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Chapter 1: Problem 8

Evaluate each of the given expressions by performing the indicated operations. $$18-21$$

Short Answer

Expert verified
The result of \(18 - 21\) is -3.

Step by step solution

01

Identify the Operation

The given mathematical expression is \(18 - 21\). Notice that the operation involved is subtraction, where 21 is subtracted from 18.
02

Apply the Subtraction

To perform the subtraction \(18 - 21\), recognize that 21 is greater than 18. This means we will end up with a negative result as subtracting a larger number from a smaller one gives a negative.
03

Perform the Calculation

Subtract 21 from 18. Since 18 is less than 21, the result of 18 minus 21 is -3. This can be visualized by moving 21 units down from 18 on a number line, landing on -3.

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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 an essential part of arithmetic that students encounter when dealing with operations like subtraction. In the context of the exercise, when we subtracted 21 from 18 and got -3, we were actually working with negative numbers. Negative numbers are numbers less than zero and are represented with a minus sign ( - ) in front of them.
  • They are found on the left side of the number line, opposite to positive numbers.
  • They indicate values below zero, which can represent a loss, a decrease, or a deficit in real-world scenarios, like owing money or feeling colder than freezing point.
Understanding negative numbers helps in performing calculations that take us below zero, which is critical for solving problems like the ones in the exercise.
Number Line
A number line is a visual tool that can greatly help in understanding subtraction involving negative numbers. It is a straight horizontal line with numbers placed at regular intervals. At the center of the number line is zero, with positive numbers to the right and negative numbers to the left. By using a number line, subtraction can be seen as a physical movement:
  • To subtract a number, move left from your starting point. The number of spaces you move is equal to the number you are subtracting.
  • In the exercise, starting at 18, moving 21 steps to the left lands us at -3, clearly showing why 18 - 21 equals -3.
Number lines help make abstract concepts more concrete, allowing students to visually track and understand arithmetic operations.
Basic Arithmetic
Subtraction is one of the four fundamental operations in basic arithmetic, alongside addition, multiplication, and division. It reveals how much one quantity differs from another. In basic arithmetic:
  • Subtraction is the operation of finding the difference between numbers or amounts.
  • When subtracting larger numbers from smaller numbers, we end up with negative results, as seen in our exercise with 18 - 21.
  • It's important to remember that the order of numbers in subtraction matters, unlike addition.
Mastering subtraction and other basic arithmetic operations is crucial because they form the foundation for more complex mathematical concepts and problems.

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