/*! 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 53 Find the absolute value. $$ ... [FREE SOLUTION] | 91影视

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Chapter 10: Problem 53

Find the absolute value. $$ \left|\frac{0}{4}\right| $$

Short Answer

Expert verified
The absolute value is 0.

Step by step solution

01

Understanding Absolute Value

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

Evaluate the Fraction

First, simplify the fraction \(\frac{0}{4}\). Any number divided by a non-zero number is 0. Thus, \(\frac{0}{4} = 0\).
03

Apply Absolute Value

Next, find the absolute value of 0. The absolute value of 0 is 0 because 0 is at zero distance from itself on the number line.
04

Conclusion

Therefore, \(\bigg| \frac{0}{4} \bigg| = 0\).

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Key Concepts

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

distance from zero
The concept of absolute value revolves around measuring how far a number is from zero on the number line.
Regardless of whether a number is positive or negative, its distance from zero is always considered in positive terms.
For example, both +3 and -3 are three units away from zero. Hence, their absolute value is the same, which is 3.
This intrinsic property of absolute value ensures it is always non-negative.
Understanding this helps in grasping the notion that the absolute value function essentially strips any number of its sign.
division by non-zero number
Division is one of the basic arithmetic operations that involves distributing a number into equal parts.
An important rule in division is that the divisor (the number we divide by) must be non-zero. Dividing by zero is undefined because it does not produce a meaningful result.
In the exercise, we divide 0 by 4, which is a non-zero number. According to arithmetic rules, any number divided by a non-zero number is 0. This operation simplifies our fraction \(\frac{0}{4}\) to 0.
Understanding this rule ensures that division operations are always meaningful and correct.
non-negative
The notion of being non-negative is important when dealing with absolute values.
By definition, an absolute value will never result in a negative number.
This is because it represents the magnitude or size of a number without considering its direction.
Therefore, the answer to any absolute value operation is either positive or zero. In the exercise given, we saw that the absolute value operation returned 0 because the value inside the absolute value, which was already 0, had no distance to move in either direction from zero on the number line.
This reiterates the key concept that absolute values are non-negative by nature.

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