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Stage 5 of 20

Complements of Ten

Knowing complements of 10 (1+9, 2+8, 3+7, 4+6, 5+5) is the single most useful skill in mental arithmetic. It speeds up addition, subtraction, and estimation.

What You'll Learn

  • Recall all pairs that sum to 10 instantly
  • Apply complements to simplify addition problems
  • Use complements to check subtraction mentally

Explanation

The five complement pairs are: 1&9, 2&8, 3&7, 4&6, and 5&5. Drill these until they are as automatic as your own name.

To add 8 + 6, notice that 8 needs 2 to reach 10. Take 2 from 6, leaving 4. Answer: 14. This is the "bridge through ten" technique.

Complements also power subtraction: 10 − 7 = 3 because 7 + 3 = 10. Every complement fact works both directions.

Extend the idea to 100: complements of 100 (e.g., 63 needs 37) appear in change-making and estimation.

Pro Tips

  • • Hold up fingers to visualize pairs — the physical link strengthens memory.
  • • Play "what makes ten?" as a quick game with a partner.
  • • Before any addition problem, ask: "Can I use a complement here?"

Practice Exercises

Work through each problem mentally. Click "Show Answer" when you're ready to check.

  1. 1. 7 + ? = 10
  2. 2. 4 + ? = 10
  3. 3. 8 + ? = 10
  4. 4. 10 − 6 = ?
  5. 5. 10 − 3 = ?
  6. 6. 8 + 5 = ?
  7. 7. 9 + 4 = ?
  8. 8. 7 + 6 = ?
  9. 9. 10 − 9 = ?
  10. 10. 5 + ? = 10