If x 0, determine the sign of the real number. (a) (x)/(y) (b) x y^2 (c) (x-y)/(x y) (d)

step 1 Now here in this problem, we are given that if X is less than 0 and Y is greater than 0 Then we

If x<0 and y>0, determine the sign of the real number. (a)...

Key Concepts

Operations with Signed Numbers

This concept refers to the rules that govern the addition, subtraction, multiplication, and division of numbers based on their signs. In particular, understanding that the product or quotient of a positive and a negative number will be negative, and the product or quotient of two negatives will be positive, is essential in determining the overall sign of algebraic expressions.

Square of a Real Number

The principle that the square of any real number is always non-negative is crucial. Even when a number is negative, squaring it results in a positive value. This property is frequently used in algebra to simplify the determination of sign in expressions, especially when variables are raised to an even power.

Fraction Sign Analysis

This concept involves determining the sign of a rational expression by separately evaluating the signs of the numerator and the denominator. If both parts have the same sign, the fraction is positive; if they differ, the fraction is negative. This systematic approach is widely applicable in algebra when working with ratios.

Inequality Reasoning

Using inequalities to infer the relative ordering of numbers or expressions is a key algebraic technique. When variables are known to be greater than or less than zero, these inequalities provide critical information about their behavior in various operations, aiding in the sign determination of more complex expressions.

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