Simplify each expression. 8+(a+7)

Verified step by step guidance

1. Identify the expression inside the parentheses: \((a + 7)\).
2. Apply the associative property of addition, which allows you to regroup terms: \(8 + (a + 7) = (8 + a) + 7\).
3. Use the commutative property of addition to rearrange the terms: \((8 + a) + 7 = (a + 8) + 7\).
4. Combine the constants \(8\) and \(7\) using the associative property: \((a + 8) + 7 = a + (8 + 7)\).
5. Simplify the expression by adding the constants: \(a + (8 + 7)\).

Key Concepts

Order of Operations

The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. The common acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. In the expression 8 + (a + 7), operations within the parentheses should be simplified first.

Combining Like Terms

Combining like terms is a fundamental algebraic process that involves simplifying expressions by adding or subtracting terms that have the same variable raised to the same power. In the expression 8 + (a + 7), the constant terms 8 and 7 can be combined to simplify the expression further, leading to a clearer result.

Algebraic Expressions

An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols. It does not contain an equality sign. Understanding how to manipulate and simplify algebraic expressions, such as 8 + (a + 7), is crucial for solving equations and performing algebraic operations effectively.