Soroban for grown-ups — Unit 4: Big friends (complements of 10)
Mixed friends and long carries →
Soroban unit 4: Big friends (complements of 10)
When a rod cannot take a number, add 10 on the next rod and take away the difference: carrying and borrowing with beads.
What the big friends are
When a rod cannot take the number you add, the soroban carries to the next rod. Adding 7 to 8 on the ones rod is impossible, so you add 10 on the tens rod and take away the 3 that was too much: 8 + 7 is 8 − 3 + 10, which is 15. Two digits that make 10 are big friends, or complements of 10: 1 and 9, 2 and 8, 3 and 7, 4 and 6, 5 and 5.
On the soroban the friend is taken away first and the 10 added after, as the demonstrations show. Subtraction works the other way round: to take 5 from 12, take 10 from the tens rod and give back 5.
Carries and borrows across several rods
If the next rod is full, the 10 travels on: 99 + 1 clears both rods and sets 1 on the hundreds rod. Borrowing from an empty rod works the same way, so 1,000 − 1 leaves 999. This is the carrying and borrowing of written arithmetic done with beads, from the left, without holding a digit in your head.
Practice in this unit
Big friends are the most used moves in soroban arithmetic. After the unit, practice them in Practice (Big friends) until each pair comes without thinking.