Long Multiplication Calculator
Multiply large numbers step-by-step with detailed explanations and partial products
Calculate Long Multiplication
The number to be multiplied (can include decimals)
The number you're multiplying by
Example: 437 × 85
Problem Setup
Multiplier: 437 (the number being multiplied)
Multiplicand: 85 (the number we're multiplying by)
Method: Multiply 437 by each digit of 85, then add results
Step-by-Step Solution
1. Multiply 437 × 5 = 2,185 (ones place)
2. Multiply 437 × 8 = 3,496, shift one place left → 34,960 (tens place)
3. Add partial products: 2,185 + 34,960 = 37,145
Final Answer: 437 × 85 = 37,145
Long Multiplication Algorithm
Align Numbers
Write numbers one under the other, right-aligned
Multiply by Ones
Multiply by the rightmost digit
Multiply by Tens
Multiply by next digit, shift left
Continue Pattern
Repeat for all digits
Add Results
Sum all partial products
Multiplication Tips
Put the longer number on top (optional but easier)
Remember to carry over when products exceed 9
Shift each partial product one place left
For decimals: count total decimal places
Skip zeros to save time (0 × anything = 0)
Understanding Long Multiplication
What is Long Multiplication?
Long multiplication is a method for multiplying large numbers by breaking the problem into smaller, manageable parts. It uses the distributive property to multiply each digit of one number by each digit of the other number.
Why Learn Long Multiplication?
- •Builds understanding of place value and multiplication
- •Essential for polynomial multiplication in algebra
- •Develops mental math and estimation skills
- •Foundation for advanced mathematical operations
Working with Decimals
Step 1: Count decimal places in both numbers
Step 2: Multiply as if they were whole numbers
Step 3: Add decimal places in the final answer
Example: 4.37 × 8.5 → 437 × 85 = 37145 → 37.145
Key Property: Multiplication is commutative (a × b = b × a)