WAEC 2022 · Paper 1 · Q5

Modular arithmetic

Evaluate $23 \times 54 \pmod 7$ .

Worked solution (try it first)

Reduce each number: $23 = 3 \times 7 + 2$ , so $23 \equiv 2$ .
$54 = 7 \times 7 + 5$ , so $54 \equiv 5 \pmod 7$ .
Multiply the remainders: $2 \times 5 = 10$ .
Reduce again: $10 = 7 + 3$ , so $23 \times 54 \equiv 3 \pmod 7$ , option B.

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