Order of operations definition: The order of operations is the shared rule for reading a math expression so different people do not get different answers from the same line of work.
PEMDAS letters: PEMDAS is a memory aid for grouping symbols first, then exponents, then multiplication and division from left to right, and then addition and subtraction from left to right.
Equal-priority pairs: Multiplication does not automatically come before division, and addition does not automatically come before subtraction. Each pair is handled in the order it appears from left to right.
Reading PEMDAS as a race: Many wrong answers happen when you treat PEMDAS like a race to multiplication or when you skip the left-to-right step inside multiplication and division or inside addition and subtraction.
Self-paced checking habit: In a self-paced setting, pause after each operation, rewrite the line neatly, and check whether you changed the expression before moving on. That habit catches more errors than rushing to the final answer.
At a kitchen table with a homework page half-finished, you look at one expression and feel sure the answer should be simple. Then a second look makes you hesitate. Do you add first, multiply first, or work straight across from the left edge?
You need the order of operations, often remembered as PEMDAS. This article answers the question students ask in class, at home, and during review: What is the order of operations, what does PEMDAS mean, and how do you use it without making the usual mistakes?
This is also the foundation Dana Mosely teaches step by step in the prealgebra video course and the arithmetic lessons. Dana has taught video math for the college divisions of D.C. Heath, Houghton Mifflin, and Cengage all have that background, and each step is explained clearly.
The Short Answer:
The order of operations is the agreed set of rules used to evaluate a math expression so everyone reads it the same way. Khan Academy describes PEMDAS as a memory aid for the sequence: grouping symbols first, then exponents, then multiplication and division from left to right, and then addition and subtraction from left to right. When you follow that sequence, the same expression gives the same result.
Without a shared rule, one expression could produce more than one answer depending on who read it. Khan Academy says the purpose of the order of operations is to give one way to interpret a mathematical statement.
That is why the rule matters whether you are using a Khan Academy review page, an IXL practice set, a classroom handout, or a College Board prep book. The goal is to read math consistently.
Grouping symbols: Start with what is enclosed first. Parentheses are the most familiar example, but brackets, braces, and even a fraction bar act as grouping signals.
Exponents: Next, evaluate powers. Khan Academy explains exponents as a way of writing repeated multiplication, so “two squared” means two times two.
Multiplication and division: Treat these as a pair with the same priority. Work from left to right as the operations appear.
Addition and subtraction: Treat these as another pair with the same priority. Again, work from left to right as written.
Final check: After each step, rewrite the expression cleanly. In self-paced study, the rewrite is often where you catch a copied sign error before it spreads.
No. This is one of the most common misunderstandings. Khan Academy says multiplication and division share the same priority, and addition and subtraction share the same priority, so each pair is done from left to right.
That means you do not scan the line and jump to every multiplication sign before every division sign. If the expression says “eighteen divided by three times two,” you divide first because division appears first. Eighteen divided by three is six, and six times two is twelve.
The same idea applies to subtraction and addition. In “twenty minus eight plus one,” you subtract first because subtraction appears first, which gives twelve, and then you add one to get thirteen.
PEMDAS: The letters stand for parentheses, exponents, multiplication, division, addition, and subtraction. IXL describes it as an acronym that helps students remember the order.
BODMAS: This version uses brackets, orders, division, multiplication, addition, and subtraction. The letters differ, but the core rule is still grouping first, powers next, then equal-priority pairs from left to right.
Orders and exponents: These terms point to the same kind of idea in this topic. They refer to powers such as squared or cubed.
Brackets and parentheses: These are both grouping symbols. The name changes, but the action does not: solve what is enclosed first.
Rule behind the letters: Do not get stuck on the letters alone. What matters is understanding the rule behind them and applying it in order.
Most students do not struggle with the definition. They struggle with the transition from the definition to actual work on the page. A neatly spoken rule feels simple until you have to apply it to a longer expression with grouping, powers, and mixed operations.
That is why the Common Core State Standards Initiative introduces grouping symbols before later expecting students to use the conventional order when grouping symbols do not set the order for them. Illustrative Mathematics says these tasks can prompt a useful discussion about why the rules are necessary and how to follow them.
In a self-paced course, this is where video helps. You can watch Dana Mosely slow the line down, compare one step to the next, and replay the exact moment where a wrong answer starts. You can see that approach across the Dana Mosely’s background page and the broader course overview.
The Short Answer:
To do order of operations reliably, use PEMDAS as a checking process. Clear grouping symbols first, evaluate exponents, handle multiplication and division in the order they appear, and finish with addition and subtraction in the order they appear. That left-to-right step prevents many wrong answers when you work through a line.
When students ask how to do order of operations, the safest answer is to begin with whatever is enclosed. Khan Academy states that the first step is to evaluate what is inside grouping symbols first, and common examples include parentheses and fraction bars.
That matters because grouping changes what the rest of the expression means. In plain language, “eight minus three, then multiply by four” is not the same as “eight minus the result of three times four.” If the grouping is there, it tells you how the expression must be read.
This is also where a self-paced video lesson helps more than a solver app. You can pause before the first move and ask yourself what the grouping is controlling.
Scan the whole expression: Before touching any number, look for grouping symbols, powers, and mixed operations. This stops the habit of charging in from the left edge.
Clear grouping first: If you see parentheses, brackets, braces, or a fraction bar, work there before anything outside it. Rewrite the full line after that step.
Handle powers next: If a number is squared or raised to another power, simplify that part before multiplication or division around it.
Work equal-priority pairs left to right: For multiplication with division, and for addition with subtraction, move in reading order. Do not reorder the line because one symbol seems stronger.
Check the rewritten line: Compare each new line to the one before it. In real student work, the hidden mistake is often not the arithmetic. It is a dropped sign, a missing parenthesis, or a changed order.
A student can understand parentheses and remember exponents, then still treat multiplication as always before division or addition as always before subtraction. That is where a correct rule becomes a wrong method.
Take the expression “eighteen divided by three times two.” Because division and multiplication share priority, you move left to right: eighteen divided by three is six, and six times two is twelve. If you multiply three times two first, you change the structure of the original expression and get the wrong answer.
The same thing happens in simpler-looking lines such as “twenty minus eight plus one.” Left to right gives thirteen. If you add first because the plus sign feels easier, the answer changes for no valid reason.
In teaching, this is a familiar moment. The student is often solid at arithmetic but rushing the reading step. That is why the math study skills course can help alongside content review, and why replay and pause tools inside the platform features matter in real practice.
Example with multiplication after addition: Read “three plus five times two.” Multiply five times two to get ten, then add three to get thirteen. You do not add three and five first because there is no grouping telling you to do that.
Example with parentheses: Read “open parenthesis eight minus three close parenthesis times four.” Solve the parentheses first to get five, then multiply by four to get twenty.
Example with an exponent: Read “two squared plus four.” Two squared means two times two, which is four. Then add four to get eight.
Example with division and multiplication: Read “eighteen divided by three times two.” Move left to right inside the equal-priority pair. The result is twelve.
Example with subtraction and addition: Read “twenty minus eight plus one.” Move left to right inside that equal-priority pair. The result is thirteen.
This article is about evaluating numerical expressions. If you are solving an equation with an equals sign, graphing a function, or simplifying an algebraic expression with variables, you are doing a related but different task.
The order of operations still matters inside those tasks, and you may also need inverse operations to isolate a variable. If you are moving from arithmetic into early algebra, the transition often goes more smoothly when you study the rule in sequence and use more than isolated worksheets, which is why many students move from arithmetic review into the common questions about self-paced courses before choosing a next step.
One reading for one expression: The order of operations exists so one expression has one agreed interpretation.
PEMDAS as a memory aid: It helps you remember grouping symbols, exponents, multiplication and division, and addition and subtraction, in that order.
Left to right for equals: Multiplication and division are equals in priority, and addition and subtraction are equals in priority, so each pair is handled from left to right.
Common error sources: Students often miss the rule by skipping grouping symbols, misreading an exponent, or reordering equal-priority operations.
Rewrite after each step: A careful rewrite after each step is usually more useful than trying to finish quickly, especially in self-paced video study.
If you want guided practice with order of operations, Cool Math Guy teaches it the way many students need to see it: slowly, clearly, and line by line on video. That approach works well when a worksheet alone is not enough and you need to watch each step unfold before you jump to an answer.
If you are deciding which course level fits your current math background, use the contact page to ask the next question. A clear starting point makes PEMDAS, prealgebra, and everything that follows much easier to build.
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