/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 66 Find each absolute value. $$\l... [FREE SOLUTION] | 91影视

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Chapter 1: Problem 66

Find each absolute value. $$\left|-\frac{2}{3}\right|$$

Short Answer

Expert verified
The absolute value of \(-\frac{2}{3}\) is \(\frac{2}{3}\).

Step by step solution

01

Understand what absolute value means

The absolute value of a number refers to its distance from zero on the number line, regardless of direction. It is always a non-negative value.
02

Identify the given expression

The given expression is \(\bigg|-\frac{2}{3}\bigg|\).
03

Apply the absolute value

Remove the negative sign because absolute value measures distance from zero and does not consider direction. Therefore, \(\bigg|-\frac{2}{3}\bigg| = \frac{2}{3}\).
04

Write the final answer

The absolute value of \(-\frac{2}{3}\) is \(\frac{2}{3}\).

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Key Concepts

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

number line
A number line is a visual representation of all real numbers laid out in a straight line. Each point on this line corresponds to a unique number. It extends infinitely in both directions, representing positive numbers to the right of zero and negative numbers to the left. Zero acts as the midpoint and origin of the number line.

When working with absolute values, the number line helps to visualize how far a number is from zero. For example, \(-\frac{2}{3}\) is situated to the left of zero, while \(\frac{2}{3}\) is situated to the right.

Understanding the number line will help you grasp other concepts such as addition, subtraction, and the relative size of numbers.
distance from zero
The distance from zero refers to how far a number is from zero on a number line, irrespective of the direction. This distance is what we calculate when finding the absolute value.

To find the absolute value of \(\-\frac{2}{3}\), we focus on its distance from zero. On the number line, it is \frac{2}{3}\ units away from zero. Hence, the absolute value is \frac{2}{3}\.

Distance from zero is always represented as a non-negative value because distance cannot be negative.
non-negative value
A non-negative value is any number that is either positive or zero. Non-negative values include all positive integers, fractions, decimal numbers, and zero itself.

Absolute value inherently gives a non-negative value because it measures how far a number is from zero on a number line. For instance, the absolute value of \(\-\frac{2}{3}\) is \(\frac{2}{3}\) and not \(\-\frac{2}{3}\) because we are only interested in the distance, not the direction.

This rule holds true for any number: whether it鈥檚 positive, negative, or zero, its absolute value will always be a non-negative number.

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Most popular questions from this chapter

Evaluate. $$ \frac{x^{2}+2^{x}}{x^{2}-2^{x}}, \text { for } x=3 $$

Simplify using a calculator. Round your answer to the nearest thousandth. $$ \frac{13.4-5|1.2+4.6|}{(9.3-5.4)^{2}} $$

Simplify. $$ 2 x-7 x-(4 x-6) $$

Simplify using a calculator. Round your answer to the nearest thousandth. $$ |13.5+8(-4.7)|^{3} $$

SYNTHESIS Write the sentence \((-x)^{2} \neq-x^{2}\) in words. Explain why \((-x)^{2}\) and \(-x^{2}\) are not equivalent.
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