What is the value of (-43 \times 15) \pmod{8} expressed in standard non-negative remainder… — JAMB UTME

What is the value of $(-43 \times 15) \pmod{8}$ expressed in standard non-negative remainder form?

Reducing

-43

modulo

8

gives

5

, and

15

modulo

8

gives

7

. Multiplying these results yields

35 \equiv 3 \pmod{8}

, which is the canonical non-negative remainder.

Reduce individual factors modulo 8

-43 \equiv 5 \pmod{8}

(since

-43 = -6 \times 8 + 5

) and

15 \equiv 7 \pmod{8}

(since

15 = 1 \times 8 + 7

)

Simplifying terms before multiplication makes arithmetic easier.

Multiply the reduced remainders

5 \times 7 = 35

Modular arithmetic preserves multiplication.

Reduce the product modulo 8 to obtain the canonical non-negative remainder

35 = 4 \times 8 + 3 \implies 35 \equiv 3 \pmod{8}

The final answer in modular arithmetic must fall within the range

[0, n-1]

Modular Arithmetic and Canonical Non-Negative Remainders

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