Final answer:
A negative quotient results from dividing a positive integer by a negative integer, or vice versa. Following the rule, when numbers with opposite signs are divided, the result is negative. Examples include 4 ÷ -2 = -2 and -2 ÷ 4 = -0.5.
Step-by-step explanation:
Two integers with a negative quotient occur when one integer is positive and the other is negative, since dividing numbers with opposite signs results in a negative number. For example, if you have the integers 4 and -2, dividing 4 by -2 (4 ÷ -2) or -2 by 4 (-2 ÷ 4) both result in a negative quotient. This concept applies to all division and multiplication operations as follows:
- When two positive numbers multiply or divide, the answer has a positive (+ve) sign, e.g., 2 x 3 = 6 or 6 ÷ 3 = 2.
- When two negative numbers multiply or divide, the answer also has a positive (+ve) sign, e.g., (-4) x (-3) = 12 or (-12) ÷ (-3) = 4.
- When numbers with opposite signs multiply or divide, the answer has a negative (-ve) sign, e.g., (-3) x 2 = -6 or 4 ÷ (-2) = -2.
Remember that a negative exponent means that you are dividing rather than multiplying, hence an expression with a negative exponent denotes the reciprocal of the number to the positive power of the exponent. For instance, x-n is equivalent to 1/xn.