- The problem introduces modular arithmetic, where numbers "wrap around" after reaching a certain value (the modulus).
- For 11 mod 4: Dividing 11 by 4 gives quotient 2 and remainder 3 → 11 mod 4 = 3.
- “Modulus Time” illustrates modular arithmetic using a clock (mod 12): 17 mod 12 = 5, so 17:00 ≡ 5:00.
- For modulus 6, there are 6 possible remainders: 0, 1, 2, 3, 4, 5.
- Each number is mapped to its remainder when divided by 6:
- 0 mod 6 = 0
- 1 mod 6 = 1
- 2 mod 6 = 2
- 3 mod 6 = 3
- 4 mod 6 = 4
- 5 mod 6 = 5
- 6 mod 6 = 0
- 7 mod 6 = 1
- 8 mod 6 = 2
- 9 mod 6 = 3
- 10 mod 6 = 4
- 11 mod 6 = 5
- 12 mod 6 = 0
- 13 mod 6 = 1
- 14 mod 6 = 2
- 15 mod 6 = 3
- 16 mod 6 = 4
- 17 mod 6 = 5
- These groupings form equivalence classes: All numbers with the same remainder belong to the same class.
- Example: 2 and 8 both have remainder 2 when divided by 6 → 2 ≡ 8 (mod 6).
Parent Tip: Review the logic above to help your child master the concept of modular arithmetic worksheet.
