34/43 Additive Inverse :

The additive inverse of 34/43 is -34/43.

This means that when we add 34/43 and -34/43, the result is zero:

34/43 + (-34/43) = 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: 34/43
  • Additive inverse: -34/43

To verify: 34/43 + (-34/43) = 0

Extended Mathematical Exploration of 34/43

Let's explore various mathematical operations and concepts related to 34/43 and its additive inverse -34/43.

Basic Operations and Properties

  • Square of 34/43: 0.62520281233099
  • Cube of 34/43: 0.49434640975008
  • Square root of |34/43|: 0.8892118276421
  • Reciprocal of 34/43: 1.2647058823529
  • Double of 34/43: 1.5813953488372
  • Half of 34/43: 0.3953488372093
  • Absolute value of 34/43: 0.7906976744186

Trigonometric Functions

  • Sine of 34/43: 0.71084415436708
  • Cosine of 34/43: 0.7033495490879
  • Tangent of 34/43: 1.010655591219

Exponential and Logarithmic Functions

  • e^34/43: 2.2049342159525
  • Natural log of 34/43: -0.2348395910774

Floor and Ceiling Functions

  • Floor of 34/43: 0
  • Ceiling of 34/43: 1

Interesting Properties and Relationships

  • The sum of 34/43 and its additive inverse (-34/43) is always 0.
  • The product of 34/43 and its additive inverse is: -1156
  • The average of 34/43 and its additive inverse is always 0.
  • The distance between 34/43 and its additive inverse on a number line is: 68

Applications in Algebra

Consider the equation: x + 34/43 = 0

The solution to this equation is x = -34/43, which is the additive inverse of 34/43.

Graphical Representation

On a coordinate plane:

  • The point (34/43, 0) is reflected across the y-axis to (-34/43, 0).
  • The midpoint between these two points is always (0, 0).

Series Involving 34/43 and Its Additive Inverse

Consider the alternating series: 34/43 + (-34/43) + 34/43 + (-34/43) + ...

The sum of this series oscillates between 0 and 34/43, never converging unless 34/43 is 0.

In Number Theory

For integer values:

  • If 34/43 is even, its additive inverse is also even.
  • If 34/43 is odd, its additive inverse is also odd.
  • The sum of the digits of 34/43 and its additive inverse may or may not be the same.

Interactive Additive Inverse Calculator

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