Order of Operations (PEMDAS) — A Parent's Guide

TL;DR

The order of operations in math — taught as PEMDAS in the US, BODMAS in the UK and India, BIDMAS in much of Europe, and BEDMAS in Canada — tells children which calculation to do first when an expression mixes operations.

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Last updated on May 21, 2026

"Please Excuse My Dear Aunt Sally" Sounds Simple — It Isn't

PEMDAS is one of those math topics that looks tidy in a textbook and breaks open the moment a real expression appears. The acronym is fine. The problem is what the acronym hides: that multiplication and division aren't actually two ranked steps but one tier, and that the same is true for addition and subtraction. Most kids learn the mnemonic and never hear the footnote — so they make the same predictable mistakes for years.

The good news: once the two missing pieces click, the order of operations stops being a trap. It becomes a checklist a child can run reliably on any expression. The trick is making the missing pieces explicit and walking through enough examples that the pattern locks in.

This article does not introduce the rule — your child has already met it. It explains where it usually goes wrong and what to do about it.

What's Actually Going On

PEMDAS stands for P arentheses, E xponents, M ultiplication, D ivision, A ddition, S ubtraction. The expression 6+2×3 equals 12, not 24, because multiplication comes before addition. So far, so clean.

Here's what the mnemonic hides.

The two-tier rule that gets lost. Multiplication and division share the same tier. So do addition and subtraction. When an expression has both multiplication and division (with no parentheses or exponents in the way), you do not do all the multiplication first — you go left to right. So 12÷4×3 equals (12÷4)×3=9, not 12÷(4×3)=1.

The same is true for + and −. 10−4+2=(10−4)+2=8, not 10−(4+2)=4.

If your child treats PEMDAS as six ranked steps (do all M before any D, all A before any S), they will get specific problems wrong in a predictable pattern.

The parenthesis trap. When parentheses contain an expression — not just one number — you still apply PEMDAS inside the parentheses, then handle what's outside. 2(3+5) means 2×8=16. Kids who learned "do the parentheses first" sometimes write 2×3+5=11 by distributing badly. The rule is: finish what's inside the parentheses, then multiply outside.

Implicit multiplication. 2(3)=6. The missing × sign is the source of more confusion than parents realise. A child who reads 2x2x2 as "two x" needs to know that the implied multiplication has the same priority as a written × — usually.

PEMDAS, BODMAS, BIDMAS, BEDMAS, GEMDAS — Same Rule, Different Letters

Regional curricula use different mnemonics. They all describe the same four-tier rule.

The D-before-M ordering in BODMAS confuses many students into thinking division strictly precedes multiplication. It does not. They are the same tier and are evaluated left to right — whichever appears first.

Patterns to Watch For

These are the exact signals that a child has memorised the mnemonic but not internalised the structure.

• They get 12÷4×3=1 (treated all M before D), instead of 9.
• They get 10−4+2=4 (treated all A before S), instead of 8.
• They get 2(3+5)=11 (distributed the 2 before adding inside), instead of 16.
• They can do problems with one operation type fine, but lose accuracy the moment an expression mixes multiplication and division.
• They argue passionately about which way is right — confidence is high, error rate is also high. (This is the memorizer archetype.)

A child who has only the mnemonic gets the easy expressions right and the medium ones wrong. A child who actually understands the order gets a wider range right and asks better questions when stuck.

Walk Through — Ten Worked Examples (Wrong Path Shown First)

The fastest way to make the four-tier rule stick is to walk through expressions where the intuitive answer is wrong. Show the slip, then show the fix.

Example 1 — 6+2×3
Wrong path. Read left to right: 6+2=8, then 8×3=24. Correct. Multiplication is on a higher tier than addition. 2×3=6 first. Then 6+6=12. Final answer: 12.

Example 2 — 20−5×2
Wrong path. Left to right: 20−5=15, then 15×2=30. Correct. Multiplication first: 5×2=10. Then 20−10=10. Final answer: 10.

Example 3 — 12÷4×3
Wrong path. "M comes before D in PEMDAS, so do multiplication first": 4×3=12, then 12÷12=1. Correct. Multiplication and division share a tier — go left to right. 12÷4=3 first. Then 3×3=9. Final answer: 9.

Example 4 — 10−4+2
Wrong path. "A comes before S, so do addition first": 4+2=6, then 10−6=4. Correct. Addition and subtraction share a tier — left to right. 10−4=6 first. Then 6+2=8. Final answer: 8.

Example 5 — 2(3+5)
Wrong path. Distribute too early: 2×3+5=11. Correct. Finish inside the parentheses first: 3+5=8. Then multiply: 2×8=16. Final answer: 16.

Example 6 — 5+4×(10−6)
Wrong path. Multiply before the parenthesis is finished: 4×10=40, then 5+40−6=39. Correct. Parentheses first: 10−6=4. Then multiplication: 4×4=16. Then addition: 5+16=21. Final answer: 21.

Example 7 — 3^2 + 4×2
Wrong path. Multiply first: 4×2=8, then 3^2=9, then 9+8=17. Correct. Exponents first: 3^2=9. Then multiplication: 4×2=8. Then addition: 9+8=17. Final answer: 17.

Example 8 — 2×[3+(4−1)^2]
Wrong path. Skip the inner parenthesis: 2×[3+4−1^2]=12. Correct. Innermost parenthesis first: 4−1=3. Then the exponent: 3^2=9. Then the outer bracket: 3+9=12. Then the multiplication: 2×12=24. Final answer: 24.

Example 9 — −6+18÷(−3)×2
Wrong path. Process the division and multiplication separately, then add: -6 + (-6)=−12. Correct. Division and multiplication left to right: 18÷(−3)=−6 first. Then (−6)×2=−12. Then −6+(−12)=−18. Final answer: −18.

Example 10 — 8÷2(2+2)
Wrong path A. Treat 2(2+2) as a single term: 2×4=8. Then 8÷8=1. Wrong path B. Strict left-to-right with explicit multiplication priority: 8÷2=4, then (2+2)=4, then 4×4=16.

This expression is genuinely ambiguous in conventional notation. Most textbooks resolve it to 16 by applying standard PEMDAS (do the parenthesis first, then divide/multiply left to right). Many handheld calculators give 1 because they treat implicit multiplication (the missing × sign) as tighter than explicit multiplication.

What to Do (Concrete Actions)

Specific things a parent can do this week.

• Write 12÷4×3 on paper and ask them to solve it twice — once as "all M first," once as "left to right." Have them check on a calculator. The reveal does the work.
• Replace the mnemonic with a four-tier summary. "Parentheses, then exponents, then × and ÷ left to right, then + and − left to right."
• Hunt for the trap problem. Give them expressions that test the left-to-right rule.
• Make them write each step. A child who writes each intermediate step doesn't rush and make predictable mistakes.
• Use a calculator strategically. Not for getting the answer. For checking their reasoning.

When to Bring in Outside Help

The honest signals.

• The mistakes persist past Grade 6. PEMDAS lives at the heart of algebra.
• They get the right answer but can't explain why. This is the memorizer signal.
• They've developed a fear of "tricky" problems.

A structured math program becomes worth the investment once one of those thresholds is hit.

Conclusion

• The order of operations in math is four tiers, not six steps: P, E, then (×/÷ left to right), then (+/− left to right).
• The two-tier rule is what the mnemonic hides — teach it explicitly with paired examples.
• Most errors come from rushing through M/D and A/S as if they were ranked.
• Writing each step out catches almost every mistake.
• Implicit multiplication is genuinely ambiguous — write parentheses to avoid the trap.