Curriculum Core Rules & Strategy
Always write out given values and the relevant formula before substituting numbers.
Substitute your final answer back into the original problem to verify correctness.
Double-check negative signs, common denominators, and arithmetic order of operations.
Mastering Order of Operations (PEMDAS/BODMAS) with SolveCalc
PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) is the universal protocol ensuring every person evaluating the same expression arrives at the same answer. Without it, 2 + 3 × 4 could equal 20 or 14.
Why Order of Operations Exists
Mathematical expressions must be unambiguous — one expression should have exactly one value. The order of operations is an agreed convention, standardised during the 20th century, that specifies which operations to perform first.
Without the convention, 2 + 3 × 4 is ambiguous:
Left-to-right: (2+3)×4 = 20
Multiplication first: 2+(3×4) = 14
The convention says multiplication comes before addition, so the correct answer is 14. This isn't a mathematical law — it's a shared agreement, like driving on the same side of the road.
PEMDAS / BODMAS — Complete Priority Order
- P / B — Parentheses (Brackets): Everything inside brackets is evaluated first, from innermost to outermost
- E / O — Exponents (Orders/Powers): Powers and roots, evaluated left to right
- M/D — Multiplication and Division: Equal priority, evaluated LEFT TO RIGHT
- A/S — Addition and Subtraction: Equal priority, evaluated LEFT TO RIGHT
Brackets: 4−1=3 → 8÷2+9×3
Exponent: 3²=9 → 8÷2+9×3
M/D (left-right): 8÷2=4, 9×3=27 → 4+27
Addition: 31
The Left-to-Right Rule for Multiplication/Division
The most common exam trap: students treat multiplication as higher priority than division. They are EQUAL priority and must be evaluated left to right.
❌ Wrong: 12 ÷ (4×3) = 12 ÷ 12 = 1
✅ Correct (left-to-right): (12÷4)×3 = 3×3 = 9
❌ Wrong: 20 − (5+3) = 12
✅ Correct (left-to-right): (20−5)+3 = 15+3 = 18
PEMDAS — Three Fully Worked Evaluations
Brackets: (5+4)=9 → 3+6×9÷3−7
M/D: 6×9=54÷3=18 → 3+18−7
A/S: 14
Brackets: 3−1=2, √16=4, 2³=8 → 8+4−4×2
M: 4×2=8 → 8+4−8 = 4
5!=120, brackets: 4+1=5, 3×5=15 → 120−15 = 105
Order of Operations Errors
- Treating M before D as a rule: It's left-to-right for equal precedence. 6÷2×3 = 9, not 1.
- Missing implicit brackets: In 3/4+5, the fraction bar acts as brackets: (3)/(4+5) ≠ (3/4)+5. Use explicit parentheses when in doubt.
- Unary minus confusion: −2² = −4 (apply exponent first, then negate). (−2)² = 4. Always use brackets to clarify the scope of a negative sign.
PEMDAS/BODMAS Memory Tricks
- PEMDAS mnemonic: "Please Excuse My Dear Aunt Sally" — Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
- BODMAS: Brackets, Orders (powers), Division, Multiplication, Addition, Subtraction — same priority, different regional name.
- The two equal-pairs rule: M and D are equal (left-to-right). A and S are equal (left-to-right). Never favour one over the other within a pair.
SolveCalc's Scientific Calculator enforces PEMDAS automatically — use it to verify complex expressions.
Common Student Pitfalls & Exam Traps
- Skipping steps: Even experienced mathematicians write every step. Skipping creates opportunities for errors.
- Not checking answers: Always substitute your answer back to verify correctness.
- Confusing similar concepts: Small differences in definitions can require completely different approaches.
- Unit errors: Always keep track of units and convert consistently when working with real-world problems.
SolveCalc Insight
DEEP DIVESolveCalc provides free, browser-based math tools for students and educators at every level. Use our interactive calculators alongside this curriculum guide to verify your calculations and explore concepts hands-on — no sign-up, no downloads, no limits.
Explore with SolveCalc's Math Tools Library→Frequently Asked Questions
What does PEMDAS stand for? +
Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
Does multiplication always come before division? +
No — multiplication and division are equal priority, worked left to right.