CALTRX

Basic Calculator

Enter two numbers and select an operation to get an instant result with the calculation steps shown. See the complete solution with step-by-step working and formula explanations.

Enter your values above to see the results.

Tips & Notes

  • ✓Order of operations: Multiplication and Division before Addition and Subtraction. 2+3×4=14, not 20.
  • ✓Negative × Negative = Positive. (−5)×(−3)=+15. Two negatives cancel each other out.
  • ✓Division by zero is undefined. 5÷0 has no answer — not infinity, not zero.
  • ✓Check your answer: for 47×8, estimate 50×8=400, so 376 is reasonable.
  • ✓Use parentheses to control order: (2+3)×4=20 vs 2+3×4=14 — parentheses change everything.

Common Mistakes

  • ✗Ignoring order of operations: 8−2×3=2 (not 18). Multiplication before subtraction.
  • ✗Sign errors with negatives: −3²=−9 (square first, then negate) vs (−3)²=+9.
  • ✗Dividing by zero — undefined, not infinity. Any division by 0 has no valid answer.
  • ✗Misplacing decimal point in multiplication: 2.5×4=10.0, not 1.00 or 100.
  • ✗Confusing subtraction with negative: 5−(−3)=5+3=8. Subtracting a negative adds.

Basic Calculator Overview

The basic calculator performs the four fundamental arithmetic operations — addition, subtraction, multiplication, and division — that form the foundation of all quantitative reasoning. While these operations seem simple, their rules for precedence (which operation happens first), behavior with negative numbers, and interaction with zero have nuances that cause frequent errors. This calculator shows full step-by-step working for every computation, making the logic transparent rather than just delivering an answer.

Order of operations (PEMDAS/BODMAS): the universal rule establishing which operations happen first:

EX: 3 + 4 × 2 = 3 + 8 = 11 (NOT 7×2=14) — multiplication before addition
EX: (3 + 4) × 2 = 7 × 2 = 14 — parentheses override the default order
EX: 8 − 2 × 3 + 4 = 8 − 6 + 4 = 6 — multiply first, then left-to-right
Hierarchy: (1) Parentheses/Brackets → (2) Exponents → (3) Multiplication and Division (left to right) → (4) Addition and Subtraction (left to right). Negative number rules:
EX: (−3) × (−4) = +12 — negative × negative = positive
EX: (−3) × 4 = −12 — negative × positive = negative
EX: 5 − (−3) = 5 + 3 = 8 — subtracting a negative adds
EX: −3² = −9 — exponent applies to 3 only, then negate | (−3)² = +9 — exponent applies to (−3)
Division rules: - Division by zero: 5÷0 is undefined — not zero, not infinity, just undefined. No valid answer exists. - 0÷5 = 0 — zero divided by any nonzero number is zero - Integer division: 7÷3 = 2 remainder 1, or as decimal 2.333... Estimation — checking reasonableness before accepting an answer:
EX: 47 × 23 → estimate 50×20=1,000 → exact answer 1,081 is reasonable | if you got 10,810 it is clearly wrong
Arithmetic properties: Commutative: a+b=b+a and a×b=b×a — order does not matter for addition and multiplication; Associative: (a+b)+c=a+(b+c) — grouping does not matter; Distributive: a×(b+c) = a×b + a×c — distributes multiplication over addition Mental math shortcuts; Multiply by 5: multiply by 10 then halve. 47×5 = 470÷2 = 235. - Multiply by 9: multiply by 10 then subtract once. 47×9 = 470−47 = 423. - Multiply by 25: multiply by 100 then divide by 4. 47×25 = 4700÷4 = 1,175.. Order of operations resolves an ambiguity that would otherwise make mathematical expressions meaningless. Without a universal convention, 3 + 4 × 2 could equal 14 or 11 depending on which operation you perform first. PEMDAS/BODMAS provides the universal agreement that makes written mathematics unambiguous: multiplication before addition, left to right for operations at the same level. This convention is not mathematically necessary — mathematicians could have chosen any consistent rule — but its universality means every correctly written expression has exactly one correct interpretation.

Frequently Asked Questions

Order of operations (PEMDAS/BODMAS): Parentheses first, then Exponents, then Multiplication and Division left-to-right, then Addition and Subtraction left-to-right. Example: 3 + 4 × 2 = 3 + 8 = 11 (not 14). (3+4) × 2 = 7 × 2 = 14. Example: 8 ÷ 4 × 2 = 2 × 2 = 4 (not 8÷8=1 — division and multiplication are equal priority, evaluated left-to-right). Parentheses are the only way to override the default order — always use them when grouping matters.

Dividing any number by zero is undefined — not infinity. Division a÷b asks how many bs fit into a. 10÷2=5 because 5 twos make 10. 10÷0 asks how many zeros fit into 10 — there is no answer that works because 0×anything=0, never 10. Calculators display Error or undefined. Note that 0÷0 is also undefined (indeterminate form in calculus). And 0÷10=0 is perfectly valid — zero divided by a non-zero number is zero.

Adding or subtracting negative numbers: rewrite as addition/subtraction without negatives by applying these rules. a+(−b) = a−b. a−(−b) = a+b. Example: 5+(−3) = 5−3 = 2. 5−(−3) = 5+3 = 8. Multiplication/division with negatives: negative × negative = positive. Negative × positive = negative. −3×−4=12. −3×4=−12. 3×(−4)=−12. Verify sign rules by thinking of negatives as reversals: reversing twice returns to the original direction.

For large numbers in everyday calculation: use estimation first to catch errors. 347 × 52 ≈ 350 × 50 = 17,500. Exact: 347×52 = 347×50+347×2 = 17,350+694 = 18,044. The estimate (17,500) is close — confirming no major error. For decimals: align decimal points for addition/subtraction. For multiplication: compute as integers, then count total decimal places and insert the decimal. 3.14 × 2.5: 314 × 25 = 7,850. Total decimal places: 2+1=3. Result: 7.850.

Percentages in calculations: percent means per hundred, so convert to decimal by dividing by 100. 25% = 0.25. To find 25% of 80: 0.25 × 80 = 20. To find the original after a 20% increase: if increased value = 120, original = 120 ÷ 1.20 = 100. For successive changes: 20% increase then 20% decrease: multiply by 1.20 × 0.80 = 0.96 → 4% net decrease (not zero). Percentage changes do not cancel because they apply to different bases.

Rounding rules for everyday calculation: round the last kept digit up if the next digit is 5 or higher, down if 4 or lower. Example: 3.456 to 2 decimals → look at third decimal (6 ≥ 5) → 3.46. To 1 decimal → look at second decimal (5 ≥ 5) → 3.5. Round-trip check: rounded results should reproduce the calculation with acceptable accuracy. For financial calculations, always round at the final step — rounding intermediate results accumulates errors and can cause discrepancies in multi-step calculations.