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Friend of 10

📘What it is

The most important soroban rule! Know the friends of 10, and adding or subtracting any number becomes easy!

🛠️How it works

10=1+9=2+8=3+7=4+6=5+5. Memorize them all — you'll be lightning fast!

🔢A worked example

The pairs that make 10 are 1+9, 2+8, 3+7, 4+6 and 5+5. Once a child memorises these friends, they do 8+2 or 6+4 without thinking and speed up addition dramatically.

🎓A closer look

The pairs that add up to 10 (1-9, 2-8, 3-7, 4-6, 5-5) become a working formula on the soroban: when a column runs out of beads, you add 10 instead of the intended number and subtract its friend. Take 9+4: four cannot be added directly, so you add 10 and remove 6, the friend of 4: 9+10−6=13. Subtraction mirrors the rule: 12−8 = 12−10+2 = 4, because the friend of 8 is 2.

These pairs are the vocabulary behind every later soroban formula — big friends, the bridge of 10 and multi-digit work all rest on them. Once the pairs are automatic, a child drops finger counting entirely and solves any sum that crosses a ten at a glance, which shows up immediately in school mental math.

  • Level: the first formula to learn after basic abacus skills.
  • Common mistake: mixing up the friends of 10 with the friends of 5 (the Big Brother technique).
  • Practice tip: play "which number completes 10?" until every answer takes under 2 seconds.

💡Why it helps

Professional calculation starts with this rule. Master it, and multi-digit numbers are no problem!

❓Frequently asked questions

Friends of 10 means knowing by heart the number pairs that add up to 10 (for example 7 and 3, 6 and 4). These pairs are the key rule for fast addition and subtraction on the soroban.
Because when the soroban runs out of beads, the child calculates not directly but through a friend of 10, which noticeably speeds up the count and reduces mistakes.
A child usually starts learning the friend pairs after they can move the beads freely on the abacus, that is once they have grasped the basics.
Yes, on MentalMath you can learn and practise the friends of 10 pairs for free and without registration.

Other methods

🧮 Abacus (Soroban) — the foundation of mental arithmetic 🤝 Big Friends 👬 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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