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Chapter 0: Problem 54

In Problems 49-58, find the value of each expression if \(x=3\) and \(y=-2\). \(\frac{|y|}{y}\)

Short Answer

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Step by step solution

01

Substitute the Given Values

Replace the variables with the given numbers. You are given that \(x = 3\) and \(y = -2\). So, substitute \(y\) with \(-2\) in the expression.
02

Evaluate the Absolute Value

Calculate the absolute value of \(y\). The absolute value of \(y\) is \(|y|\), which is \(|-2|\). This equals to 2 because the absolute value of a number is always positive.
03

Divide the Absolute Value by \(y\)

Now, divide \(|y|\) by \(y\). So, \(\frac{|y|}{y} = \frac{2}{-2}\).
04

Simplify the Fraction

Finally, simplify the fraction \(\frac{2}{-2}\). Dividing 2 by -2 gives -1.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

absolute value
Absolute value is a concept that helps us understand the distance of a number from zero on the number line, regardless of its direction. It's represented by vertical bars, like this: \(|-|y||\). For example, consider \(|-2||\) and \(2||\). Though -2 and 2 are on opposite sides of zero on the number line, they are both 2 units away from zero.
variable substitution
Variable substitution is fundamental in algebra to solve equations and expressions with given values. For instance, if we are given \(y = -2||\), we directly replace 'y' in all expressions with -2. Hence, \(\frac{\|y\|}{y} ||\) becomes \(\frac{\|-2\|}{-2} ||\) upon substitution.
fraction simplification
Simplifying fractions involves reducing them to their simplest form. This means making the numerator and denominator as small as possible. Consider the expression \(\frac{|y|}{y} ||\). Substituting \(y||\) with -2, we get \(\frac{2}{-2} ||\). Here, the fraction simplifies to -1 because \(1||\) is the highest common factor of 2 and -2, enabling cancellation.
algebraic expressions
Algebraic expressions are mathematical phrases that can include numbers, variables, and operations. For example, \(\frac{|y|}{y} ||\) is an algebraic expression where \(y||\) is a variable, \(|-|y||\) is the absolute value operation, and \(\frac{a}{b}||\) represents the division. Through substitution and simplification, we can evaluate these expressions.

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Most popular questions from this chapter

Simplify each expression. $$\left(-\frac{64}{125}\right)^{-2 / 3}$$

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