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Chapter 2: Problem 17

Subtract. $$15-18$$

Short Answer

Expert verified
The result of 15 - 18 is -3.

Step by step solution

01

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.
02

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.
03

Perform the Addition

Now add \(15\) and \(-18\) together. The result will be negative because \(-18\) has a larger absolute value than \(15\). Calculate: \(15 + (-18) = -3\).
04

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.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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.

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