Order of Operations: Solving Multi-Step Problems

In this lesson, we will explore how to solve multi-step problems using the order of operations. The order of operations is a set of rules that dictates the sequence in which calculations are performed to ensure consistent results.

The Order of Operations

The order of operations can be remembered using the acronym PEMDAS:

• Parentheses
• Exponents
• Multiplication and Division (from left to right)
• Addition and Subt\fraction (from left to right)

Example Problem

Let's solve the following expression step-by-step:

$$8 + 2 \times (3^{2} - 1)$$

Step 1: Solve inside the parentheses

First, we calculate the expression inside the parentheses:

$$3^{2} - 1 = 9 - 1 = 8$$

Now our expression looks like:

$$8 + 2 \times 8$$

Step 2: Perform multiplication

Next, we perform the multiplication:

$$2 \times 8 = 16$$

Now we have:

$$8 + 16$$

Step 3: Perform addition

Finally, we add:

$$8 + 16 = 24$$

Thus, the solution to the problem is:

$$8 + 2 \times (3^{2} - 1) = 24$$

Key Questions

• What does PEMDAS stand for?
• Why is it important to follow the order of operations?
• How would you solve an expression with both multiplication and addition?

Keywords

• Order of Operations
• PEMDAS
• Parentheses
• Exponents
• Multiplication
• Addition