Long Multiplication Calculator

SCHOOL / HOMEWORK

Multiply two numbers and see the partial products that long multiplication adds up. Enter both numbers.

Product
—
The two multiplied.

Usage Tip

The number of digits in a product is roughly the sum of the digit counts of the two factors.

THE MATH
Multiply by each digit of the second number, shifted by place
Add the partial products
Long multiplication multiplies one number by each digit of the other, shifting by place value, then sums the partial products.
It is how multi-digit multiplication is done by hand.
Inputs are treated as whole numbers.
Each non-zero digit of the second number produces one partial product.
The partial products are listed in the explanation.
Practical Notes

Long multiplication breaks a multiplication into smaller steps. Each digit of the second number is multiplied by the whole first number, giving a partial product shifted one place to the left for every step, and the partial products are then added together. Seeing those partial products makes it easier to follow the method or check homework.

A quick way to check an answer is to estimate by rounding both numbers, so 48 times 52 is about 50 times 50, or 2500, which is close to the exact result of 2496. Another check is that the last digit of the product depends only on the last digits of the two numbers being multiplied.

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