If you already know what the beads mean, the next question is the interesting one: how do you actually calculate with them? Adding small numbers is easy. Adding slightly bigger ones runs straight into a wall, and the way around that wall is the single most useful idea in the whole method.
The Easy Part First
Say you want to add 1 and 2. Set 1 on a rod (one bead up), then push 2 more beads up. Done, the rod now reads 3. This is what Level 1 teaches first, called direct addition, and it works perfectly as long as there are enough spare beads on the rod to push, which on a single rod means the two numbers you're adding must add up to 4 or less.
The trouble starts the moment they add up to more than that.
What Happens When You Run Out?
Each rod only has five beads worth counting: one worth 5 above the bar, four worth 1 below it. So try adding 4 to a rod that already shows 3. You need four more beads, but only one is free. You physically cannot push four beads that are not there. A child who only knows direct addition gets stuck right here, and it feels like the method broke.
It didn't break. It just needs a different move, and that move is built from two small sets of number pairs.
Friends of 5
Any two numbers that add up to 5 are called "friends of 5." There are only two pairs to know:
Once a child knows these, a stuck rod stops being a wall. Need to add 4 but only 2 beads are free? Think of 4 as 5 minus 1. Push the top bead (that's the "add 5" part), then pull one bottom bead back down (that's the "minus 1" part). Same answer, different route.
Friends of 10
The same idea scales up once a rod is completely full. Any two numbers that add up to 10 are "friends of 10," and there are five pairs:
This is the pair that lets you carry a value into the next rod over, which is the same "carrying the 1" your child already does with pen and paper, just done with a bead instead of a tiny number written above the column.
Friends Combo: A Sequence Drill for This Exact Move
Beads pop up in random order and your child has to catch the friend pair before the timer runs out, built specifically to make this reflex automatic.
Play Friends ComboWhy Should Kids Learn Abacus?
This kind of small, repeated substitution is exactly what builds the focus and working memory parents notice later.
Read the benefits articleLet's Actually Do One
Here is 8 + 6, worked through the friends of 10 move, step by step.
Start
Set 8 on the first rod. That is the top bead down (worth 5) plus three bottom beads up (worth 3).
Try to add 6 directly
Now add 6. But the rod only has one bottom bead left free, not six. There is nowhere for six more beads to go. This is exactly the wall every child hits in Level 1.
Reach for a friend of 10
Instead of forcing it, think of 6 as its friend of 10: 6 = 10 − 4. So adding 6 is the same as adding 10 and taking away 4.
Add 10, then subtract 4
Add 1 bead on the tens rod (that is the "add 10" part), then clear 4 from the ones rod. The ones rod now shows 4, the tens rod shows 1. Read it together: 14.
Check it
8 + 6 = 14. No finger counting, no memorized fact, just one small substitution. This exact move is what Level 4 drills until it becomes automatic.
That substitution, add 10 and take away the difference, is the entire trick. Every "hard" addition problem on an abacus is really just an easy one wearing a disguise.
Level 3 & Level 4: Friends of 5 and 10
The same idea from this article, broken into short guided lessons with practice built in after each one.
Start Level 3Now Try It Yourself
Reading about a friend pair and actually reaching for one under time pressure are different skills. The second one only comes from repetition.
Drill Friends of 5 & 10 in Practice Mode
Short, timed problem sets that specifically target the complement pairs from this article, no login needed to try it.
Open practice modeCommon Questions
Do kids need to memorize the friends of 5 and 10 pairs like times tables?
Not by rote drilling. They come up so often in normal practice that most children absorb them naturally within a few weeks, the same way you didn't memorize which shoe goes on which foot, you just did it enough times.
Why is it called "friends"?
It is a translation from the original Japanese and Chinese teaching terms for these number pairs. The name stuck worldwide because it is easier for a six year old to remember than "complements."
Does this work the same way for subtraction?
Yes, in reverse. If a rod does not have enough beads to take away directly, you borrow from the next rod using the same friend pair, just flipped. Level 2 and Level 3 build subtraction the same way addition is built here.
Is this the same trick used in Vedic Math?
They overlap in spirit, both are shortcuts for awkward carries, but the abacus version is tied to a physical bead move, while Vedic Math methods are usually pure mental arithmetic. We compare the two properly in our Abacus vs. Vedic Math article.