Ch. R - Algebra Review

Lial12th EditionTrigonometryISBN: 9780136552161Not the one you use?Change textbook

Lial 12th Edition

Ch. R - Algebra Review

Problem 51

Chapter 1, Problem 51

Give (a) the additive inverse and (b) the absolute value of each number. -6⁄5

Verified step by step guidance

Identify the given number, which is \(-\frac{6}{5}\).

To find the additive inverse of a number, recall that it is the number that, when added to the original number, results in zero. For any number \(x\), the additive inverse is \(-x\).

Apply this to the given number: the additive inverse of \(-\frac{6}{5}\) is \(-\left(-\frac{6}{5}\right)\), which simplifies to \(\frac{6}{5}\).

To find the absolute value of a number, remember that it is the distance of the number from zero on the number line, always expressed as a non-negative value. The absolute value of \(x\) is denoted as \(|x|\).

Apply this to the given number: the absolute value of \(-\frac{6}{5}\) is \(\left|-\frac{6}{5}\right|\), which equals \(\frac{6}{5}\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Additive Inverse

The additive inverse of a number is the value that, when added to the original number, results in zero. For any real number 'a', its additive inverse is '-a'. For example, the additive inverse of -6/5 is 6/5 because (-6/5) + (6/5) = 0.

Absolute Value

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always non-negative. For a number 'a', the absolute value is denoted |a|. For example, | -6/5 | = 6/5.

Rational Numbers

Rational numbers are numbers that can be expressed as the quotient of two integers, where the denominator is not zero. Understanding that -6/5 is a rational number helps in applying operations like finding additive inverses and absolute values correctly.

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