Why Kids Get PEMDAS Wrong Even When They Know the Rule
August 24, 2026
At a glance
• PEMDAS stands for parentheses, exponents, multiplication, division, addition, and subtraction.
• Multiplication and division share one step and run left to right. Addition and subtraction work the same way. The letters do not require multiplication before division or addition before subtraction, a common source of mistakes.
• Order of operations gives everyone the same answer to an expression. Without a shared order, different sequences could produce different results.
• Use the mistakes section to diagnose wrong answers. Then jump to the grade-tagged examples for guided practice at your child's level.
• Multiplication and division share one step and run left to right. Addition and subtraction work the same way. The letters do not require multiplication before division or addition before subtraction, a common source of mistakes.
• Order of operations gives everyone the same answer to an expression. Without a shared order, different sequences could produce different results.
• Use the mistakes section to diagnose wrong answers. Then jump to the grade-tagged examples for guided practice at your child's level.
What PEMDAS stands for and why order matters
PEMDAS is a memory aid for the agreed order of operations in math. P stands for parentheses, which tell you to simplify grouped expressions first. E stands for exponents. M and D stand for multiplication and division, while A and S stand for addition and subtraction.
Multiplication and division share the same priority. Work through them from left to right. Addition and subtraction also share a priority, so work through that pair from left to right. The letters do not tell you to complete every multiplication problem before any division problem or every addition problem before any subtraction problem.
Use PEMDAS in four stages. Simplify expressions inside parentheses first, then evaluate exponents. Next, complete multiplication and division from left to right. Finally, complete addition and subtraction from left to right.
A shared order prevents one expression from producing several answers. For example, 6 + 2 × 5 equals 16 under PEMDAS because multiplication comes before addition. Calculating strictly from left to right would produce 40 instead.
The left-to-right rule within paired operations causes frequent confusion. In 8 ÷ 2 × 4, divide 8 by 2 first, then multiply 4 by 4 to get 16. A student who assumes multiplication always comes first may calculate 2 × 4 and then 8 ÷ 8, producing 1. The standard rule gives 16 because division appears first when reading the expression from left to right.
Multiplication and division share the same priority. Work through them from left to right. Addition and subtraction also share a priority, so work through that pair from left to right. The letters do not tell you to complete every multiplication problem before any division problem or every addition problem before any subtraction problem.
Use PEMDAS in four stages. Simplify expressions inside parentheses first, then evaluate exponents. Next, complete multiplication and division from left to right. Finally, complete addition and subtraction from left to right.
A shared order prevents one expression from producing several answers. For example, 6 + 2 × 5 equals 16 under PEMDAS because multiplication comes before addition. Calculating strictly from left to right would produce 40 instead.
The left-to-right rule within paired operations causes frequent confusion. In 8 ÷ 2 × 4, divide 8 by 2 first, then multiply 4 by 4 to get 16. A student who assumes multiplication always comes first may calculate 2 × 4 and then 8 ÷ 8, producing 1. The standard rule gives 16 because division appears first when reading the expression from left to right.
The three mistakes kids make with PEMDAS
Multiplication always comes before division
Kids often read PEMDAS as six separate steps because the acronym places M before D. The actual rule gives multiplication and division equal priority, so you perform whichever appears first when reading left to right. Math Doctors identifies the acronym's wording as a common source of this confusion.
Wrong way:
In 8 ÷ 2 × 4, a student multiplies 2 × 4 first because M appears before D. The student then calculates 8 ÷ 8 = 1.
Right way:
Start with the first multiplication or division operation. Calculate 8 ÷ 2 = 4, then 4 × 4 = 16.
You can make the relationship clearer by describing division as multiplication by a fraction. The expression 8 ÷ 2 × 4 becomes 8 × ½ × 4, which helps a child see why multiplication and division belong at the same priority level.
Wrong way:
In 8 ÷ 2 × 4, a student multiplies 2 × 4 first because M appears before D. The student then calculates 8 ÷ 8 = 1.
Right way:
Start with the first multiplication or division operation. Calculate 8 ÷ 2 = 4, then 4 × 4 = 16.
You can make the relationship clearer by describing division as multiplication by a fraction. The expression 8 ÷ 2 × 4 becomes 8 × ½ × 4, which helps a child see why multiplication and division belong at the same priority level.
Addition always comes before subtraction
The same literal reading causes kids to perform every addition operation before any subtraction. PEMDAS places A before S, but addition and subtraction share one priority level. A child who has practiced sorting operations by letter may group the addition instead of reading the expression in order.
Wrong way:
In 2 − 3 + 4, a student adds 3 + 4 first. The expression becomes 2 − 7 = −5.
Right way:
Work left to right because addition and subtraction have equal priority. Calculate 2 − 3 = −1, then −1 + 4 = 3.
Subtraction can also be written as adding a negative number. The expression becomes 2 + (−3) + 4, which shows that the minus sign belongs to 3 rather than to the whole expression that follows.
Wrong way:
In 2 − 3 + 4, a student adds 3 + 4 first. The expression becomes 2 − 7 = −5.
Right way:
Work left to right because addition and subtraction have equal priority. Calculate 2 − 3 = −1, then −1 + 4 = 3.
Subtraction can also be written as adding a negative number. The expression becomes 2 + (−3) + 4, which shows that the minus sign belongs to 3 rather than to the whole expression that follows.
Every operation should be completed left to right
Some kids learn the left-to-right correction and apply it to the entire expression. They stop using PEMDAS to separate priority levels and simply calculate each operation as it appears. The left-to-right rule applies only within the multiplication and division pair or within the addition and subtraction pair.
Wrong way:
In 6 + 2 × 3, a student starts with 6 + 2 because it appears first. The student calculates 8 × 3 = 24.
Right way:
Multiplication has higher priority than addition. Calculate 2 × 3 = 6 first, then 6 + 6 = 12.
Ask your child to mark parentheses and exponents first, then underline every multiplication or division operation. After completing those operations from left to right, the child can handle addition and subtraction from left to right. The markings reveal whether the child understands priority or merely follows the expression across the page.
Wrong way:
In 6 + 2 × 3, a student starts with 6 + 2 because it appears first. The student calculates 8 × 3 = 24.
Right way:
Multiplication has higher priority than addition. Calculate 2 × 3 = 6 first, then 6 + 6 = 12.
Ask your child to mark parentheses and exponents first, then underline every multiplication or division operation. After completing those operations from left to right, the child can handle addition and subtraction from left to right. The markings reveal whether the child understands priority or merely follows the expression across the page.
Elementary-level PEMDAS examples
These elementary-level PEMDAS examples use one set of parentheses and the four basic operations. They avoid exponents and nested grouping.
Elementary example 1:
Solve 8 + (12 ÷ 3) × 2.
Start inside the parentheses, where 12 ÷ 3 = 4. The expression becomes 8 + 4 × 2. Multiply 4 × 2 = 8, then add 8 + 8 = 16.
Elementary example 2:
Solve (10 - 4) ÷ 2 × 3.
Complete the parentheses first, so 10 - 4 = 6. The expression becomes 6 ÷ 2 × 3. Division and multiplication share a level, so work across the expression. Divide 6 ÷ 2 = 3, then multiply 3 × 3 = 9.
Elementary example 3:
Solve 20 - (6 + 2) + 3.
Add inside the parentheses first, so 6 + 2 = 8. The expression becomes 20 - 8 + 3. Subtraction appears first as you read across the expression, so calculate 20 - 8 = 12, then 12 + 3 = 15.
Elementary example 1:
Solve 8 + (12 ÷ 3) × 2.
Start inside the parentheses, where 12 ÷ 3 = 4. The expression becomes 8 + 4 × 2. Multiply 4 × 2 = 8, then add 8 + 8 = 16.
Elementary example 2:
Solve (10 - 4) ÷ 2 × 3.
Complete the parentheses first, so 10 - 4 = 6. The expression becomes 6 ÷ 2 × 3. Division and multiplication share a level, so work across the expression. Divide 6 ÷ 2 = 3, then multiply 3 × 3 = 9.
Elementary example 3:
Solve 20 - (6 + 2) + 3.
Add inside the parentheses first, so 6 + 2 = 8. The expression becomes 20 - 8 + 3. Subtraction appears first as you read across the expression, so calculate 20 - 8 = 12, then 12 + 3 = 15.
Middle school PEMDAS examples with exponents and nested parentheses
Exponents take priority over multiplication and division. In 24 ÷ 3 × 2² − 5, calculate 2² first to get 4. The expression becomes 24 ÷ 3 × 4 − 5. Work division and multiplication from left to right to get 8 × 4 − 5, then 32 − 5, for an answer of 27. A student who calculates 3 × 4 first has made the common mistake of treating multiplication as higher priority than division.
Nested grouping symbols require you to start with the innermost group and work outward. Consider 40 − [18 ÷ (2 + 1) × 2] + 5. Calculate 2 + 1 first, which leaves 40 − [18 ÷ 3 × 2] + 5. Inside the brackets, work division and multiplication from left to right to get 40 − 12 + 5. Finally, work subtraction and addition from left to right, producing 28 + 5 and an answer of 33.
Brackets and parentheses both group operations. Different symbols make nested groups easier to read, but each group follows the same PEMDAS rules.
Nested grouping symbols require you to start with the innermost group and work outward. Consider 40 − [18 ÷ (2 + 1) × 2] + 5. Calculate 2 + 1 first, which leaves 40 − [18 ÷ 3 × 2] + 5. Inside the brackets, work division and multiplication from left to right to get 40 − 12 + 5. Finally, work subtraction and addition from left to right, producing 28 + 5 and an answer of 33.
Brackets and parentheses both group operations. Different symbols make nested groups easier to read, but each group follows the same PEMDAS rules.
Why PEMDAS trips kids up more than other math rules
PEMDAS requires a new decision at each step, which makes it harder to apply than a single math fact. A child may recite the acronym correctly but still assume multiplication always comes before division. The same child might forget to work left to right when multiplication and division share an expression.
One incorrect choice can remain hidden through several lines of accurate arithmetic. In 24 ÷ 6 × 2, a child might multiply 6 × 2 first and get 2. The division itself is correct, but the child chose the wrong operation first. A completed worksheet shows the wrong answer without revealing why the child made that choice, while a video demonstrates a correct solution without seeing the child's work.
A person watching the work can catch the exact moment when the rule breaks down. A tutor can ask why the child selected an operation, correct the choice immediately, and provide another similar problem for practice. Repeated feedback helps the child connect the memorized acronym to the decisions PEMDAS requires.
One incorrect choice can remain hidden through several lines of accurate arithmetic. In 24 ÷ 6 × 2, a child might multiply 6 × 2 first and get 2. The division itself is correct, but the child chose the wrong operation first. A completed worksheet shows the wrong answer without revealing why the child made that choice, while a video demonstrates a correct solution without seeing the child's work.
A person watching the work can catch the exact moment when the rule breaks down. A tutor can ask why the child selected an operation, correct the choice immediately, and provide another similar problem for practice. Repeated feedback helps the child connect the memorized acronym to the decisions PEMDAS requires.
How 1-on-1 tutoring corrects PEMDAS mistakes faster
A 1-on-1 tutor can correct a PEMDAS error as soon as your child makes it. The tutor watches each written step and can see whether your child divided before multiplying, added before subtracting, or skipped a set of parentheses. Instead of marking the final answer wrong, the tutor identifies the first incorrect step and helps your child redo it using the right rule.
Immediate feedback keeps a repeated mistake from becoming a habit. A video presents a fixed explanation, while a worksheet usually reports only whether the final answer is correct. A tutor can choose the next problem based on the error. For example, a child who treats multiplication as higher priority than division can practice short expressions that require left-to-right work until the rule becomes familiar.
Cosmo provides 1-on-1 online tutoring based on your child's current understanding. A tutor can model one step at the right pace and then watch your child apply it independently. If your child keeps getting stuck on order of operations, you can book a free trial class with no credit card required.
Immediate feedback keeps a repeated mistake from becoming a habit. A video presents a fixed explanation, while a worksheet usually reports only whether the final answer is correct. A tutor can choose the next problem based on the error. For example, a child who treats multiplication as higher priority than division can practice short expressions that require left-to-right work until the rule becomes familiar.
Cosmo provides 1-on-1 online tutoring based on your child's current understanding. A tutor can model one step at the right pace and then watch your child apply it independently. If your child keeps getting stuck on order of operations, you can book a free trial class with no credit card required.
Common questions about PEMDAS
Does PEMDAS apply to all math?
PEMDAS governs expressions that combine grouping symbols, exponents, multiplication or division, and addition or subtraction. Cosmo tutors can help students recognize when these operations appear in arithmetic and algebra. Students can then evaluate each expression in a consistent order.
How do BODMAS and BEDMAS differ from PEMDAS?
BODMAS and BEDMAS use different words for grouping symbols and exponents, but they follow the same order. Cosmo tutors emphasize that multiplication and division share one level, while addition and subtraction share another. Within each pair, students work left to right.
How do negative numbers interact with exponents?
Standard order of operations evaluates an exponent before a negative sign unless parentheses group the negative number. Therefore, −3² equals −9, while (−3)² equals 9. Cosmo tutors can show students how parentheses determine whether the negative sign gets squared.
How should students handle nested parentheses?
Nested parentheses place one grouped expression inside another. Cosmo tutors teach students to solve the innermost group first and then move outward one layer at a time. Brackets and braces work like parentheses when they group parts of an expression.
PEMDAS governs expressions that combine grouping symbols, exponents, multiplication or division, and addition or subtraction. Cosmo tutors can help students recognize when these operations appear in arithmetic and algebra. Students can then evaluate each expression in a consistent order.
How do BODMAS and BEDMAS differ from PEMDAS?
BODMAS and BEDMAS use different words for grouping symbols and exponents, but they follow the same order. Cosmo tutors emphasize that multiplication and division share one level, while addition and subtraction share another. Within each pair, students work left to right.
How do negative numbers interact with exponents?
Standard order of operations evaluates an exponent before a negative sign unless parentheses group the negative number. Therefore, −3² equals −9, while (−3)² equals 9. Cosmo tutors can show students how parentheses determine whether the negative sign gets squared.
How should students handle nested parentheses?
Nested parentheses place one grouped expression inside another. Cosmo tutors teach students to solve the innermost group first and then move outward one layer at a time. Brackets and braces work like parentheses when they group parts of an expression.
The takeaway for parents
An occasional PEMDAS mistake usually reflects a missed step, not a larger problem with math. Your child may understand each operation but apply two equal-priority operations in the wrong order.
Short, focused practice can correct the habit. Ask your child to write one step per line and explain each choice aloud. When you catch the first incorrect step and correct it right away, your child can practice the rule accurately and build confidence through repetition.
Short, focused practice can correct the habit. Ask your child to write one step per line and explain each choice aloud. When you catch the first incorrect step and correct it right away, your child can practice the rule accurately and build confidence through repetition.
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