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环 · Modulo
Scroll of the Mantra
Modulo is clock arithmetic. Numbers go round and round, and you only care where you land.
Clock Remainder
a (mod n) is the remainder when you divide a by n. Remove whole rounds of n.
47 (mod 6)
- → 6 × 7 = 42 is the last full round
- → 47 − 42 = 5
Answer: 5
Practice: Try 29 (mod 4) and 100 (mod 7).
Last Digit
Mod 10 is just the last digit. Mod 100 is the last two digits.
55 (mod 10)
- → Look at the ones digit
Answer: 5
Practice: Try 1234 (mod 10) and 1234 (mod 100).
Gather then Reduce
Add or multiply first, then take the remainder — or reduce each number first. Both give the same answer.
17 + 5 (mod 9)
- → 17 + 5 = 22
- → 22 − 18 = 4
Answer: 4
Mod 9 shortcut: add the digits. 22 → 2 + 2 = 4.
Practice: Try 38 + 25 (mod 9).
Into the dojo
Practise with the Mantra 环 technique from blue belt.
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