Question

Difficulty: EasyPositive and Negative Number Properties

If $x$ is a negative real number and $y$ is a positive real number, what is the value of $\frac{x}{|x|} + \frac{|y|}{y}$ ?

Answer: 0

The value of the expression is 0.

For any negative number

x

, the ratio

\frac{x}{|x|}

evaluates to

-1

because

|x| = -x

. For any positive number

y

, the ratio

\frac{|y|}{y}

evaluates to

1

because

|y| = y

. Summing

-1

and

1

results in

0

Evaluate the first term for a negative variable

-1

By definition of absolute value, if

x < 0

, then

|x| = -x

, making

\frac{x}{|x|} = \frac{x}{-x} = -1

Evaluate the second term for a positive variable

y > 0

, then

|y| = y

, making

\frac{|y|}{y} = \frac{y}{y} = 1

Sum the simplified values

Combining

-1

and

1

yields

-1 + 1 = 0

Properties of Absolute Value and Signs of Numbers

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