Understanding Two-Step Expressions and Order of Operations

When you see a math problem with more than one operation—like addition and multiplication together—how do you know which one to do first? To get the right answer, mathematicians use a special set of rules called the Order of Operations.

The Rules for Order of Operations

When solving two-step expressions, always follow this order:

1. Parentheses ( ): Always solve whatever is inside the parentheses first.
2. Multiplication \times and Division \div: Do these next.
3. Addition + and Subtraction -: Do these last.

If you have operations of the same level (like addition and subtraction), just work from left to right.

Step-by-Step Examples

Let's look at a few examples to see how this works in action.

Example 1: Multiplication Before Addition

Evaluate: $3 + 4 \times 2$

• Step 1: Look for multiplication or division. We have $4 \times 2$.
• Step 2: Multiply first: $4 \times 2 = 8$.
• Step 3: Rewrite the expression with the new number: $3 + 8$.
• Step 4: Add: $3 + 8 = 11$.

Warning: If you added $3 + 4$ first to get $7$, and then multiplied by $2$, you would get $14$. That is incorrect! Always multiply before you add.

Example 2: Parentheses Always Go First

Evaluate: $5 \times (6 - 2)$

• Step 1: Look for parentheses. We have $(6 - 2)$.
• Step 2: Subtract inside the parentheses first: $6 - 2 = 4$.
• Step 3: Rewrite the expression: $5 \times 4$.
• Step 4: Multiply: $5 \times 4 = 20$.

Even though multiplication usually comes before subtraction, parentheses have the highest priority!

Example 3: Multiplication Before Subtraction

Evaluate: $20 - 3 \times 5$

• Step 1: Look for multiplication. We see $3 \times 5$.
• Step 2: Multiply first: $3 \times 5 = 15$.
• Step 3: Rewrite the expression: $20 - 15$.
• Step 4: Subtract: $20 - 15 = 5$.

Quick Summary

To solve two-step expressions perfectly every time, just remember: Parentheses first, then Multiply/Divide, then Add/Subtract.