Absolute value - Examples, Exercises and Solutions

Understanding Absolute value

Complete explanation with examples

The "absolute value" may seem complicated to us, but it is simply the distance between a given number and the figure 0 0

What is absolute value?

An absolute value is denoted by ││ and expresses the distance from zero points.
The absolute value of a positive number - will always be the number itself.
For example: 2=2│2│= 2
The absolute value of a negative number: will always be the same number, but positive.
For example: 3=3│-3│=3
Note that the absolute value of a number will always be a positive number given that distance is always positive.

Un valor absoluto se denota por ││

The absolute value of a number is the distance between the number itself and 0 along a number line.

For example:

  • The distance between the number +7 +7 and 0 0 is 7 7 units. Therefore, the absolute value of +7 +7 is 7 7 .
  • The distance between the number 7 -7 and 0 0 is also 7 7 units. Therefore, the absolute value of 7 -7 will also be 7 7

As we can see, from the point of view of absolute value, it doesn't matter if the number is positive or negative.

To denote the absolute value, the number is written between two vertical lines.

Detailed explanation

Practice Absolute value

Test your knowledge with 14 quizzes

\( \left|-2\right|= \)

Examples with solutions for Absolute value

Step-by-step solutions included
Exercise #1

Determine the absolute value of the following number:

18= \left|18\right|=

Step-by-Step Solution

The "absolute value" can be viewed as the distance of a number from 0.
Therefore, the absolute value will not change the sign from negative to positive, it will always be positive.

Answer:

18 18

Video Solution
Exercise #2

712= \left|-7\frac{1}{2}\right|=

Step-by-Step Solution

The absolute value of a number is always its positive value. It represents the distance of the number from zero on the number line, regardless of direction. The absolute value of any negative number is its opposite positive number.

Step 1: Identify the number to find the absolute value of: 712 -7\frac{1}{2}

Step 2: Change the negative sign to positive: 712 7\frac{1}{2}

Hence, the absolute value of 712 -7\frac{1}{2} is 712 7\frac{1}{2} .

Answer:

712 7\frac{1}{2}

Exercise #3

Solve for the absolute value of the following integer:

34= \left|34\right|=

Step-by-Step Solution

The absolute value of a number is always non-negative because it represents the distance from zero. Therefore, the absolute value of 34 34 is 34 34 .

Answer:

34 34

Exercise #4

7= \left|-7\right|=

Step-by-Step Solution

The absolute value of a number is its distance from zero on the number line, regardless of the direction. To find the absolute value of 7 -7 , we need to look at the distance of 7 -7 from zero, which is 7 7 . Therefore, 7=7 \left|-7\right| = 7 .

Answer:

7 7

Exercise #5

5= \left|5\right|=

Step-by-Step Solution

The absolute value of a number is its distance from zero on the number line, without considering its direction. To find the absolute value of 5 5 , consider the distance of 5 5 from zero, which is just 5 5 . Therefore, 5=5 \left|5\right| = 5 .

Answer:

5 5

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