38/47 Additive Inverse :

The additive inverse of 38/47 is -38/47.

This means that when we add 38/47 and -38/47, the result is zero:

38/47 + (-38/47) = 0

Additive Inverse of a Fraction

For fractions, the additive inverse is found by negating the numerator or denominator, but not both. In this case:

  • Original fraction: 38/47
  • Additive inverse: -38/47

To verify: 38/47 + (-38/47) = 0

Extended Mathematical Exploration of 38/47

Let's explore various mathematical operations and concepts related to 38/47 and its additive inverse -38/47.

Basic Operations and Properties

  • Square of 38/47: 0.65368945224083
  • Cube of 38/47: 0.52851487627982
  • Square root of |38/47|: 0.89917219613257
  • Reciprocal of 38/47: 1.2368421052632
  • Double of 38/47: 1.6170212765957
  • Half of 38/47: 0.40425531914894
  • Absolute value of 38/47: 0.80851063829787

Trigonometric Functions

  • Sine of 38/47: 0.72325945888394
  • Cosine of 38/47: 0.69057639340981
  • Tangent of 38/47: 1.047327226627

Exponential and Logarithmic Functions

  • e^38/47: 2.2445625305267
  • Natural log of 38/47: -0.21256144198367

Floor and Ceiling Functions

  • Floor of 38/47: 0
  • Ceiling of 38/47: 1

Interesting Properties and Relationships

  • The sum of 38/47 and its additive inverse (-38/47) is always 0.
  • The product of 38/47 and its additive inverse is: -1444
  • The average of 38/47 and its additive inverse is always 0.
  • The distance between 38/47 and its additive inverse on a number line is: 76

Applications in Algebra

Consider the equation: x + 38/47 = 0

The solution to this equation is x = -38/47, which is the additive inverse of 38/47.

Graphical Representation

On a coordinate plane:

  • The point (38/47, 0) is reflected across the y-axis to (-38/47, 0).
  • The midpoint between these two points is always (0, 0).

Series Involving 38/47 and Its Additive Inverse

Consider the alternating series: 38/47 + (-38/47) + 38/47 + (-38/47) + ...

The sum of this series oscillates between 0 and 38/47, never converging unless 38/47 is 0.

In Number Theory

For integer values:

  • If 38/47 is even, its additive inverse is also even.
  • If 38/47 is odd, its additive inverse is also odd.
  • The sum of the digits of 38/47 and its additive inverse may or may not be the same.

Interactive Additive Inverse Calculator

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