Problem 28 - Algebra 1: Concepts and Skills

Question

Evaluate the expression. $$4+8 \cdot 4-1$$

Step-by-Step Solution

Answer

Given expression simplifies to 35.

Step 1: Identify and Perform Multiplication

The first operation to perform according to the order of operations (PEMDAS) is multiplication. In this equation, you will need to multiply \(8 \) by \(4\).

Step 2: Continue With Addition and Subtraction

The result from the multiplication in step 1 is then used to do addition and subtraction. So firstly, add \(4\) to the multiplied result. Then take away \(1\) from the addition result. Both operations are done in left to right manner.

Key Concepts

Understanding PEMDAS

The order of operations is crucial to solving mathematical expressions correctly. The acronym **PEMDAS** helps you remember this order:

• **P**arentheses
• **E**xponents
• **M**ultiplication
• **D**ivision
• **A**ddition
• **S**ubtraction

When we evaluate expressions, we begin with any calculations inside parentheses, then move to exponents. Afterward, we perform any multiplication and division, working from left to right, followed by addition and subtraction, again from left to right.
This order ensures that calculations are not only accurate but also consistent across different scenarios. Following PEMDAS can simplify complex expressions and avoid common mistakes.

Working with Arithmetic Operations

Arithmetic operations form the foundation of most mathematical calculations. There are four primary operations:

• **Addition**: Combining numbers to get a sum.
• **Subtraction**: Taking one number away from another to find the difference.
• **Multiplication**: Repeated addition of a number a specified number of times.
• **Division**: Splitting a number into equal parts.

In the given exercise, these operations need to be performed in the correct order (following PEMDAS). For example, multiplication must occur before addition or subtraction.
Understanding each operation and its place in the order of operations helps simplify the process of evaluating expressions, preventing potential errors.

Evaluating Expressions Step-by-Step

To evaluate expressions efficiently, you should follow a structured approach, which includes:

• Identify operations: Determine which arithmetic operations to perform first.
• Apply PEMDAS: Use the order of operations as a guide.
• Calculate progressively: Work through calculations step-by-step.

In the example expression \(4 + 8 \cdot 4 - 1\), you start by multiplying \(8\) by \(4\), obtaining \(32\). Then you add \(4\) to \(32\), resulting in \(36\). Finally, subtract \(1\) to get the final result of \(35\).
This methodical process ensures that the expression is evaluated correctly and consistently, leading to accurate results every time.