The document outlines key mathematical properties, including the commutative, associative, and distributive properties for addition and multiplication, as well as various properties of equality. It provides definitions and examples for each property, emphasizing their applications, such as changing the order or grouping of numbers. Additionally, the document addresses properties associated with real numbers and equality, aimed at enhancing understanding of fundamental mathematical concepts.

2.  refer to rules that indicate a
standard procedure or
method to be followed

3. Commutative Property
Associative Property
Distributive Property

4. Commutative Property of Addition
 changing the order of the addends
does not change the sum
Examples:
𝟐 + 𝟑 = 𝟑 + 𝟐
𝟒 + 𝟕 = 𝟕 + 𝟒

5. Commutative Property of Addition
𝒂 + 𝒃 = 𝒃 + 𝒂

6. Commutative Property of Multiplication
 changing the order of the factors does
not change the product
Examples:
𝟑 ∙ 𝟔 = 𝟔 ∙ 𝟑
(𝟓) −𝟐 = (−𝟐)(𝟓)

7. Commutative Property of Multiplication
𝒂𝒃 = 𝒃𝒂

8. 1. 4 + 5 = _____
2. 8 3 − 2 = _____
3. (di)(lo) = _____
Complete the examples using
the commutative property.

9. Associative Property of Addition
 changing the grouping of the addends
does not change the sum
Examples:
(𝟓 + 𝟐) + 𝟑 = 𝟓 + (𝟐 + 𝟑)
𝟒 + 𝟏 + 𝟐 = 𝟒 + 𝟏 + 𝟐

10. Associative Property of Addition
𝒂 + 𝒃 + 𝒄 = 𝒂 + (𝒃 + 𝒄)

11. Associative Property of Multiplication
 changing the grouping of the factors
does not change the product
Examples:
𝟐(𝟓 ∙ 𝟑) = (𝟐 ∙ 𝟓)𝟑
𝟒 𝟏 ∙ 𝟐 = 𝟒 ∙ 𝟏 𝟐

12. Associative Property of Multiplication
𝒂𝒃 𝒄 = 𝒂(𝒃𝒄)

13. 1. 2 + (4 + 5) = _____
2. 8 3 ∙ 2 = _____
3. pet + (ma + lu) =
_____
Complete the examples using
the associative property.

14.  multiplication distributes over addition
Example:
𝟑 𝟐 + 𝟓
= 𝟑 ∙ 𝟐 + 𝟑 ∙ 𝟓

15. 𝒂 𝒃 + 𝒄 = 𝒂𝒃 + 𝒂𝒄

16. 1. 2(4 + 5) = _____
2. 8 3 + 2 = _____
3. 3(a + b) = _____
Complete the examples using
the distributive property.

17. Reflexive Property
Symmetric Property
Transitive Property
Addition Property
Subtraction Property
Multiplication Property
Division Property
Substitution Property
Zero Product Property

18. Examples:
𝑎 = 𝑎
𝑚 + 𝑛 = 𝑚 + 𝑛
10 = 10
A real number is
always equal to
itself.

19. Example:
If 10 = 7 + 3,
then 7 + 3 = 10.
For any numbers 𝑎 and 𝑏,
𝑰𝒇 𝒂 = 𝒃, 𝒕𝒉𝒆𝒏 𝒃 = 𝒂.

20. Example:
If 8 + 4 = 12
and 12 = 7 + 5,
then 8 + 4 = 7 + 5.
For any numbers 𝑎, 𝑏 and 𝑐,
𝑰𝒇 𝒂 = 𝒃 𝒂𝒏𝒅 𝒃 = 𝒄, 𝒕𝒉𝒆𝒏 𝒂 = 𝒄.

21. Example:
If 3(3) =9
and 9 = 4 + 5,
then 3(3) = 4 + 5.
For any numbers 𝑎, 𝑏 and 𝑐,
𝑰𝒇 𝒂 = 𝒃 𝒂𝒏𝒅 𝒃 = 𝒄, 𝒕𝒉𝒆𝒏 𝒂 = 𝒄.

22. Example:
1. If 𝑥 = 10, then 𝑥 +
3 = 10 + 3.
2. If 5 + 2 = 7, then
5 + 2 + 1 = 7 + 1.
𝑰𝒇 𝒂 = 𝒃, 𝒕𝒉𝒆𝒏 𝒂 + 𝒄 = 𝒃 + 𝒄.

23. Example:
1. If 𝑥 = 10, then
𝑥 − 3 = 10 − 3.
2. If 5 + 2 = 7, then
5 + 2 − 1 = 7 − 1.
𝑰𝒇 𝒂 = 𝒃, 𝒕𝒉𝒆𝒏 𝒂 − 𝒄 = 𝒃 − 𝒄.

24. Example:
1. If 𝑥 = 10, then
𝑥 ∙ 3 = 10 ∙ 3.
2. If 5 + 2 = 7, then
(5 + 2)(3) = 7(3).
𝑰𝒇 𝒂 = 𝒃, 𝒕𝒉𝒆𝒏 𝒂𝒄 = 𝒃𝒄.

25. Example:
1. If 𝑥 = 10, then
𝑥
3
=
10
3
.
2. If 5 + 1 = 6,
then
5+1
2
=
6
2
.
𝑰𝒇 𝒂 = 𝒃 𝒂𝒏𝒅 𝒄 ≠ 𝟎, 𝒕𝒉𝒆𝒏
𝒂
𝒄
=
𝒃
𝒄
.

26. Example:
1. If 𝑥 = 5 and 𝑥 + 𝑦 = 𝑧,
then 5 + 𝑦 = 𝑧.
2. If 𝑥 = 2 and 𝑥 2 + 1 =
6, then 2 2 + 1 = 6.
𝐈𝐟 𝒂 = 𝒃, 𝐭𝐡𝐞𝐧 𝒂 𝐦𝐚𝐲 𝐛𝐞
𝐬𝐮𝐛𝐬𝐭𝐢𝐭𝐮𝐭𝐞𝐝 𝐟𝐨𝐫 𝒃, 𝐨𝐫 𝐜𝐨𝐧𝐯𝐞𝐫𝐬𝐞𝐥𝐲.

27. Properties of Real Numbers
 Commutative Property
 Associative Property
 Distributive Property
Properties of Equality
 Reflexive Property
 Symmetric Property
 Transitive Property
 Addition Property
 Subtraction Property
 Multiplication Property
 Division Property
 Substitution Property

28. Thanks!MR. CARLO JUSTINO J. LUNA
Malabanias Integrated School
Angeles City