Long Multiplication Calculator – Step-by-Step Multiplication
Multiply numbers with step-by-step partial products.
Table of Contents
How to Use
- Enter the first number (multiplicand)
- Enter the second number (multiplier)
- Click calculate to see the step-by-step solution
- Review partial products and the final result
What is Long Multiplication?
Long multiplication (also called column multiplication) is a method for multiplying multi-digit numbers by breaking the problem into smaller, simpler multiplications. Each digit of the multiplier is multiplied by the entire multiplicand, creating partial products that are then added together.
This method is taught in elementary schools worldwide and forms the foundation for understanding how multiplication works with larger numbers.
How Long Multiplication Works
- Write the numbers vertically, aligning the rightmost digits
- Multiply the multiplicand by each digit of the multiplier, starting from the right
- Shift each partial product left by one position for each digit position
- Add all partial products together to get the final result
Example: 234 × 56
- 234 × 6 = 1,404 (ones place)
- 234 × 5 = 1,170, shifted one place = 11,700 (tens place)
- Sum: 1,404 + 11,700 = 13,104
Tips for Long Multiplication
- Keep columns aligned to avoid errors
- Remember to shift partial products for each digit position
- Double-check by estimating: 234 × 56 ≈ 200 × 60 = 12,000
- Practice with smaller numbers first before tackling larger ones
Frequently Asked Questions
- Why learn long multiplication when calculators exist?
- Long multiplication builds number sense and understanding of place value. It helps you estimate answers, catch calculator errors, and provides a foundation for algebra and more advanced math concepts.
- Does this work with negative numbers?
- Yes! The calculator handles negative numbers. Multiply the absolute values using long multiplication, then apply the sign rule: negative × positive = negative, negative × negative = positive.
- What about decimal numbers?
- For decimals, multiply as if they were whole numbers, then count the total decimal places in both factors and place the decimal point that many places from the right in the answer.