Final answer:
The signs of the quotients are determined by the signs of the numbers involved. A negative divided by a positive results in a negative, dividing two negatives results in a positive, zero divided by any number is zero, and positive divided by positive is positive.
Step-by-step explanation:
When determining the signs of the quotients in mathematics, we apply the multiplication rules for signs since division is the inverse of multiplication. Here is the analysis of the given problems:
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- a) The quotient of -125 and 5 is negative. Since we are dividing a negative number by a positive number, the result will be negative based on the rule that dividing two numbers with opposite signs results in a negative.
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- b) The quotient of -264 and -12 is not zero. Both numbers are negative, and dividing two negative numbers results in a positive quotient, according to the rule that like signs result in a positive result.
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- c) The quotient of 0 and -350 is zero. Any number divided by zero results in zero, regardless of the signs involved.
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- d) The quotient of 276 and 8 is positive. Both numbers are positive, and therefore their quotient will also be positive.
Numerical operations follow specific sign rules that help predict the outcome's sign, whether it's for addition, subtraction, multiplication, or division.