Cross Multiplication Method Calculator (Indian Vertically and Crosswise)
Multiply two numbers digit by digit using the Indian vertically-and-crosswise method. Each place value is built from crosswise digit products with carries, shown step by step in a table.
Input
An Indian mental-math method that multiplies two numbers digit by digit, pairing digits crosswise and carrying as you go. See how each place value is built.
Enter whole numbers from 0 up to 999999.
Result
Product of 23 × 41
943
Step by step
Split into digits
Lay out 23 (2 digits) and 41 (2 digits) digit by digit, starting from the ones place.
Build each place crosswise
For each place, pick the digit pairs whose positions add up to that place, multiply them, and sum the partial products.
Handle the carry
Add the carry from the lower place, then take the remainder divided by 10 as the digit and the quotient as the carry into the next place.
Read off the product
Reading the resolved digits from the highest place down gives the product 943.
Crosswise calculation by place
Working from the lowest place upward, resolving the crosswise sum and carry.
| Place | Crosswise pairs | Raw sum | Carry in | Total | Digit | Carry out |
|---|---|---|---|---|---|---|
| 1 place | 3×1 | 3 | 0 | 3 | 3 | 0 |
| 10 place | 3×4 + 2×1 12 + 2 | 14 | 0 | 14 | 4 | 1 |
| 100 place | 2×4 | 8 | 1 | 9 | 9 | 0 |
Resolved digits
Check: 23 × 41 = 943
The sum at place k is the total of the products of all digit pairs whose positions add up to k. Add the carry, then split by 10 into a digit and a carry, working upward.
How it works
- The vertically-and-crosswise method splits each number into digits and builds every place value (ones, tens, and so on) by crosswise pairing the digits whose positions add up to that place, then summing the partial products.
- Add the raw sum at a place to the carry from the lower place, take the remainder when divided by 10 as the digit that stays, and the quotient as the carry into the next place.
- Repeat from the lowest place upward, then read the resolved digits from the highest place down to form the product.
- Inputs accept whole numbers from 0 up to 999999.
- A normal product is also shown so you can check the result.
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Cross Multiplication Method Calculator (Indian Vertically and Crosswise)