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Chapter 2: Problem 44

Find the opposite of each integer. $$ 123 $$

Short Answer

Expert verified
The opposite of 123 is -123.

Step by step solution

01

Understanding the Problem

To find the opposite of an integer, you need to take the additive inverse of that integer, which simply means to change the sign of the number. The opposite of a positive number is negative, and the opposite of a negative number is positive.
02

Identifying the Integer Given

The integer given in the problem is 123. This is a positive number.
03

Calculating the Opposite

Since 123 is positive, the opposite will be negative. Thus, the opposite of 123 is \(-123\).

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Key Concepts

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

Additive Inverse
When dealing with integers, an important concept to understand is the additive inverse. The additive inverse of a number is what you need to add to a number to get zero. For any integer, this just means switching its sign.
  • If you start with a positive number, its additive inverse will be the same number but negative. For example, the additive inverse of 5 is -5.
  • Conversely, if you have a negative number, its additive inverse will be positive. For example, the additive inverse of -3 is 3.

This concept helps balance equations and is essential in algebra. It's like using a mirror that flips the sign of the integer.
Positive and Negative Numbers
In mathematics, numbers can be either positive or negative, and understanding this is crucial for working with integers.
  • Positive numbers are greater than zero and are usually penned without any sign or with a plus sign, like +7 or just 7.
  • Negative numbers are less than zero and have a minus sign in front of them, like -5.

These numbers exist on a number line with zero acting as the center point.
  • Numbers to the right of zero are positive.
  • Numbers to the left of zero are negative.
Understanding positive and negative numbers helps you visualize operations involving these numbers, making it a foundational skill in mathematics.
Integer Operations
Integer operations involve the basic arithmetic actions performed on integers, specifically addition, subtraction, multiplication, and division.
Let's break them down:
  • Addition: When adding integers, the rule of thumb is to keep the sign of the larger number and subtract the smaller number from the larger when signs differ. If both integers are positive, or both are negative, just add the numbers and keep the sign.
  • Subtraction: To subtract integers, change the sign of the number being subtracted and then follow the rules for addition. For example, 7 - (-2) equals 7 + 2 = 9.
  • Multiplication and Division: The product or quotient of two integers will be positive if their signs are the same, and negative if their signs are different. For example, -3 multiplied by 4 is -12, whereas -3 multiplied by -4 is 12.
Mastering these operations allows one to handle any problem involving integers efficiently, building a solid base for more advanced mathematical concepts.

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