Beadbay: the soroban
Adding on a soroban
To add a digit on a soroban, move the beads if they are free. If the lower beads run out, bring the five down and take away the digit's small friend. If the rod cannot hold the answer, take away the digit's big friend and carry one to the rod on the left.
Try these
Each button sets up a sum and shows the next move as ghost beads.
When the beads are there
2 + 5: the five bead is free, so bring it down. 12 + 25: add 2 on the tens rod, then 5 on the ones rod. Always the biggest digit first.
Small friends: when the lower beads run out
One and four are small friends. So are two and three. When there are not enough earth beads, bring the five down and take the small friend away.
3 + 4: there is only one lower bead left, not four. Bring the five down and take one away. Five on, one off is the same as four on.
Big friends: when the rod is full
One and nine, two and eight, three and seven, four and six, five and five. When a rod is too full, take the big friend away and carry one to the left.
8 + 5: the rod cannot hold thirteen. Take five away (the big friend of 5) and carry one to the tens rod. Ten on, five off is the same as five on.
Both at once
Sometimes the big friend needs a small friend to help. Six add seven: take three and carry one. But taking three from six means add two, then take five.
A carry that runs on
49 + 6: take 4 from the ones rod and carry one. But the tens rod holds 4 and cannot simply take one more: it needs a small friend, five down and four off. A carry can need a friend too, and so can a borrow. Follow it along the rods until it settles.
Questions
What are small friends?
Pairs that make five: 1 and 4, 2 and 3. They are used when a rod has room for the answer but not enough lower beads.
What are big friends?
Pairs that make ten: 1 and 9, 2 and 8, 3 and 7, 4 and 6, 5 and 5. They are used when the answer on a rod would be ten or more.
Do I add from the left or the right?
From the left: the biggest digit first. It is the opposite of written sums and it is why soroban sums can be read aloud as you go.