Long Multiplication Calculator

How Long Multiplication Works

Long multiplication is the standard method for multiplying numbers by hand. It breaks down the multiplication into smaller, more manageable steps.

Steps for Long Multiplication:

1. Align Numbers: Place the numbers on top of each other, aligning them by place value (ones, tens, etc.). It’s easiest to put the number with more digits on top.
2. Multiply by Ones Digit: Multiply the ones digit of the bottom number (multiplier) by each digit of the top number (multiplicand), from right to left. Write the result below the line. If a product is more than 9, carry over the tens digit.
3. Multiply by Tens Digit: Next, multiply the tens digit of the multiplier by each digit of the multiplicand. Write this result in a new row, shifted one place to the left.
4. Continue for Other Digits: Repeat for any remaining digits in the multiplier, shifting each new row of partial products one more place to the left.
5. Add Partial Products: Add all the partial product rows together using standard addition to get the final product.

Handling Decimals:

When multiplying decimals:

• First, ignore the decimal points and multiply the numbers as if they were whole numbers.
• Count the total number of decimal places in both original numbers.
• Place the decimal point in the final product so that it has the same number of decimal places as you counted in the previous step.

Handling Negative Numbers:

The rules for signs are simple:

• Positive × Positive = Positive
• Negative × Negative = Positive
• Positive × Negative = Negative