How to Use Order of Operations? (+FREE Worksheet!)

Use the order of operations to evaluate expressions: grouping, exponents, multiplication and division, then addition and subtraction. Work left to right within each of the multiplication/division and addition/subtraction groups.

Whenever a math expression contains more than one operation, you need the order of operations to get the right answer. Without a consistent set of rules, two people could evaluate the same expression and reach two different results. The acronym PEMDAS — Parentheses, Exponents, Multiplication/Division, Addition/Subtraction — tells you exactly which steps to take first.

What Is the Order of Operations?

The order of operations is the agreed-upon sequence for evaluating a mathematical expression. It ensures that every mathematician in the world gets the same answer for a given expression. PEMDAS is the most common mnemonic for remembering the sequence:

• P — Parentheses (and all grouping symbols)
• E — Exponents (powers and roots)
• (color{blue}{frac{M}{D}}) — Multiplication and Division (left to right)
• (color{blue}{frac{A}{S}}) — Addition and Subtraction (left to right)

The PEMDAS Rules in Detail

Step 1 — Parentheses and Grouping Symbols

Always simplify inside parentheses, brackets, or braces first.

• (color{blue}{(3 + 4) times 2 = 7 times 2 = 14})

Step 2 — Exponents

Evaluate all powers (and roots) after clearing grouping symbols.

• (color{blue}{2^{3} + 5 times (10 – 3) = 8 + 5 times 7 = 8 + 35 = 43})

Step 3 — Multiplication and Division (left to right)

Work multiplication and division together, moving left to right. Neither takes priority over the other. Want to practice this in a game? In Equation Guess, a free math Wordle, every guess must be a true equation, so you use the order of operations on every try.

• (color{blue}{18 div (3 + 3) – 1 = 18 div 6 – 1 = 3 – 1 = 2})

Step 4 — Addition and Subtraction (left to right)

Finally, work addition and subtraction left to right.

• (color{blue}{3 + 4 times 2 = 3 + 8 = 11})  (multiply first, then add)

Step-by-Step Summary

1. Simplify inside all Parentheses (innermost first).
2. Evaluate all Exponents.
3. Perform Multiplication and Division left to right.
4. Perform Addition and Subtraction left to right.

Watch: Order of Operations Explained (PEMDAS)

Math Antics walks through PEMDAS with step-by-step numerical examples:

Order of Operations – Worked Examples

Example 1: Evaluate (color{blue}{3 + 4 times 2}).

No parentheses or exponents. Multiply first: (color{blue}{4 times 2 = 8}). Then add: (color{blue}{3 + 8 = 11}).

Example 2: Evaluate (color{blue}{2^{3} + 5 times (10 – 3)}).

Parentheses first: (color{blue}{10 – 3 = 7}). Exponent: (color{blue}{2^{3} = 8}). Multiply: (color{blue}{5 times 7 = 35}). Add: (color{blue}{8 + 35 = 43}).

Example 3: Evaluate (color{blue}{18 div (3 + 3) – 1}).

Parentheses: (color{blue}{3 + 3 = 6}). Divide: (color{blue}{18 div 6 = 3}). Subtract: (color{blue}{3 – 1 = 2}).

Example 4: Evaluate (color{blue}{7 + 2 times (3 + 4^{2})}).

Inside parentheses, exponent first: (color{blue}{4^{2} = 16}). Add inside: (color{blue}{3 + 16 = 19}). Multiply: (color{blue}{2 times 19 = 38}). Add: (color{blue}{7 + 38 = 45}).

More Practice: Khan Academy Video on PEMDAS

Khan Academy works through challenging order of operations problems:

Exercises for Order of Operations

Evaluate each expression using PEMDAS.

1. (color{blue}{5 + 3 times (8 – 2)})
2. (color{blue}{(12 – 4) div 2 + 3^{2}})
3. (color{blue}{4 times 3 + 6 div 2 – 1})
4. (color{blue}{(5 + 3)^{2} div 4})
5. (color{blue}{7 + 2 times (3 + 4^{2})})
6. (color{blue}{60 div (2 + 3) times 2 – 1})

Answers

1. (color{blue}{23})
2. (color{blue}{13})
3. (color{blue}{14})
4. (color{blue}{16})
5. (color{blue}{45})
6. (color{blue}{23})

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Frequently Asked Questions

What is the order of operations in math?

The order of operations is the agreed set of rules for which step to do first in an expression with more than one operation. Work inside parentheses, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right. Without these rules, 10 − 2 × 3 could give two answers; with them, it is 10 − 6 = 4.

Is the order of operations PEMDAS?

Yes, PEMDAS is the most common memory aid in the United States: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. Other countries use BODMAS or BIDMAS, where B means brackets and O or I means orders or indices, but the rules are the same. Remember that M and D share one level, and so do A and S.

Is the order of operations left to right?

Only within the same level. Multiplication and division are done together from left to right, and so are addition and subtraction. For 12 ÷ 3 × 2, divide first because it comes first: 12 ÷ 3 = 4, then 4 × 2 = 8. Doing the multiplication first would give the wrong answer of 2.

How do you use the order of operations with fractions?

Fractions follow exactly the same order. In 1/2 + 3/4 × 2/3, multiply first: 3/4 × 2/3 = 6/12 = 1/2. Then add: 1/2 + 1/2 = 1. A fraction bar also acts like a grouping symbol, so simplify the whole numerator and the whole denominator before dividing, as in (4 + 6)/(7 − 2) = 10/5 = 2.

How does the order of operations work with integers?

The steps stay the same, but track signs carefully. For −3 + 4 × (−2), multiply first to get −8, then −3 + (−8) = −11. Exponents need extra care: (−3)² = 9 because the negative is inside the parentheses, but −3² = −9 because only the 3 is squared and the negative is applied afterward.

When do you use the order of operations?

Use it any time an expression has two or more different operations, whether you are simplifying a numerical expression, evaluating an algebra formula or using a calculator. For example, in 2 + 3 × 4² you square first (16), multiply (48) and then add, giving 50. Scientific calculators follow the same rules.

Related Topics

• Adding and Subtracting Integers
• Multiplying and Dividing Integers
• The Distributive Property
• Translate Phrases into an Algebraic Statement
• Integers and Absolute Value