Simple Subtraction

Subtraction on the soroban is the mirror image of addition. Where adding pushes beads toward the bar, subtracting pulls beads away from the bar. Taking away simply means turning beads off. In this lesson we practise the simple case where the rod always has enough beads to remove.

The idea of subtracting

To subtract a number from a rod, move that many beads away from the bar. If a rod shows 5 and you subtract 3, you push down three earth beads and the rod now shows 2. Subtracting always makes a rod smaller, unless you subtract zero.

Subtracting earth beads

Start with sums that only need earth beads. If a rod shows 4 and you subtract 2, push down two earth beads to reach 2. If a rod shows 3 and you subtract 1, push down one earth bead to reach 2. This direct method works whenever the rod already has enough earth beads at the bar to remove.

Subtracting the heaven bead

To subtract 5, push the heaven bead back up away from the bar. If a rod shows 7 and you subtract 5, move the heaven bead up and the rod now shows 2. You can subtract larger amounts using both the heaven bead and earth beads. To subtract 6 from a rod showing 8, push the heaven bead up (removing 5) and push down one earth bead (removing 1), leaving 2.

Subtracting on more than one rod

For bigger numbers, subtract each place value on its own rod. To work out 47 minus 23, first set 47. Then subtract 2 from the tens rod (leaving 2 tens) and subtract 3 from the ones rod (leaving 4 ones). Reading the soroban now shows 24. Work one rod at a time and read the answer at the end.

• 9 minus 4 equals 5: push down four earth beads.
• 6 minus 5 equals 1: push the heaven bead up.
• 8 minus 6 equals 2: heaven bead up plus one earth bead down.

Practise until pulling beads away feels as natural as pushing them in. Addition and subtraction together let you solve almost any everyday calculation on the soroban.