Number Opposites

The concept of number opposites is often associated with positive and negative numbers. In mathematics, every real number has an opposite, which is the additive inverse.

The concept of the opposite of a number is fundamental in mathematics, providing a clear understanding of the relationship between positive and negative values. In this article, we will explore the notion of number opposites, discuss how to determine them, and provide five examples along with detailed solutions.

The opposite of a number is essentially its reflection across the origin on the number line. For any real number “a,” its opposite is denoted as “-a.” The opposite of a positive number is negative, and vice versa.

The concept of number opposites can better be explained from the diagram given below:

For example:

The opposite of 5 is -5.

The opposite of -3 is 3.

The opposite of 0 is 0 (since adding 0 to any number does not change its value).

In a more general sense, the idea of opposites can also be applied to other mathematical operations. For multiplication, the multiplicative inverse or reciprocal serves as a kind of opposite. For instance:

The reciprocal of 2 is 1/2.

The reciprocal of -1/3 is -3.

It’s important to note that not all operations have clear opposites. For example, exponentiation and division do not have simple opposites in the same way addition and multiplication do.

Solved Examples

Example 1

Opposite of 7

Solution:

The opposite of 7 is -7. This can be visualized on the number line, where 7 and -7 are equidistant from zero but lie on opposite sides.

Example 2

Opposite of -12

Solution:

The opposite of -12 is 12. In this case, the original number is negative, and its opposite is a positive value.

Example 3

Opposite of 0

Solution:

The opposite of 0 is 0 itself. This is because 0 is its own reflection across the origin, and the distance from zero remains unchanged.

Example 4

Opposite of -3/4

Solution:

The opposite of -3/4 is 3/4. In fractions, finding the opposite involves changing the sign while keeping the absolute value the same.

Example 5

Opposite of √25

Solution:

The original number is √25, which is 5. Therefore, the opposite of √25 is -5.

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