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Chapter 2: Problem 43

Find the opposite of each integer. $$ 23 $$

Short Answer

Expert verified
The opposite of 23 is -23.

Step by step solution

01

Understanding integers and opposites

To find the opposite of an integer, we simply need to change its sign. If an integer is positive, its opposite is negative. Conversely, if an integer is negative, its opposite is positive. For the integer given in this task, which is 23, we recognize it as a positive integer.
02

Calculate the opposite integer

The integer given is 23, which is a positive number. To find the opposite of 23, we change its sign from positive to negative. Thus, the opposite of 23 is -23.

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Key Concepts

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

Integers
Integers are a set of numbers that include all whole numbers, both positive and negative, as well as zero. Think of integers as numbers along a continuous line, starting from negative infinity, moving through zero, and marching off to positive infinity. They do not have fractions or decimal parts.
This means integers can be:
  • Positive (e.g., 1, 2, 3, ...)
  • Negative (e.g., -1, -2, -3, ...)
  • Zero (which is neutral, not positive or negative)
Understanding integers is essential in learning mathematics as they represent whole amounts and positions on a number line. For example, 23 is an integer, specifically a positive one. Recognizing it as an integer means acknowledging it does not have fractional or decimal components.
Negative Numbers
Negative numbers are numbers less than zero and are always indicated by a minus sign (鈭�). On a number line, negative numbers are located to the left of zero, often representing quantities such as debts or temperatures below freezing. They are an integral part of the integer family.
Here are some quick highlights about negative numbers:
  • They are the opposite of positive numbers.
  • They get progressively smaller as you move further left on a number line (e.g., -1, -2, -3).
  • Adding a negative number means moving to the left on the number line.
To find the opposite of a positive integer like 23, you simply turn it into its negative counterpart, such as -23. This occurs by changing from a positive to a negative sign, which points it to the opposite direction on a number line.
Positive Numbers
Positive numbers are numbers greater than zero. They are found to the right of zero on a number line and signify amounts greater than nothing. In day-to-day life, you often use positive numbers to represent things you gain, such as adding up money or measuring distances.
Positive numbers:
  • Do not have a plus sign when written, they're assumed positive.
  • Increase in value as they move right on a number line (e.g., 1, 2, 3, ...).
  • Are direct opposites of negative numbers.
For example, the number 23 is a positive number. When you flip it, you make it negative (-23). This process of flipping or finding the 'opposite' is simply about changing its sign. This concept helps in various mathematical operations where positive and negative effects or actions are compared.

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Most popular questions from this chapter

Evaluate. $$ |-x| \text { if } x=-6 $$

Represent each quantity by an integer. A scuba diver is swimming 25 feet below the surface of the water in the Gulf of Mexico.

Solve. Check each solution. See Examples 5 through 8. $$ -10 x=-10 $$

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Find each quotient. See Examples 10 through 14. $$ \frac{56}{-4} $$
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