The result of multiplying or dividing integers is determined by

• A. The magnitude of the last numbers.
• B. The parity of the numbers.
• C. The signs of the factors.
• D. The sum of the numbers.

Answer: (C)

The key idea is how signs affect multiplication and division of integers. The sign of the result depends on whether the numbers have the same sign or opposite signs. If both numbers are positive or both are negative, the result is positive. If one is negative and the other is positive, the result is negative. The size of the result comes from multiplying or dividing their absolute values (the numbers without signs).

For example, 7 × 5 equals 35 (both positive, result positive); 7 × (-5) equals -35 (opposite signs, result negative); (-7) × (-5) equals 35 (same signs, result positive). The same rule applies to division: 20 ÷ (-4) equals -5; (-18) ÷ 3 equals -6; (-18) ÷ (-3) equals 6.

So the factor that determines the result’s sign is the signs of the numbers. The ideas of parity (even/odd) or the sum of the numbers aren’t what sets the sign in multiplication or division, and the magnitude only affects how big the result is, not whether it’s positive or negative.