70/81 Additive Inverse :
The additive inverse of 70/81 is -70/81.
This means that when we add 70/81 and -70/81, the result is zero:
70/81 + (-70/81) = 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: 70/81
- Additive inverse: -70/81
To verify: 70/81 + (-70/81) = 0
Extended Mathematical Exploration of 70/81
Let's explore various mathematical operations and concepts related to 70/81 and its additive inverse -70/81.
Basic Operations and Properties
- Square of 70/81: 0.74683737235178
- Cube of 70/81: 0.64541501314351
- Square root of |70/81|: 0.92962225170453
- Reciprocal of 70/81: 1.1571428571429
- Double of 70/81: 1.7283950617284
- Half of 70/81: 0.4320987654321
- Absolute value of 70/81: 0.8641975308642
Trigonometric Functions
- Sine of 70/81: 0.76057450495796
- Cosine of 70/81: 0.64925066223143
- Tangent of 70/81: 1.1714651200261
Exponential and Logarithmic Functions
- e^70/81: 2.3731009813918
- Natural log of 70/81: -0.14595391262308
Floor and Ceiling Functions
- Floor of 70/81: 0
- Ceiling of 70/81: 1
Interesting Properties and Relationships
- The sum of 70/81 and its additive inverse (-70/81) is always 0.
- The product of 70/81 and its additive inverse is: -4900
- The average of 70/81 and its additive inverse is always 0.
- The distance between 70/81 and its additive inverse on a number line is: 140
Applications in Algebra
Consider the equation: x + 70/81 = 0
The solution to this equation is x = -70/81, which is the additive inverse of 70/81.
Graphical Representation
On a coordinate plane:
- The point (70/81, 0) is reflected across the y-axis to (-70/81, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 70/81 and Its Additive Inverse
Consider the alternating series: 70/81 + (-70/81) + 70/81 + (-70/81) + ...
The sum of this series oscillates between 0 and 70/81, never converging unless 70/81 is 0.
In Number Theory
For integer values:
- If 70/81 is even, its additive inverse is also even.
- If 70/81 is odd, its additive inverse is also odd.
- The sum of the digits of 70/81 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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