85/88 Additive Inverse :

The additive inverse of 85/88 is -85/88.

This means that when we add 85/88 and -85/88, the result is zero:

85/88 + (-85/88) = 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: 85/88
  • Additive inverse: -85/88

To verify: 85/88 + (-85/88) = 0

Extended Mathematical Exploration of 85/88

Let's explore various mathematical operations and concepts related to 85/88 and its additive inverse -85/88.

Basic Operations and Properties

  • Square of 85/88: 0.93298037190083
  • Cube of 85/88: 0.90117422285875
  • Square root of |85/88|: 0.98280674138362
  • Reciprocal of 85/88: 1.0352941176471
  • Double of 85/88: 1.9318181818182
  • Half of 85/88: 0.48295454545455
  • Absolute value of 85/88: 0.96590909090909

Trigonometric Functions

  • Sine of 85/88: 0.8225662283546
  • Cosine of 85/88: 0.56866932392252
  • Tangent of 85/88: 1.446475471335

Exponential and Logarithmic Functions

  • e^85/88: 2.6271749120231
  • Natural log of 85/88: -0.03468555798789

Floor and Ceiling Functions

  • Floor of 85/88: 0
  • Ceiling of 85/88: 1

Interesting Properties and Relationships

  • The sum of 85/88 and its additive inverse (-85/88) is always 0.
  • The product of 85/88 and its additive inverse is: -7225
  • The average of 85/88 and its additive inverse is always 0.
  • The distance between 85/88 and its additive inverse on a number line is: 170

Applications in Algebra

Consider the equation: x + 85/88 = 0

The solution to this equation is x = -85/88, which is the additive inverse of 85/88.

Graphical Representation

On a coordinate plane:

  • The point (85/88, 0) is reflected across the y-axis to (-85/88, 0).
  • The midpoint between these two points is always (0, 0).

Series Involving 85/88 and Its Additive Inverse

Consider the alternating series: 85/88 + (-85/88) + 85/88 + (-85/88) + ...

The sum of this series oscillates between 0 and 85/88, never converging unless 85/88 is 0.

In Number Theory

For integer values:

  • If 85/88 is even, its additive inverse is also even.
  • If 85/88 is odd, its additive inverse is also odd.
  • The sum of the digits of 85/88 and its additive inverse may or may not be the same.

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