34/35 Additive Inverse :

The additive inverse of 34/35 is -34/35.

This means that when we add 34/35 and -34/35, the result is zero:

34/35 + (-34/35) = 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: 34/35
  • Additive inverse: -34/35

To verify: 34/35 + (-34/35) = 0

Extended Mathematical Exploration of 34/35

Let's explore various mathematical operations and concepts related to 34/35 and its additive inverse -34/35.

Basic Operations and Properties

  • Square of 34/35: 0.94367346938776
  • Cube of 34/35: 0.91671137026239
  • Square root of |34/35|: 0.98561076060916
  • Reciprocal of 34/35: 1.0294117647059
  • Double of 34/35: 1.9428571428571
  • Half of 34/35: 0.48571428571429
  • Absolute value of 34/35: 0.97142857142857

Trigonometric Functions

  • Sine of 34/35: 0.82569244210259
  • Cosine of 34/35: 0.5641205465631
  • Tangent of 34/35: 1.4636808517845

Exponential and Logarithmic Functions

  • e^34/35: 2.6417156445013
  • Natural log of 34/35: -0.028987536873252

Floor and Ceiling Functions

  • Floor of 34/35: 0
  • Ceiling of 34/35: 1

Interesting Properties and Relationships

  • The sum of 34/35 and its additive inverse (-34/35) is always 0.
  • The product of 34/35 and its additive inverse is: -1156
  • The average of 34/35 and its additive inverse is always 0.
  • The distance between 34/35 and its additive inverse on a number line is: 68

Applications in Algebra

Consider the equation: x + 34/35 = 0

The solution to this equation is x = -34/35, which is the additive inverse of 34/35.

Graphical Representation

On a coordinate plane:

  • The point (34/35, 0) is reflected across the y-axis to (-34/35, 0).
  • The midpoint between these two points is always (0, 0).

Series Involving 34/35 and Its Additive Inverse

Consider the alternating series: 34/35 + (-34/35) + 34/35 + (-34/35) + ...

The sum of this series oscillates between 0 and 34/35, never converging unless 34/35 is 0.

In Number Theory

For integer values:

  • If 34/35 is even, its additive inverse is also even.
  • If 34/35 is odd, its additive inverse is also odd.
  • The sum of the digits of 34/35 and its additive inverse may or may not be the same.

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