This document provides an overview of absolute value and integers. It defines integers as whole numbers including positive, negative, and zero. Absolute value is defined as the distance of a number from zero on the number line. Examples are provided to illustrate finding the absolute value of positive and negative integers. Key points are that the absolute value of a number is always positive, and that the placement of signs can affect whether expressions with absolute values are positive or negative.

1. Absolute Value
of Integers
Presented by: Mark Ian Nicolas Olivar
Teacher

2. “
On this number line, where would
you place 5?
How about -9?
And how about -3?

3. Objectives
At the end of the Lesson, students will be able
to:
1. define the absolute value of a number;
2. illustrate the absolute value of a number
on the number line; and
3. appreciate the importance of knowing the
absolute value of a number.

4. What is an integer
anyway?

5. Basics of Integers
“Integer” is a Latin word meaning “whole”.
Integers are whole numbers which include
positive numbers, negative numbers, and
zero. Integers do not include decimals,
percents, and fractions.
A number line marked with integers

6. Basics of Integers
The numbers to the right of zero (0) are
positive numbers, while those to its left are
negative numbers.
When arranged in increasing order, the
negative numbers are the lowest while the
positive numbers are the highest.
For example, 4 is greater than 1, but 1 is
greater than -5.

7. Positive Numbers
Numbers which have plus signs on them are
called positive numbers. These numbers can
be found to the right side of zero.
As a general rule, numbers that don’t have a
sign are considered positive numbers.
All positive numbers are greater than their
negative counterpart and zero.
For example, 5 is greater than -5.

8. Negative Numbers
A negative number is the opposite of a
positive number. It is written with a “-” sign
before the number.
The larger the negative number, the less its
value becomes.
For example, -5 is less than -1.

9. Zero
Zero is a neutral number that is neither
negative nor positive.
It can be found at the center of the number
line, and is always less than any positive
number, but is always greater than any
negative number.

10. Absolute Value of
an Integer

11. Absolute Value of an Integer
The absolute value of an integer is its distance
from zero.
You write the absolute value of a number by
using 2 vertical bars.
|-5| is the absolute value of -5

12. Absolute Value of an Integer
|-5| is the absolute value of -5
Try imagining a number line to find the
absolute value of a number.
-5 is 5 units away from 0. Therefore, |-5| = 5.

13. Absolute Value of an Integer
|+7| is the absolute value of positive 7
Again, lets try imagining a number line to find
its absolute value.
+7 is 7 units away from 0. Therefore, |+7| = 7.

14. Absolute Value of an Integer
|+7| is the absolute value of positive 7
Again, lets try imagining a number line to find
its absolute value.
+7 is 7 units away from 0. Therefore, |+7| = 7.

15. Which is
greater?
+8 or -19?
Answer:
+8 is greater than -19

16. Which is
greater?
|+8| or |-19|?
Answer:
The absolute value of +8 is 8
The absolute value of -19 is 19
19 is greater than 8
Therefore, |-19| is greater than |+8|

17. “
Even if the original value of the
number is greater than the other
number, that doesn’t always mean
that its absolute value will also be
greater than the other number’s.

18. Is -|5| = |-5|?
No. Take careful note of
where the signs are on
each expression:
-|5| is the negative of the
absolute value of 5,
which is equal to -5.
|-5| is the absolute value
of negative 5, which is
equal to 5.
-5 is not equal to 5.
More Examples
What is -|-5|?
It is -5. The expression is
read as the negative of
the absolute value of
negative 5.
First we find the absolute
value of negative 5,
which is 5.
Then we find the
negative of this value,
which leads to the final
answer of negative 5.

19. “
Be careful when you look at where
the signs are placed on absolute
values. Absolute values of numbers
are always positive, but sometimes
operations outside of the absolute
value signs can change your final
answer to a negative value.

20. Is there a point to
knowing the absolute
value of a number?
Why or why not?
Question to ponder

21. You can check the following links to delve deeper into the
topic if you want
Basics of Integers | Toppr
◎https://www.toppr.com/guides/maths/integers/basics
-of-integers/
Absolute Value | Math Antics
◎https://youtu.be/BrYy1bgh3Y0
End of Lesson