This document discusses properties of integers (I) including: 1) Closure property - the sum and product of integers is an integer 2) Commutative property - the order of addition or multiplication does not change the value 3) Associative property - changing groupings does not change the value of addition or multiplication 4) Identity properties - the additive identity is 0 and multiplicative identity is 1 5) Inverse properties - the additive inverse of a number is its negation and the multiplicative inverse is 1 divided by the number

5. a , b ∈ 𝐼 ,
then a + b ∈ 𝐼,
𝑎 × 𝑏 ∈ 𝐼.
Notations and
Symbols

6. Example 1:

7. Example 2:

8. Commutative Property
Changing the order of two
numbers that are either being
added or multiplied does not
change its value.
a, b ∈ 𝐼 , then a + b ∈ 𝐼, 𝑎 × 𝑏 ∈ 𝐼
Notations and
Symbols
For multiplication:
For addition:

9. Example 1:

10. Example 2:

11. Notations and
Symbols
For addition:
Associative Property
Changing the grouping of numbers
that are either being added or
multiplied does not change its value.

12. Example 1:

13. Example 2:

14. Notations and
Symbols

15. Example 1:

16. Example 2:

17. Additive Identity is 0.
Multiplicative Identity is 1.
Notations and Symbols
Identity Property
Additive Identity
- states that the sum is the
of any number and 0 is the
given number. Zero,”0” is the
additive identity.
Multiplicative Identity
- states that the product of
any number and 1 is the given
number. One, “1” is the
multiplicative identity.

18. Example 1:

19.  Example 1:
Example 2:

20. Inverse Property
In Addition
- states that the sum of any
number additive inverse and its
additive inverse, is zero. The
additive inverse of the number a is
–a.
In Multiplication
- states that the product of any
number and its multiplicative
inverse or reciprocal, is 1. The
multiplicative inverse of the
number a is
1
𝑎
.
The Additive Inverse is the negation
of the element.
The Multiplicative Inverse is one
divided by the element.
Notations and Symbols

21. Example 1:

22. Example 2:

24. Thank You & God Bless !!!!!
By : Airen T. Magadan