The table above displays the mnemonic rules for multiplying by eight. In abacus calculation, as you multiply each digit, you "change" the physical position of the counters on the rod to reflect the new total.

Eight times five gives forty; change the 5 to a 4. The 5 on the current rod is replaced by the 4 from "40," and the 0 is ignored as it adds nothing to the next rod.
Eight times four is thirty-two; change the 4 to a 3.
Eight times three is twenty-four; change the 3 to a 2.
Eight times one is eight; add 8 to the position below. Since 8 is a single digit, it is added to the rod immediately to the right of the current one.

Add 8 to the lower position. Remove from the current position.

Restoration Restoration (huanyuan): The process of using division to check a multiplication result, essentially "returning" to the original number. by dividing by eight. The method is detailed below.

Division by Eight Mnemonic:
Eight into one: one, then add 2 below.
Eight into two: two, then add 4 below.
Four below: for 5, remove 1. These are "Guichu" or "Return-Division" rhymes. They tell the abacus operator how to manipulate the beads when the divisor is 8. For example, "Eight into one, add 2" means when 1 is divided by 8, you set the quotient and add the remainder to the next rod.
When you reach eight, advance 1 to the tens.
Eight into three: three, then add 6 below.
When you reach eight, advance 1 to the tens.
Eight into four: change to 5.
Eight into five: sixty-two.
Eight into six: seventy-four.
Eight into seven: eighty-six.
When you reach eight, advance 1 to the tens.

Calculation for Wet Grain

Suppose there is 1,234 shi, 5 dou, 6 sheng, 7 ge, and 9 shao shi, dou, sheng, ge, shao: standard units of dry volume. 1 shi = 10 dou; 1 dou = 10 sheng; 1 sheng = 10 ge; 1 ge = 10 shao. of wet grain. For every shi...