What you need to know

Things to remember:

  • To find the absolute value of a number we find its distance from 0.
  • A positive number doesn’t change when you find the absolute value.
  • A negative number becomes its positive self when finding the absolute value.

So, what is the absolute value of a number? Simply put, it is the distance from 0!

What is the absolute value of 5?

 

 

Counting up from 0 to 5, we can see that 5 is 5 away from 0. The absolute value is therefore 5. We have special notation for writing absolute values, which is two straight lines.

|5|=5

A positive number is always its own distance away from 0, so the absolute value of positive number is itself!

|9|=9

|2.7|=2.7

|\pi|=\pi

What about if we wanted to find the absolute value of a negative number, say |-8| ?

-8 is 8 away from 0, so |-8| =8. But wait, we counted back 8. Why isn’t the absolute value -8?  Think about leaving your house and walking 20m down the street. Now imagine you had walked 20m up the street instead. You would have gone in the other direction, but it is still 20m, not -20m!

When we find the absolute value of a negative number, it is just its positive self!

|-9|=9

|-2.7|=2.7

|-\pi|=\pi

Let’s try and put this new knowledge into practice with something we have learned before, substitution.

If x=6 what is the value of |3x+2| ?

|3x+2|

|3\times x+2|

|3\times 6+2|

|18+2|

|20|

20

We will look at two more examples. What do you think will be the value of |-3x-2| and -|3x+2| ?

|-3x-2|

|-3\times x-2|

|-3\times 6-2|

|-18-2|

|-20|

20

-|3x+2|

-|3\times x+2|

-|3\times 6+2|

-|18+2|

-|20|

-20

It is important to remember that the absolute value of a negative number is its positive self. However, in the last question, it is asking for the negative of the absolute value!

Example Questions

Question 1: What is the value of |-7.8| ?

Answer

|-7.8| =7.8

Question 2: If x=9 what is the value of |12-4x| ?

Answer

|12-4x|

 

|12-4\times x|

 

|12-4\times 9|

 

|12-36|

 

|-24|

 

24

 

|12-4x|=24