69/74 Additive Inverse :
The additive inverse of 69/74 is -69/74.
This means that when we add 69/74 and -69/74, the result is zero:
69/74 + (-69/74) = 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: 69/74
- Additive inverse: -69/74
To verify: 69/74 + (-69/74) = 0
Extended Mathematical Exploration of 69/74
Let's explore various mathematical operations and concepts related to 69/74 and its additive inverse -69/74.
Basic Operations and Properties
- Square of 69/74: 0.86943024105186
- Cube of 69/74: 0.8106849544943
- Square root of |69/74|: 0.96562540999729
- Reciprocal of 69/74: 1.0724637681159
- Double of 69/74: 1.8648648648649
- Half of 69/74: 0.46621621621622
- Absolute value of 69/74: 0.93243243243243
Trigonometric Functions
- Sine of 69/74: 0.80307175873527
- Cosine of 69/74: 0.59588232925791
- Tangent of 69/74: 1.3477019191614
Exponential and Logarithmic Functions
- e^69/74: 2.5406817040251
- Natural log of 69/74: -0.06995858860691
Floor and Ceiling Functions
- Floor of 69/74: 0
- Ceiling of 69/74: 1
Interesting Properties and Relationships
- The sum of 69/74 and its additive inverse (-69/74) is always 0.
- The product of 69/74 and its additive inverse is: -4761
- The average of 69/74 and its additive inverse is always 0.
- The distance between 69/74 and its additive inverse on a number line is: 138
Applications in Algebra
Consider the equation: x + 69/74 = 0
The solution to this equation is x = -69/74, which is the additive inverse of 69/74.
Graphical Representation
On a coordinate plane:
- The point (69/74, 0) is reflected across the y-axis to (-69/74, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 69/74 and Its Additive Inverse
Consider the alternating series: 69/74 + (-69/74) + 69/74 + (-69/74) + ...
The sum of this series oscillates between 0 and 69/74, never converging unless 69/74 is 0.
In Number Theory
For integer values:
- If 69/74 is even, its additive inverse is also even.
- If 69/74 is odd, its additive inverse is also odd.
- The sum of the digits of 69/74 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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