Problem 29 - Algebra 1: Concepts and Skills

Question

RULES OF ADDITION Find the sum. $$-7+(-4)$$

Step-by-Step Solution

Answer

The sum of -7 and -4 is -11

Step 1: Identify the Numbers

First, identify the numbers involved. In this case, it's -7 and -4

Step 2: Apply Rule for Adding Negative Numbers

The rule for adding two negative numbers is that the result will be negative, and the magnitude will be the sum of original numbers. So, add 7 and 4 to get 11

Step 3: Apply Negative Sign

Finally, because the rule indicates that the answer will be negative, apply the negative sign to the magnitude obtained to get the result. Thus, the answer is -11.

Key Concepts

Rules of Addition

Adding numbers seems straightforward, but applying the rules correctly ensures clarity, especially when dealing with negatives. Here's a quick rundown:

• When adding two positive numbers, simply add their magnitudes. Example: 3 + 5 = 8.
• When adding two negative numbers, also add their magnitudes, but keep the sign negative. Example: \(-3 + (-5) = -8\).
• When adding a negative number to a positive number, consider subtracting the magnitudes and retaining the sign of the larger magnitude. Example: \(7 + (-3)\): subtract 3 from 7 to get 4, the sign of the larger magnitude (7) stays, so the result is 4.

Practice these rules, and adding negative numbers will soon become second nature.

Integer Operations

Integer operations encompass addition, subtraction, multiplication, and division of whole numbers, including positives and negatives. Let's focus on addition here. Consider an integer as a directional value on a number line:

• The addition of positive numbers moves you right.
• The addition of negative numbers moves you left.

So, when adding \(-7\) and \(-4\), you move left from zero 7 steps and then another 4 steps. The more negative the sum, the further left you find yourself! Integer operations require regular practice to perfect, especially when you start juggling positives and negatives.

Negative Numbers in Mathematics

Negative numbers introduce the world of values less than zero, essential in many mathematical concepts. When dealing with them:

• Keep in mind negative is a direction, not a "less" or "more."
• They have a direct real-world connection, like temperatures below freezing or financial debts.

Mathematically, when adding negative numbers, you're essentially combining their potential or effect. The operation \(-7 + (-4)\) results in \(-11\), indicating a deeper dive to the left on the number line. Comprehending negative numbers develops your ability to navigate through more complex equations and enhances problem-solving skills.