Multiply a 3-Digit by 2-Digit Number - Arithmetic Step by Step

Multiply 234 by 56. The ones digit 6 multiplies all three digits of 234 with carries; the tens digit 5 does the same and its partial product shifts one column left. Adding the two partials gives 13104.

Example

multiply-234x56.math

   234
x   56
------

step: 6 x 4 = 24 -> write 4, carry 2
step: 6 x 3 = 18, + carry 2 = 20 -> write 0, carry 2
step: 6 x 2 = 12, + carry 2 = 14 -> write 4, carry 1
step: carry 1 -> write 1
step: partial 1: 1404
step: tens digit 5: shift 1 left
step: 5 x 4 = 20 -> write 0, carry 2
step: 5 x 3 = 15, + carry 2 = 17 -> write 7, carry 1
step: 5 x 2 = 10, + carry 1 = 11 -> write 1, carry 1
step: carry 1 -> write 1
step: partial 2: 11700
step: add partials: 1404 + 11700
step: product = 13104

multi-digit-carry Carries can build up across three or more digit positions; each is added to the next column before multiplying there.

place-value-shift The partial product for the tens digit starts in the tens column; the leading zero in the ones column records the shift.