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Big Friends

📘What it is

Adding numbers that go past 10! On the soroban, this means "carrying" — sliding a bead to the left!

🛠️How it works

6+7=13, 8+5=13 — both cross 10. Learn to fill up to 10 first!

🔢A worked example

Add 8 + 7 on the soroban: treat 7 as 5 + 2. First add 5 (the upper bead), then 2 — and since the units rod is full, you move into the tens → 15.

🎓A closer look

Big Friends is the stage where the pairs of 10 are applied to multi-digit numbers: when the ones column overflows, the child uses the "+10 minus the friend" formula and pushes one bead in the next column — a physical carry. For 47+8, eight does not fit into the ones, so you add 1 to the tens and subtract 2, the friend of 8: 47+10−2=55. The same logic gives 68+7 = 68+10−3 = 75.

This technique is the main workhorse for adding two- and three-digit numbers and long chains such as 34+9+8+7. It also makes the school idea of "carrying the one" tangible: the bead moved into the tens column is exactly that carried one, so column-addition errors drop as well.

  • Level: start once the friends-of-10 pairs are fully automatic.
  • Common mistake: subtracting the friend but forgetting to add the ten — the result comes out 10 too small.
  • Practice tip: do five minutes of chained sums with several ten-crossings every day.

💡Why it helps

The Big Friends technique is the key to fast calculation with multi-digit numbers!

❓Frequently asked questions

Big Friends are pairs built relative to 5 (for example, the numbers needed to complete up to 5). They are used for additions that cross into the upper bead on the soroban.
Friends of 10 work around 10, while Big Friends work around 5: when a child uses the upper five-bead, they rely on these pairs to pick the right complement.
This technique is a bit harder than the friends of 10, so it is best learned after the child has mastered the abacus basics and working with the beads around 5.
Yes, on MentalMath you can learn the Big Friends technique and do the exercises for free and without registration.

Other methods

🧮 Abacus (Soroban) — the foundation of mental arithmetic 🔟 Friend of 10 👬 Big Brother 🌉 Bridge to 10 ✨ ×11 Magic 9️⃣ ×9 Technique 🕛 ×12 Technique 🕉️ Vedic Math (100) 🔱 Vedic Math (1000) ✖️ Urdhva-Tiryagbhyam — vertical and crosswise multiplication 🔲 Squaring a number — the fast way ➗ Division
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