Multiplication Calculator
Multiply numbers with step-by-step solutions and detailed mathematical explanations
Calculate Multiplication
Multiplication Result
Calculation Steps:
Example Calculations
Basic Multiplication
Simple two-factor multiplication
Decimal Multiplication
Multiplying decimal numbers
Multiple Factors
Multiplying three numbers together
Large Numbers
Multiplication of larger integers
Multiplication Methods
Repeated Addition
5 × 3 = 5 + 5 + 5 = 15
Long Multiplication
Standard algorithm for large numbers
Decimal Multiplication
Count decimal places in factors
Scientific Notation
For very large or small numbers
Multiplication Tips
Any number × 0 = 0
Any number × 1 = that number
Negative × Negative = Positive
Positive × Negative = Negative
Order doesn't matter (commutative)
Understanding Multiplication
What is Multiplication?
Multiplication is one of the four basic arithmetic operations. It represents repeated addition of the same number. When we multiply a × b, we're adding 'a' to itself 'b' times, or adding 'b' to itself 'a' times.
Key Terms
- Multiplicand: The first number being multiplied
- Multiplier: The second number in multiplication
- Factors: Numbers being multiplied together
- Product: The result of multiplication
Multiplication Properties
Commutative Property
a × b = b × a
Example: 3 × 4 = 4 × 3 = 12
Associative Property
(a × b) × c = a × (b × c)
Example: (2 × 3) × 4 = 2 × (3 × 4) = 24
Distributive Property
a × (b + c) = (a × b) + (a × c)
Example: 2 × (3 + 4) = (2 × 3) + (2 × 4) = 14
Multiplying Decimals
Steps:
- Multiply the numbers ignoring decimal points
- Count total decimal places in both factors
- Place decimal point in result from right
2.3 × 1.5 = 23 × 15 = 345
2 decimal places total → 3.45
Special Multiplication Rules
Zero Property
Any number × 0 = 0
Identity Property
Any number × 1 = that number
Sign Rules
Positive × Positive = Positive
Negative × Negative = Positive
Positive × Negative = Negative