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

Multiply 23 by 47 using two partial products: one for the ones digit of 47 and one for the tens digit. Each partial is computed digit by digit; then the two partials are added to give the final product.

Example

multiply-23x47.math

    23
x   47
------

step: 7 x 3 = 21 -> write 1, carry 2
step: 7 x 2 = 14, + carry 2 = 16 -> write 6, carry 1
step: carry 1 -> write 1
step: partial 1: 161
step: tens digit 4: shift 1 left
step: 4 x 3 = 12 -> write 2, carry 1
step: 4 x 2 = 8, + carry 1 = 9 -> write 9
step: partial 2: 920
step: add partials: 161 + 920
step: product = 1081

partial-product Each digit of the multiplier generates its own partial product, which is shifted left by the digit's place value before adding.

two-pass-multiplication The standard long-multiplication algorithm works one multiplier digit at a time, building one partial product per digit.