PEMDAS is an acronym for remembering the order of operations: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. Multiplication and division share one step and are done from left to right, and so are addition and subtraction. Many students learn it as “Please Excuse My Dear Aunt Sally.”
In Spanish
PEMDAS (orden de las operaciones)
Also called
Please Excuse My Dear Aunt Sally, GEMDAS, BODMAS, BIDMAS, order of operations acronym
PEMDAS is a ladder of four rungs. M and D sit on one rung and A and S on another, so within a rung you simply work from left to right.
Formal definition and notation
PEMDAS names the conventional precedence for evaluating a numerical expression: (1) evaluate inside grouping symbols, innermost first; (2) evaluate exponents (powers and roots); (3) perform all multiplications and divisions in order from left to right; (4) perform all additions and subtractions in order from left to right. It is a memory aid for the order of operations, not a separate rule, and the six letters describe only four ranks.
Symbol
Read it as
Meaning
P
parentheses
also brackets, braces, absolute value bars and fraction bars: anything that groups
E
exponents
powers such as 32, and roots such as √16
MD
multiplication and division
one rank, done left to right
AS
addition and subtraction
one rank, done left to right
Key facts
PEMDAS has six letters but only four steps, because M and D share a step and so do A and S.
Inside a step, work left to right: 20 ÷ 5 × 2 = 4 × 2 = 8.
A fraction bar groups like parentheses: in 6 + 93, add first, then divide, to get 5.
Multiplication written by juxtaposition, as in 2(3 + 1), is still multiplication in the M step.
Calculators that follow the order of operations agree with PEMDAS; a simple four-function calculator that works left to right may not.
The four ranks of PEMDAS
The four ranks of PEMDAS
P → E → (M and D, left to right) → (A and S, left to right)
GEMDAS
G for grouping symbols, a reminder that brackets and fraction bars count too
BODMAS / BIDMAS
Brackets, Orders or Indices, Division and Multiplication, Addition and Subtraction (used in the UK and elsewhere)
BODMAS lists D before M and PEMDAS lists M before D, which shows the letter order inside a rank does not matter.
PEMDAS examples, step by step
Example 1: Multiplication before addition
Warm-up
Evaluate 6 + 4 × 3.
No parentheses or exponents.
M before A: 4 × 3 = 12.
Then add: 6 + 12 = 18.
Answer:6 + 4 × 3 = 18.
Example 2: Left to right inside a rung
Core
Evaluate 48 ÷ 4 × 2 − 32.
E: 32 = 9.
MD left to right: 48 ÷ 4 = 12, then 12 × 2 = 24.
AS: 24 − 9 = 15.
Answer: The value is 15.
Example 3: All four rungs
Test-style
What is the value of 3 + 2(8 − 5)2 ÷ 6?
P: 8 − 5 = 3.
E: 32 = 9.
MD left to right: 2 × 9 = 18, then 18 ÷ 6 = 3.
AS: 3 + 3 = 6.
Answer: The value is 6.
Common mistakes
✗ MistakeDoing every multiplication before any division because M comes first in PEMDAS: 36 ÷ 6 × 3 = 36 ÷ 18 = 2.
✓ InsteadLeft to right: 36 ÷ 6 = 6, then 6 × 3 = 18.
M and D are one step. The order of the letters in the word is not an order of operations.
The distributive property lets you multiply into parentheses, 2(3 + 4) = 6 + 8. It gives the same answer as doing P first, 2 × 7 = 14.
Quick check: 3 questions
Question 1 of 3
What is 18 − 12 ÷ 3 × 2?
Show answer and explanation
Answer: B. MD left to right: 12 ÷ 3 = 4, 4 × 2 = 8; then 18 − 8 = 10. 4 works left to right from the start, 16 divides by 6 (multiplying first), and 6 is a slip.
Question 2 of 3
In PEMDAS, which pair of operations is done in the same step?
Show answer and explanation
Answer: D. M and D share one step, worked left to right, and so do A and S. The other pairs are on different steps.
Question 3 of 3
What is 5 + (6 − 2)2 ÷ 8?
Show answer and explanation
Answer: A. P: 6 − 2 = 4. E: 42 = 16. D: 16 ÷ 8 = 2. A: 5 + 2 = 7. 218 adds before dividing, 2 forgets to add the 5, and 5.5 skips the exponent.
PEMDAS: frequently asked questions
What does PEMDAS stand for?
Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. The sentence “Please Excuse My Dear Aunt Sally” helps people remember the letters. Keep in mind that it describes four steps: parentheses, then exponents, then multiplication and division together from left to right, then addition and subtraction together from left to right.
Is PEMDAS ever wrong?
The rules behind it are correct, but the word can mislead. Students who read it letter by letter do all multiplication before division and all addition before subtraction, which gives wrong answers like 8 ÷ 2 × 4 = 1 instead of 16. Some teachers write it as P, E, MD, AS on four lines to show the pairs.
What is GEMDAS?
GEMDAS replaces P with G for grouping symbols. The rules are the same as PEMDAS, but the G reminds you that brackets, braces, absolute value bars, square-root signs and fraction bars group things too, not just parentheses. For example, in 4 + 83 the addition on top is done first because the fraction bar groups it.
ExpressionAn expression is a number, variable, or combination of numbers and variables joined by operations, without an equal sign. Examples are 7, 4x + 9 and 3(a − 2). Expressions can be simplified, but they are not solved unless they are part of an equation. You evaluate one by replacing each variable with a number.Algebra · Grade 6, Grade 7, Grade 8EvaluateEvaluate means to find the single number value of an expression. Replace each variable with the number you are given, then calculate using the order of operations. For example, 2x + 7 evaluated at x = 3 is 2(3) + 7 = 13. The result is one number, not a new expression.Algebra · Grade 6, Grade 7, Algebra 1ExponentAn exponent tells how many times to use a base as a factor. It is the small raised number to the upper right of the base: in 53, the base is 5 and the exponent is 3, so 53 = 5 × 5 × 5 = 125. Any nonzero number with an exponent of 0 equals 1.Algebra · Grade 6, Grade 7, Grade 8PowerA power is a number written as a base with an exponent, such as 53, or the value that results, 53 = 5 × 5 × 5 = 125. We say 125 is the third power of 5, or “5 to the third power”. The second power is called the square and the third power the cube.Number System · Grade 5, Grade 6, Grade 7RootsThe roots of an equation are the values of the variable that make it true; for a polynomial equation set equal to 0, they are the solutions. The roots of x2 + 3x − 10 = 0 are 2 and −5, because each makes the left side 0. Real roots appear as the x-intercepts of the graph.Algebra · Algebra 1, Algebra 2MultiplicationMultiplication is the operation that combines equal groups to find a total. The fact 4 × 6 = 24 means 4 groups of 6, or 6 + 6 + 6 + 6. The numbers you multiply are called factors, and the result is the product. Order does not matter: 6 × 4 is also 24.Operations · Grade 2, Grade 3, Grade 4DivisionDivision is the operation of splitting a number into equal groups. In 12 ÷ 3 = 4, the dividend 12 is shared into 3 equal groups (the divisor), and each group gets 4 (the quotient). Division undoes multiplication, because 3 × 4 = 12. If the groups do not come out even, the amount left over is the remainder.Operations · Grade 3, Grade 4, Grade 5AdditionAddition is the operation that puts amounts together to find the total. The numbers you add are called addends, the answer is the sum, and the sign is the plus sign, +. For example, 7 + 5 = 12. On a number line, adding a positive number means moving to the right.Operations · Kindergarten, Grade 1, Grade 2SubtractionSubtraction is the operation that finds how much is left when you take one amount away from another, or how far apart two numbers are. It is written with a minus sign: 9 − 4 = 5. The answer is called the difference. Subtraction undoes addition, so you can check 9 − 4 = 5 by adding 5 + 4 = 9.Operations · Grade 1, Grade 2, Grade 3Order of OperationsThe order of operations is the agreed sequence for evaluating an expression: parentheses first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right. Without it the same expression would have several answers. Many students remember it as PEMDAS.Algebra · Grade 5, Grade 6, Grade 7Absolute ValueThe absolute value of a number is its distance from zero on the number line, so it is never negative. It is written with two vertical bars: |−6| = 6 and |6| = 6. A positive number and 0 keep their value; a negative number loses its minus sign.Number System · Grade 6, Grade 7, Grade 8Distributive PropertyThe distributive property says that multiplying a number by a sum gives the same result as multiplying it by each term and then adding: a(b + c) = ab + ac. It multiplies a factor by each term inside parentheses, so 3(x + 4) = 3x + 12. It works with subtraction too, and using it backward is factoring.Algebra · Grade 6, Grade 7, Grade 8EquationAn equation is a statement that two expressions are equal. It always has an equal sign, such as x + 5 = 12 or 3a = 18. Solving an equation means finding the value of the variable that makes it true: here x = 7 and a = 6. An expression like 4x + 7 has no equal sign, so it is not an equation.Algebra · Grade 6, Grade 7, Grade 8