Opposites and Absolute Value of Integers

Opposite integers are two integers that are the same distance from zero on the number line but in opposite directions. They have the 1 same magnitude (absolute value) but different signs.

Every integer has an opposite.

1. The opposite of zero is zero itself.
2. The opposite of a positive integer is a negative integer with the same absolute value. For example: The opposite of 5 is -5.
3. The opposite of a negative integer is a positive integer with the same absolute value. For example: The opposite of -10 is 10.

The following diagram shows opposite integers on the number line. Scroll down the page for more examples and solutions on opposite integers and absolute values.

 

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Key Properties of Opposite Integers:

1. The absolute value of an integer is its distance from 0 on the number line. Opposite integers have the same absolute value (distance from zero). For example: |-5| = |5| = 5
2. When you add two opposite integers together, the result is always zero. For example: 5 + (-5) = 0

Opposite integers are like mirror images of each other across zero on the number line. They represent quantities that are equal in magnitude but in reverse directions or have reverse effects.

Real-World Examples of Opposites:

1. Temperature: If the temperature is 5 degrees above zero (+5°C), its opposite is 5 degrees below zero (-5°C).
2. Finances: If you have a gain of 10(+10), its opposite is a loss of 10(−10).
3. Elevation: If you are 20 meters above sea level (+20m), its opposite is 20 meters below sea level (-20m).

How to determine the Opposites of Integers?
To find the opposite of an integer, we just change its sign. If it is negative, change to positive. If it is positive change to negative.
Opposite integers are the pairs of integers that have the same absolute value, or the same distance from zero.
The sum of two opposites is always zero.

This video provides two examples of determining the opposite of a given integer.
Examples:
What is the opposite of 4?
What is the opposite of -9?

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Simplifying the Opposites of Negatives Integers
Shortcut:
An even number of negatives results in a positive.
An odd number of negatives results in a negative.

This video provides several examples of simplifying opposites of negative integers.

Examples:
Evaluate
−(5)
−(−3)
−(−(−1))
−(−(−(−8)))

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Opposite and absolute value of an integer
Opposites: Two numbers that are the same distance from zero but on opposite sides.
Absolute value: The integer’s distance from zero on the number line.

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Absolute Value and Opposite of Integers
Example:
Write the absolute value and opposite of
a) −16
b) 140
c) −1
d) 0

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Opposites and Absolute Values of Integers
Learn about the opposites and absolute values of integers.
Examples:

1. Find the additive inverse of −1
   
2. Evaluate the expressions:
   a. |−9| + |−7|
   b. |−2 × 9|
   c. |18 / −3|

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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