Problem 22 - Introductory Algebra for College Students

Question

Perform the indicated subtraction. $$15-(-15)$$3

Step-by-Step Solution

Answer

The answer is 30

Step 1: Identify the operation

The operation provided is \(15 - (-15)\). The process will involve subtraction and understanding how to deal with negative numbers.

Step 2: Apply the rule for subtracting negative numbers

When you subtract a negative number, it becomes addition of a positive number. This means subtracting \(-15\) is the same as adding \(+15\). So, \(15 - (-15)\) becomes \(15 + 15\).

Step 3: Perform the addition

Add the numbers together, \(15 + 15 = 30\).

Key Concepts

Integer Operations

Understanding integer operations is fundamental in mathematics. Integers include whole numbers and their negatives, like -3, 0, 5. These numbers are commonly involved in operations such as addition, subtraction, multiplication, and division.

• **Addition:** Combining two numbers to make a larger or equal value.
• **Subtraction:** Finding the difference between numbers, which often involves understanding direction on a number line.
• **Multiplication and Division:** Repeated addition or determining how many times one number is contained in another.

For example, in subtracting integers like in the problem \(15 - (-15)\), you're dealing with subtracting a negative, which requires specific knowledge about how negative numbers behave.

Negative Numbers

Negative numbers are numbers less than zero and are often represented with a minus sign (-). They allow us to express values below zero and are crucial for balancing equations, calculating debts, temperatures, and more.

• **On the number line:** Negative numbers lie to the left of zero.
• **Behavior in operations:** They behave differently than positive numbers, especially in multiplication, division, and subtraction.
• **Importance in contexts:** Used in various real-life scenarios like temperatures or financial calculations.

For instance, subtracting a negative number - like in \(15 - (-15)\) - essentially means you are increasing the value, as it turns into an addition operation.

Addition and Subtraction Rules

When dealing with integers, addition and subtraction have specific rules to follow, particularly with negative numbers.

• **Subtracting a Negative:** This turns into adding a positive. For instance, \(15 - (-15)\) becomes \(15 + 15\).
• **Adding Negatives:** Combine the numbers as if they were positive and then apply the negative sign.
• **Using a Number Line:** It helps visualize moving left for negative and right for positive operations.

These rules simplify calculations and help avoid mistakes. In the example \(15 - (-15) = 15 + 15 = 30\), applying these rules ensures you achieve the correct result quickly and accurately.