Identify the property illustrated in each statement. Assume all variables represent real numbers. (38+99) +1 = 38+(99+1)

Verified step by step guidance

1. Identify the given equation: $(38+99)+1=38+(99+1)$.
2. Recognize that the equation involves grouping of numbers using parentheses.
3. Recall the Associative Property of Addition, which states that the way in which numbers are grouped in an addition problem does not change their sum.
4. Apply the Associative Property of Addition to the given equation: $(a+b)+c=a+(b+c)$.
5. Conclude that the property illustrated by the equation $(38+99)+1=38+(99+1)$ is the Associative Property of Addition.

Key Concepts

Associative Property of Addition

The Associative Property of Addition states that the way in which numbers are grouped in an addition operation does not affect the sum. This means that for any real numbers a, b, and c, the equation (a + b) + c = a + (b + c) holds true. In the given statement, (38 + 99) + 1 = 38 + (99 + 1) exemplifies this property by showing that regardless of how the numbers are grouped, the total remains the same.

Real Numbers

Real numbers include all the numbers on the number line, encompassing rational numbers (like integers and fractions) and irrational numbers (like √2 and π). In the context of the question, it is important to recognize that the variables represent real numbers, ensuring that the properties discussed apply universally to this set of numbers. This understanding is crucial for validating the operations and properties being analyzed.

Equality in Mathematics

Equality in mathematics signifies that two expressions represent the same value. The symbol '=' indicates that the expressions on either side are equivalent. In the context of the statement (38 + 99) + 1 = 38 + (99 + 1), the equality asserts that both sides yield the same result, reinforcing the validity of the Associative Property of Addition. Understanding equality is fundamental for solving equations and verifying mathematical statements.