Final answer:
In Mathematics, representing the statement 'the quotient of a number and four is less than negative one' as an inequality gives x/4 < -1. Multiplying both sides by 4 reveals that x < -4. This follows basic arithmetic rules, including those for negative numbers and exponents.
Step-by-step explanation:
When the question states that the quotient of a number and four is less than negative one, we can represent this as an inequality in Mathematics.
If 'x' is the unknown number, then the inequality can be written as x/4 < -1.
To solve for 'x', you would multiply both sides of the inequality by 4, adhering to the rules of negative numbers and division. Following this step, we find that x < -4.
In this case, the rules we use are similar to those for division and multiplication of positive and negative numbers, such as when negative exponents flip the base from the numerator to the denominator, indicating division.
For instance, negative exponents like x-n is equal to 1/(xn), demonstrating the 'inversion' or 'flipping' when dealing with powers.
Similarly, when dividing by a negative number, according to multiplication or division rules for the sign, the result will take on the sign opposite to the positive counterpart, just as with multiplications like (-3) x 2 = -6 or 4 x (-4) = -16.