Evaluate each expression. See Example 5.18 - 4² + 5 - (3 - 7)

Verified step by step guidance

1. Start by evaluating the exponent: calculate \(4^2\).
2. Subtract the result of \(4^2\) from 18.
3. Evaluate the expression inside the parentheses: \(3 - 7\).
4. Subtract the result of the parentheses from the previous result.
5. Add 5 to the result from the previous step.

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 evaluating expressions, operations within parentheses are performed first, followed by exponents, and then multiplication and division from left to right, before finally performing addition and subtraction.

Evaluating Expressions

Evaluating expressions involves calculating the value of a mathematical expression by substituting variables with numbers and performing the operations according to the order of operations. This process requires careful attention to detail to ensure that each step is executed correctly. For example, in the expression given, one must first resolve the parentheses before proceeding with the other operations.

Negative Numbers

Negative numbers are values less than zero and are essential in arithmetic operations, particularly in subtraction and addition. When evaluating expressions that involve negative numbers, it is crucial to understand how they interact with positive numbers. For instance, subtracting a negative number is equivalent to adding its positive counterpart, which can affect the final result of the expression being evaluated.