70/71 Additive Inverse :
The additive inverse of 70/71 is -70/71.
This means that when we add 70/71 and -70/71, the result is zero:
70/71 + (-70/71) = 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: 70/71
- Additive inverse: -70/71
To verify: 70/71 + (-70/71) = 0
Extended Mathematical Exploration of 70/71
Let's explore various mathematical operations and concepts related to 70/71 and its additive inverse -70/71.
Basic Operations and Properties
- Square of 70/71: 0.97202935925412
- Cube of 70/71: 0.95833880489842
- Square root of |70/71|: 0.99293277363462
- Reciprocal of 70/71: 1.0142857142857
- Double of 70/71: 1.9718309859155
- Half of 70/71: 0.49295774647887
- Absolute value of 70/71: 0.98591549295775
Trigonometric Functions
- Sine of 70/71: 0.83377788344881
- Cosine of 70/71: 0.55210002813949
- Tangent of 70/71: 1.5101935173931
Exponential and Logarithmic Functions
- e^70/71: 2.6802645248596
- Natural log of 70/71: -0.014184634991956
Floor and Ceiling Functions
- Floor of 70/71: 0
- Ceiling of 70/71: 1
Interesting Properties and Relationships
- The sum of 70/71 and its additive inverse (-70/71) is always 0.
- The product of 70/71 and its additive inverse is: -4900
- The average of 70/71 and its additive inverse is always 0.
- The distance between 70/71 and its additive inverse on a number line is: 140
Applications in Algebra
Consider the equation: x + 70/71 = 0
The solution to this equation is x = -70/71, which is the additive inverse of 70/71.
Graphical Representation
On a coordinate plane:
- The point (70/71, 0) is reflected across the y-axis to (-70/71, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 70/71 and Its Additive Inverse
Consider the alternating series: 70/71 + (-70/71) + 70/71 + (-70/71) + ...
The sum of this series oscillates between 0 and 70/71, never converging unless 70/71 is 0.
In Number Theory
For integer values:
- If 70/71 is even, its additive inverse is also even.
- If 70/71 is odd, its additive inverse is also odd.
- The sum of the digits of 70/71 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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