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Chapter 3: Problem 46

Find the opposite of the number. 22

Short Answer

Expert verified
The opposite of 22 is -22.

Step by step solution

01

Analyze the Number

We have been given the number 22. This number is positive and located on the right side of the number line, if we consider zero as our starting point.
02

Find the Opposite Number

The opposite of 22 would be the same distance away from zero, but on the left side of the number line. The opposite number of 22, therefore, is -22.

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Key Concepts

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

Number Line
A number line is a visual representation of numbers on a straight line. It serves as a useful tool to help understand and compare numbers. On the number line, each tick or point corresponds to a unique integer. Usually, zero is placed at the center, with positive numbers extending to the right and negative numbers stretching to the left.

Key features of a number line include:
  • Origin: The central point which is zero, marking the transition from negative to positive numbers.
  • Uniform Spacing: Equal spacing between consecutive numbers to ensure accuracy in measurement and comparison.
  • Infinite Extension: The line theoretically extends infinitely in both directions, suggesting the limitless nature of integers.
For instance, if you want to find -22 on the number line, start at zero, and count 22 steps to the left. This visual method helps in understanding the concept of moving from positive to negative values.
Positive and Negative Numbers
In mathematics, numbers are categorized into positive and negative, based on their position relative to zero on the number line. Positive numbers are all greater than zero and appear on the right side of zero. Negative numbers, on the other hand, are less than zero and are displayed on the left side of zero.

Understanding these categories is crucial for performing arithmetic operations and solving equations.
  • Positive Numbers: Examples include 1, 2, 3, and any number larger than zero. These can represent quantities, such as 22, which imply more, gain, or above zero in terms of measurement.
  • Negative Numbers: Examples include -1, -2, -3, and so forth, representing values less than zero, often linked with concepts like loss, decrease, or below zero.
For example, when you think of 22 as a positive number, it's positioned on the right side of the number line. Its opposite, -22, is considered a negative number.
Opposite Numbers
Opposite numbers are pairs of numbers that are exactly the same distance from zero, but in different directions on the number line. The concept of "opposite" is straightforward: if you have a number going a certain distance to the right of zero, its opposite is the same distance to the left.

This idea is useful in solving problems involving symmetry and balance in mathematics.
  • Finding Opposites: Simply change the sign of a number to find its opposite. For example, the opposite of +22 is -22; and the opposite of -5 is +5.
  • Zero as Its Own Opposite: Zero is the only number that is its own opposite, as it is neither positive nor negative.
So, when finding the opposite of 22, you simply change its sign to get -22. This concept helps in understanding how numbers relate to each other through symmetry and inversion on the number line.

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Most popular questions from this chapter

Subtract. $$7-14$$

Subtract. $$(-41)-65$$

Evaluate the expression for the given values of the variables. \(a-b-c,\) for \(a=-1, b=7,\) and \(c=-15\)

Is \(-8\) a solution of the equation \(-7+m=-15 ?\)

Simplify. $$4-5-12$$
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