Answer:
1) Subtraction Property of Equality
2) Multiplication Property of Equality
3) Addition Property of Equality
4) Division Property of Equality
Step-by-step explanation:
We proceed to present the correct answer to this question and explain the reason behind the election of each option below:
1) [tex](6+3)-3 = 9 - 3[/tex] Subtraction Property of Equality
Reason - Subtraction is a particular form of addition based on the consideration of the existence of additive inverses. The subtraction property of equality is defined as: [tex]a = b[/tex] if and only if [tex]a+(-c) = b+(-c)[/tex].
2) [tex](6+3)\times 3 = 9 \times 3[/tex] Multiplication Property of Equality
Reason - The multiplication property of equality is defined as: [tex]a = b[/tex] if and only if [tex]a\cdot c = b\cdot c[/tex].
3) [tex](6+3)+3 = 9+3[/tex] Addition Property of Equality
Reason - The addition property of equality is defined as: [tex]a = b[/tex] if and only if [tex]a+c = b+c[/tex].
4) [tex](6+3)\div 3 = 9 \div 3[/tex] Division Property of Equality
Reason - The division is a particular form of multiplication based on the consideration of the existence of multiplicative inverses. The division property of equality is defined as: [tex]a = b[/tex] if and only if [tex]a\cdot c^{-1} = b\cdot c^{-1}[/tex].
