Problem 17 - Prealgebra

Question

Subtract. $$15-18$$

Step-by-Step Solution

Answer

The result of 15 - 18 is -3.

Step 1: Identify the Problem Type

We are given the subtraction problem \(15 - 18\). The problem involves subtracting a larger number from a smaller number, which will result in a negative number.

Step 2: Rewrite the Subtraction

Change the subtraction operation into a negative addition: \(15 - 18\) can be rewritten as \(15 + (-18)\). This shows that we're adding a negative number to a positive number.

Step 3: Perform the Addition

Now add \(15\) and \(-18\) together. The result will be negative because \(-18\) has a larger absolute value than \(15\). Calculate: \(15 + (-18) = -3\).

Step 4: Check Your Work

Verify the solution by considering the number line. Starting at 15, moving left 18 places brings you to -3. Thus, the solution is correct.

Key Concepts

Negative Numbers

Negative numbers are numbers less than zero. They are commonly represented with a minus sign, such as -1, -2, -3, and so on. When you subtract a larger number from a smaller one, you get a negative result.

In the example given, subtracting 18 from 15 leads us to a negative number. If you're not used to working with negative numbers, keep these key points in mind:

• A negative number is always less than zero.
• Negative numbers are the mirror of positive numbers on the number line.
• Think of them as debts or temperatures below freezing.

Imagine you have 15, but owe 18. This gives you a remaining balance of -3. Negative numbers are essential in real-world contexts like temperature and finance.

Number Line

A number line is a visual representation of numbers. It helps in understanding both positive and negative numbers in relation to each other.

A number line has zeros in the center, positive numbers to the right, and negative numbers to the left. It's a powerful tool:

• For visualizing subtraction and addition.
• To see how negative and positive numbers are arranged.
• To easily track changes in values step by step.

Take the exercise, for example: starting at 15 on the number line, move 18 steps to the left. You end up at -3. This movement illustrates how subtraction can create a negative result.

Absolute Value

Absolute value measures the distance of a number from zero on the number line, ignoring direction. It is always a positive number or zero.

The absolute value is crucial in subtraction involving negative numbers:

• It helps determine which number has a greater influence when added or subtracted.
• Helps in understanding the size of numbers independent of their sign.
• Is denoted by vertical bars, for example, \(|-18| = 18\).

In the subtraction problem, 18 has a greater absolute value than 15, hence the negative result, -3. Understanding absolute value gives you clearer insight into why the result is negative.