Absolute Value Explained for 6th Graders

The absolute value is the distance the number is from 0 on a number line.

Distance is always positive, so the absolute value is always positive (or can also be zero).

For any positive number, the absolute value of the number does not change - it is just the number itself.

For example, the absolute value of 13 is 13.

For any negative number, the absolute value is also the opposite value of the number.

For example, the absolute value of -7 is 7.

In the example above, we can see that the number 5 is 5 away from 0, so the absolute value of 5 is 5.

We can also see that the number -2 is 2 away from 0. So the absolute value of -2 is 2.

The symbol we use for absolute value are two vertical bars on either side of the number.

|5| means the absolute value of 5.

|-0.47| means the absolute value of -0.47

|7 − 10| means the absolute value of the expression 7 − 10.

|n| means the absolute value of the variable n.

|3 + y| means the absolute value of the expression 3 + y

A number line is really useful for visualising how absolute value works.

As you can see from the number line, the numbers -4 and 4 are exactly the same distance from 0.

They are both 4 away from zero.

This means that they both have the same absolute value which is 4.

We can also use the number line to tell us which numbers have an absolute value of 2.

We can either go 2 steps left of zero, or 2 steps right of zero.

2 steps left of zero is -2.

2 steps right of zero is 2.

So both -2 and 2 have an absolute value of 2.

We can write |-2| = |2| = 2 to show this

Examples

• The absolute value of 10 is 10. We write this |10| = 10
• The absolute value of -2 is 2. We write this |-2| = 2
• The absolute value of -16 is 16. We write this |-16| = 16
• The absolute value of 2.5 is 2.5. We write this |2.5| = 2.5
• The absolute value of -½ is ½. We write this |-½| = ½
• The absolute value of 0 is 0. We write this |0| = 0
• |4 − 9| means the absolute value of 4 − 9 = |-5| = 5.
• |-7 + 5| means the absolute value of -7 + 5 = |-2| = 2

The opposite value of a number is the number on the opposite side of the number line the same distance from 0.

The opposite value of any number n is -n. Also the opposite value of -n is n.

In the exampe above, we can see that the opposite value of 4 is the number which is the the same distance from 0 on the opposite side of the number line which is -4.

So the opposite value of 4 is -4.

We can also see that the opposite value of -4 is 4.

Examples

• The opposite value of 5 is -5.
• The opposite value of -5 is 5.
• The opposite value of 23 is -23.
• The opposite value of -12 is 12.
• The oppositve value of -3.5 is 3.5.
• The opposite value of 0 is 0.

For any negative number (or zero), the absolute value is the same as the opposite value of a number.

For any positive number, the opposite value is negative, but the absolute value remains positive.

We use absolute value in real life in context that involve negative numbers.

This means that in context such as money, measurements and time we might see absolute value being used.

Here are some contexts where we might use absolute value:

• Temperature
  • If the temperature changes by –7 degrees or +7 degrees, the size of the change is 7 degrees.
• Elevation
  • A diver at –20 feet and a hiker at +20 feet are both 20 feet from sea level.
• Money
  • If you owe $10 (–10) or have $10 (+10), the absolute value tells the size of the amount: $10.
• Time
  • If we are at T -5 minutes or T + 5 minutes, then we are 5 minutes from launch time
• Sports
  • If the absolute value of a team's goal difference is 12 points, then they might have score 12 more points than they have conceded (+12 points), or scored 12 fewer points than they conceded (-12 points).

Here are a few of the commonest mistakes when students are learning about absolute value:

1) Confusing absolute value with opposite value

• |5| = -5 INCORRECT
• |5| = 5 CORRECT

2) Forgetting that the absolute value is the distance from 0 to the number and is always positive (or zero).

• The absolute value of a number can NEVER be negative!

3) Forgetting that the absolute value of zero is zero.

• |0| = 0

We have a range of different absolute value worksheets that cater for a range of different levels of ability and age, from 6th grade and upwards.

Our worksheets skills include:

• reading negative numbers on a number line;
• finding the opposite value of a number.
• finding the absolute value of a number;
• comparing absolute values;
• find the values of expressions involving absolute values;
• solving equations involving absolute values.

Our absolute value calculator will find the absolute value of any integer or fraction.

Take a look at this Interactive Number Line app created by PhET.

This interactive area explorer is provided by PhET Interactive Simulations University of Colorado Boulder https://phet.colorado.edu

You can use the app to help you to understand negative numbers and absolute values using the number line to show the distance between two points.

The link below will open the quiz in a dedicated quiz page or you can preview a copy of the quiz underneath.

The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources.

If you have any questions or need any information about our site, please get in touch with us using the 'Contact Us' tab at the top and bottom of every page.