Multiply When the Multiplier Has a Zero Digit

Multiply 143 by 30. The ones digit is 0, so the entire ones-row partial product is 0. Only the tens-digit partial product matters; it shifts one column left. This lesson shows why multiplying by a multiple of 10 just appends a zero and then multiplies the rest.

Example

multiply-143x30.math

   143
x   30
------

step: 0 x 3 = 0 -> write 0
step: 0 x 4 = 0 -> write 0
step: 0 x 1 = 0 -> write 0
step: partial 1: 0
step: tens digit 3: shift 1 left
step: 3 x 3 = 9 -> write 9
step: 3 x 4 = 12 -> write 2, carry 1
step: 3 x 1 = 3, + carry 1 = 4 -> write 4
step: partial 2: 4290
step: add partials: 0 + 4290
step: product = 4290

zero-partial-product When a multiplier digit is 0, its partial product row is all zeros. You can skip the row and just shift the next partial left.

multiply-by-10 Shifting one column left is the same as multiplying by 10.