QuickCalculators multiplies multi-digit numbers with a stacked long-multiplication layout that shows each partial product, carry, and place-value shift. Enter two factors, then read the traditional paper method beside the final product so every column step stays visible.
Long multiplication breaks a large product into smaller products by each digit of the multiplier, then adds those partial products with the correct shifts. The page exists to show that algorithm, not only the final number. Lattice multiplication on the related page is a different grid for the same product.
Multiply large numbers with long multiplication
Long multiplication multiplies one factor by each digit of the other, writing a partial product for every digit, then adds those rows with place-value shifts. QuickCalculators renders that stack with carries labeled so the written method matches the total. The final sum of the partial products is the answer.
The method scales to any digit length the engine accepts. Mental shortcuts help for small facts, but the stacked layout remains the school standard for multi-digit work. A text alternative of each carry and partial product accompanies the visual grid for accessibility.
Set up the long multiplication
Setting up long multiplication means writing the factors one above the other, aligned on the right for whole numbers, with the usually longer factor on top. Place-value columns must line up before any digit multiply begins. QuickCalculators aligns those columns automatically so ones sit under ones and tens under tens.
Decimal factors need the total count of decimal places remembered for the final product, while the digit multiplies still run as if the points were absent until the end. Whole-number examples keep the setup simpler for learning the carries first. Misaligned digits shift every partial product by a power of ten.
Multiply by each digit
Each digit of the multiplier produces one partial product by multiplying through the multiplicand, with carries written into the next place when a product reaches ten or more. QuickCalculators shows those carries above the working digits. Starting from the ones digit of the multiplier keeps place value consistent with the paper algorithm.
When the multiplier's tens digit is used, the partial product shifts one column left before writing, which is the same as multiplying by ten. Hundreds digits shift two columns, and so on. Forgetting the shift is the usual source of an answer that is off by a factor of ten.
Add the partial products
After every digit of the multiplier has a partial-product row, add those rows column by column with ordinary carrying. The sum is the product of the original factors. QuickCalculators adds the shifted rows and labels any carries in the addition stage so the last step is as clear as the multiplies.
Partial products that were shifted correctly will align so ones, tens, and hundreds add in the right places. A missing zero placeholder for a shift shows up as a column that looks short. Checking one small multiply by reversing with division or a calculator total confirms the stacked work.
Multiply 23 by 47 step by step
The worked case multiplies 23 by 47 on QuickCalculators. First multiply 23 by 7 to get 161. Next multiply 23 by 4, shift one place for the tens digit, to get 92 representing 920. Add 161 and 920 to obtain 1,081. That product is the reference fixture for this page.
- Multiply 23 by 7: write partial product 161.
- Multiply 23 by 4 and shift one column: write 920 as the second partial product.
- Add 161 + 920 to get 1,081.
The same factors in either order yield the same product when both layouts are completed carefully.
Avoid this common mistake
The misconception named "skip the zero when multiplying by the tens digit" drops the place-value shift on the second partial product. Multiplying 23 by 4 without shifting gives 92 added under 161 as if it were ones, producing 253 instead of 1,081. Always shift one column left for the tens digit, two for hundreds, and so on.
Frequently asked questions
What is long multiplication?
Long multiplication is the written method of multiplying multi-digit numbers by forming a partial product for each digit of the multiplier, shifting for place value, and adding the rows. QuickCalculators draws that stack for the entered factors.
How do you multiply 23 by 47 with long multiplication?
To multiply 23 by 47, compute 23 times 7 equals 161, compute 23 times 40 equals 920 as a shifted partial product, then add to get 1,081. The work panel replays those rows.
Why do partial products shift?
Partial products shift because each digit of the multiplier sits in a different place value. The tens digit means multiply by that digit times ten, which is a one-column left shift. Skipping the shift undercounts by a factor of ten.
What is a carry in long multiplication?
A carry appears when a single-digit multiply produces a value of ten or more; the tens part moves into the next column. The same idea appears again when partial products are added. The layout labels those carries.
How is long multiplication different from lattice multiplication?
Long multiplication uses stacked partial products and addition. Lattice multiplication uses a grid of digit products with diagonals. Both can yield the same product; this page teaches the stacked method.
Can long multiplication handle decimals?
Long multiplication can handle decimals by multiplying as whole numbers, then placing the decimal point so the product has as many decimal digits as the factors have in total. Align whole-number examples first when learning carries.
Summary
QuickCalculators multiplies with a stacked long-multiplication layout that shows partial products, carries, and place-value shifts. The fixture 23 times 47 equals 1,081 from partial products 161 and 920. Skipping the tens shift is the common error that wrecks the total. Use lattice multiplication when a grid method is preferred for the same product.