Absolute value - Examples, Exercises and Solutions

Question Types:
Absolute value: Identifying Number oppositesAbsolute value: Solve absolute value equations with a number outside the absolute value barsAbsolute value: Solving the Absolute value

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

Question 1

Determine the absolute value of the following number:

\( \left|18\right|= \)

Question 2

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

Question 3

\( \left|-19\frac{1}{4}\right|= \)

Question 4

\( \left|3\right|= \)

Question 5

\( \left|0.8\right|= \)

Examples with solutions for Absolute value

Exercise #1

Determine the absolute value of the following number:

∣18∣= \left|18\right|=

Video Solution

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

Exercise #2

∣−2∣= \left|-2\right|=

Video Solution

Step-by-Step Solution

When we have an exercise with these symbols || we understand that it refers to absolute value.

Absolute value does not relate to whether a number is positive or negative, but rather checks how far it is from zero.

In other words, 2 is 2 units away from zero, and -2 is also 2 units away from zero,

Therefore, absolute value essentially "zeroes out" the negativity of the number.

 

|-2| = 2

 

Answer

2 2

Exercise #3

∣−1914∣= \left|-19\frac{1}{4}\right|=

Video Solution

Step-by-Step Solution

These signs in the exercises refer to the concept of "absolute value",

In absolute value we don't have "negative" or "positive", instead we measure the distance from point 0,

In other words, we always "cancel out" the negative signs.

In this exercise, we'll change the minus to a plus sign, and simply remain with 19 and a quarter.

And that's the solution!

Answer

1914 19\frac{1}{4}

Exercise #4

∣3∣= \left|3\right|=

Video Solution

Answer

3 3

Exercise #5

∣0.8∣= \left|0.8\right|=

Video Solution

Answer

0.8 0.8

Question 1

\( −\left|-18\right|= \)

Question 2

\( \left|x\right|= \)

Question 3

\( -\lvert4^2\rvert= \)

Question 4

\( \left|3^2\right|= \)

Question 5

Are the numbers opposite?

\( \left|-3\right|,\left|3\right| \)

Exercise #6

−∣−18∣= −\left|-18\right|=

Video Solution

Answer

−18 -18

Exercise #7

∣x∣= \left|x\right|=

Video Solution

Answer

x x

Exercise #8

−∣42∣= -\lvert4^2\rvert=

Video Solution

Answer

−16 -16

Exercise #9

∣32∣= \left|3^2\right|=

Video Solution

Answer

9 9

Exercise #10

Are the numbers opposite?

∣−3∣,∣3∣ \left|-3\right|,\left|3\right|

Video Solution

Answer

No

Question 1

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

Question 2

Are the numbers opposite?

\( -\left|-801\right|,\left|+801\right| \)

Question 3

Are the numbers opposite?

\( -\left|-81\right|,\left|9^2\right| \)

Question 4

Are the numbers opposite?

\( \left|56\right|,\left|-5.6\right| \)

Question 5

Are the numbers opposite?

\( \left|-\frac{1}{3}\right|,\left|\frac{3}{1}\right| \)

Exercise #11

−∣−y2∣= -\left|-y^2\right|=

Video Solution

Answer

−y2 -y^2

Exercise #12

Are the numbers opposite?

−∣−801∣,∣+801∣ -\left|-801\right|,\left|+801\right|

Video Solution

Answer

Yes

Exercise #13

Are the numbers opposite?

−∣−81∣,∣92∣ -\left|-81\right|,\left|9^2\right|

Video Solution

Answer

Yes

Exercise #14

Are the numbers opposite?

∣56∣,∣−5.6∣ \left|56\right|,\left|-5.6\right|

Video Solution

Answer

No

Exercise #15

Are the numbers opposite?

∣−13∣,∣31∣ \left|-\frac{1}{3}\right|,\left|\frac{3}{1}\right|

Video Solution

Answer

No

Topics learned in later sections

  1. Numerical Value
  2. Absolute Value
  3. Absolute Value Inequalities
  4. Inequalities with Absolute Value