Multiply Each Digit
Hover over a variable in the formula above, or see glossary below:
Start from the rightmost digit of the multiplier. Multiply it by each digit of the multiplicand, right to left, carrying any tens digit.
Shift & Add Partial Products
For each digit in the multiplier, write the partial product on a new row, shifted one place to the left. Then add all partial products together.
Long Multiplication
Long multiplication is a method of multiplying two numbers by breaking the problem into smaller, simpler steps using the distributive property of multiplication.
The Distributive Property
Every multi-digit number can be broken into its place values:
Standard Algorithm
- Write the two numbers vertically, larger on top.
- Multiply the top number by the ones digit of the bottom — this is the first partial product.
- Multiply the top number by the tens digit of the bottom, placing a zero placeholder in the ones column — this is the second partial product.
- Add the partial products together.
Carrying
When a multiplication produces a two-digit result (e.g. ), write down the ones digit and carry the tens digit to the next column to be added.
References
AI Assistance Disclaimer: This module uses AI-assisted educational models and interactive visual representations to help explain scientific and mathematical concepts. For formal research or academic evaluation, please verify formulas and data against standard primary reference materials.