding the negative is the same as subtracting its magnitude from the first number.

• The expression \( 7 + (-12) \) becomes \( 7 - 12 \).
• Conceptually, we are subtracting 12 from 7.

This technique helps transform complex-looking problems into simpler subtraction problems. It highlights how, in arithmetic, sign adjustment maintains equivalence while aiding us in computations.

Subtraction of Integers

When subtracting integers, think in terms of subtracting smaller from larger with an eye on sign. With \( 7 - 12 \), look at the numbers independently of their order. Here, 12's magnitude outweighs 7, so we subtract 7 from 12, giving 5.

• Subtract the smaller magnitude from the larger.
• Keep the sign of the integer with the larger absolute value.

Therefore, your resultant sign will reflect the larger number's sign, i.e., negative, because 12 is the bigger integer here. Evaluating \( 7 - 12 \) yields \(-5\). This results from keeping the negative sign of the larger number.