What property does the equation 2 + (a + b) = (2 + a) + b illustrate?

What property does the equation 2 + (a + b) = (2 + a) + b illustrate?

• A. Associative (Property of Addition)
• B. Distributive (Property)
• C. Commutative (Property)
• D. Identity (Property)

Answer: (A)

The equation 2 + (a + b) = (2 + a) + b illustrates the Associative Property of Addition. This property states that when adding three or more numbers, the way in which the numbers are grouped does not change the sum. In this equation, the parentheses indicate how the numbers are grouped. The left-hand side shows that we add '2' to the sum of 'a' and 'b' first, while the right-hand side shows that '2' is added to 'a' first, and then 'b' is added to that result. Both sides of the equation yield the same sum, demonstrating that the grouping of the addends does not affect the overall total. This property is fundamental in arithmetic and algebra, allowing for flexibility in calculations and simplifications. Other properties, like the Distributive Property or the Commutative Property, involve different operations or arrangements of numbers that do not apply in this situation. The Identity Property would pertain to an operation that does not change a number, such as adding 0 to a number.

The equation 2 + (a + b) = (2 + a) + b illustrates the Associative Property of Addition. This property states that when adding three or more numbers, the way in which the numbers are grouped does not change the sum.

In this equation, the parentheses indicate how the numbers are grouped. The left-hand side shows that we add '2' to the sum of 'a' and 'b' first, while the right-hand side shows that '2' is added to 'a' first, and then 'b' is added to that result. Both sides of the equation yield the same sum, demonstrating that the grouping of the addends does not affect the overall total.

This property is fundamental in arithmetic and algebra, allowing for flexibility in calculations and simplifications. Other properties, like the Distributive Property or the Commutative Property, involve different operations or arrangements of numbers that do not apply in this situation. The Identity Property would pertain to an operation that does not change a number, such as adding 0 to a number.