Contenu connexe Similaire à Properties of Real Numbers and Equality - Mathematics 8 (3rd Quarter) (20) Properties of Real Numbers and Equality - Mathematics 8 (3rd Quarter)2. refer to rules that indicate a
standard procedure or
method to be followed
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
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)
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
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
13. 1. 2 + (4 + 5) = _____
2. 8 3 ∙ 2 = _____
3. pet + (ma + lu) =
_____
Complete the examples using
the associative property.
16. 1. 2(4 + 5) = _____
2. 8 3 + 2 = _____
3. 3(a + b) = _____
Complete the examples using
the distributive property.
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