Mathematics 8 (3rd Quarter) 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 * Zero Product Property

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