Problem 70 - Elementary and Intermediate Algebra

Question

Subtract. $$ -9-16 $$

Step-by-Step Solution

Answer

-25

Step 1: Understand the Problem

The exercise requires the subtraction of two numbers: (-9) and 16.

Step 2: Convert Subtraction to Addition

To subtract a positive number, you can add its negative counterpart. So, the expression -9 - 16 can be rewritten as -9 + (-16).

Step 3: Add the Numbers

Now, add -9 and -16. When adding two negative numbers, you add their absolute values and keep the negative sign. So, |-9| + |-16| = 9 + 16 = 25 and the negative sign remains: -25.

Key Concepts

Negative Numbers

Negative numbers represent values less than zero. Think of a thermometer sinking below freezing point or an elevator going below ground level. Here are some key points about negative numbers:

• Negative numbers have a minus sign (-) before them, like -1, -2, -3, etc.
• They are used to describe deficits, temperatures below zero, or depths below sea level.
• When comparing, negative numbers are less than zero and less than any positive number.

Understanding negative numbers is crucial for arithmetic operations like subtraction and addition.

Absolute Value

The absolute value of a number is its distance from zero on the number line, ignoring whether it is positive or negative. Here are the essentials of absolute value:

• The symbol for absolute value is two vertical lines, like \(|x|\).
• For positive numbers or zero, the absolute value is the number itself, \(|3| = 3\) and \(|0| = 0\).
• For negative numbers, the absolute value is the number without its negative sign, \(|-5| = 5\).

Using absolute values helps simplify the process of adding and subtracting numbers, especially when dealing with negative numbers.

Addition of Negative Numbers

Adding negative numbers follows a pattern that involves summing up their absolute values and then applying the negative sign. Let's break down the steps:

• Rewrite as Addition: When you see subtraction involving a negative number, convert it to addition. For example, \(-9 - 16 = -9 + (-16)\).
• Sum Absolute Values: Add the absolute values of the numbers involved. For \(-9 + (-16)\), calculate \(|-9| + |-16| = 9 + 16 = 25\).
• Apply Negative Sign: Keep the negative sign for the sum of negative numbers, resulting in -25 in this case.

Understanding this simple process ensures accuracy when dealing with multiple negative numbers in mathematical operations.