Question

Draw a line from each equation to the property of equality it illustrates.

(6 + 3) - 3 = 9 - 3 • • Addition Property of Equality
(6 + 3) × 3 = 9 × 3 • • Division Property of Equality
(6 + 3) + 3 = 9 + 3 • • Multiplication Property of Equality
(6 + 3) ÷ 3 = 9 ÷ 3 • • Subtraction Property of Equality

Answer 1

1) Subtraction Property of Equality

2) Multiplication Property of Equality

3) Addition Property of Equality

4) Division Property of Equality

Explanation:

We proceed to present the correct answer to this question and explain the reason behind the election of each option below:

1)
`(6+3)-3 = 9 - 3` 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:
`a = b` if and only if
`a+(-c) = b+(-c)`.

2)
`(6+3)* 3 = 9 * 3` Multiplication Property of Equality

Reason - The multiplication property of equality is defined as:
`a = b` if and only if
`a\cdot c = b\cdot c`.

3)
`(6+3)+3 = 9+3` Addition Property of Equality

Reason - The addition property of equality is defined as:
`a = b` if and only if
`a+c = b+c`.

4)
`(6+3)/ 3 = 9 / 3` 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:
`a = b` if and only if
`a\cdot c^(-1) = b\cdot c^(-1)`.