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Enhanced Basic Arithmetic Calculator

Master the fundamentals of mathematics with comprehensive tools and educational content

➕ Addition
➖ Subtraction
✖️ Multiplication
➗ Division
🔢 Exponents
√ Roots

Addition Calculator

+
Sum = a + b
0
Enter numbers to calculate sum

Subtraction Calculator

−
Difference = a − b
0
Enter numbers to calculate difference

Multiplication Calculator

×
Product = a × b
0
Enter numbers to calculate product

Division Calculator

÷
Quotient = a ÷ b
0
Enter numbers to calculate quotient

Exponents Calculator

^
Result = base^exponent
0
Enter base and exponent to calculate power

Roots Calculator

√
Result = ⁿ√number
0
Enter root index and number to calculate root
📚 Mathematical Fundamentals
Commutative Property
Addition and multiplication are commutative: a + b = b + a and a × b = b × a. Order doesn't matter for these operations.
Associative Property
Addition and multiplication are associative: (a + b) + c = a + (b + c) and (a × b) × c = a × (b × c). Grouping doesn't matter.
Distributive Property
Multiplication distributes over addition: a × (b + c) = (a × b) + (a × c). This is fundamental for algebra.
Identity Elements
0 is the additive identity (a + 0 = a) and 1 is the multiplicative identity (a × 1 = a). These numbers don't change other numbers.
Inverse Operations
Addition and subtraction are inverse operations, as are multiplication and division. They "undo" each other.
Order of Operations
Follow PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).
💡 Step-by-Step Examples
➕ Addition Example
347 + 289 = ?
  • Step 1: Align numbers by place value
  • Step 2: Add ones place: 7 + 9 = 16 (write 6, carry 1)
  • Step 3: Add tens place: 4 + 8 + 1 = 13 (write 3, carry 1)
  • Step 4: Add hundreds place: 3 + 2 + 1 = 6
  • Result: 347 + 289 = 636
➖ Subtraction Example
523 - 187 = ?
  • Step 1: Align numbers by place value
  • Step 2: Ones place: 3 - 7 requires borrowing
  • Step 3: Borrow from tens: 13 - 7 = 6
  • Step 4: Tens place (after borrowing): 1 - 8 requires borrowing
  • Step 5: Borrow from hundreds: 11 - 8 = 3
  • Step 6: Hundreds place: 4 - 1 = 3
  • Result: 523 - 187 = 336
✖️ Multiplication Example
34 × 26 = ?
  • Step 1: Multiply 34 × 6 = 204
  • Step 2: Multiply 34 × 20 = 680
  • Step 3: Add partial products: 204 + 680
  • Step 4: Calculate sum: 884
  • Result: 34 × 26 = 884
➗ Division Example
756 ÷ 18 = ?
  • Step 1: How many times does 18 go into 75? Answer: 4
  • Step 2: 4 × 18 = 72, subtract: 75 - 72 = 3
  • Step 3: Bring down 6 to make 36
  • Step 4: How many times does 18 go into 36? Answer: 2
  • Step 5: 2 × 18 = 36, subtract: 36 - 36 = 0
  • Result: 756 ÷ 18 = 42
🔢 Exponent Example
2⁶ = ?
  • Step 1: 2⁶ means 2 × 2 × 2 × 2 × 2 × 2
  • Step 2: 2 × 2 = 4
  • Step 3: 4 × 2 = 8
  • Step 4: 8 × 2 = 16
  • Step 5: 16 × 2 = 32
  • Step 6: 32 × 2 = 64
  • Result: 2⁶ = 64
√ Square Root Example
√144 = ?
  • Step 1: Find what number multiplied by itself equals 144
  • Step 2: Try perfect squares: 10² = 100 (too small)
  • Step 3: Try 12²: 12 × 12
  • Step 4: Calculate: 12 × 12 = 144
  • Step 5: Verify: 12 × 12 = 144 ✓
  • Result: √144 = 12
🌍 Real-World Applications
💰 Financial Planning
Use addition to sum income sources, subtraction for expenses, multiplication for repeated payments, and division for average calculations. Essential for budgeting and financial planning.
🏠 Home Improvement
Calculate material quantities, room areas, paint coverage, and project costs. Multiplication and division are crucial for scaling measurements and estimating materials.
🍳 Cooking & Recipes
Scale recipes up or down using multiplication and division. Calculate cooking times, ingredient ratios, and nutritional values for meal planning.
🎓 Education & Testing
Calculate grades, averages, percentages, and test scores. Essential for academic progress tracking and standardized test preparation.