70/83 Additive Inverse :
The additive inverse of 70/83 is -70/83.
This means that when we add 70/83 and -70/83, the result is zero:
70/83 + (-70/83) = 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: 70/83
- Additive inverse: -70/83
To verify: 70/83 + (-70/83) = 0
Extended Mathematical Exploration of 70/83
Let's explore various mathematical operations and concepts related to 70/83 and its additive inverse -70/83.
Basic Operations and Properties
- Square of 70/83: 0.71127885034112
- Cube of 70/83: 0.59987372920336
- Square root of |70/83|: 0.91835368675467
- Reciprocal of 70/83: 1.1857142857143
- Double of 70/83: 1.6867469879518
- Half of 70/83: 0.42168674698795
- Absolute value of 70/83: 0.8433734939759
Trigonometric Functions
- Sine of 70/83: 0.74689056033491
- Cosine of 70/83: 0.66494698351267
- Tangent of 70/83: 1.1232332484454
Exponential and Logarithmic Functions
- e^70/83: 2.3241944223201
- Natural log of 70/83: -0.17034536574724
Floor and Ceiling Functions
- Floor of 70/83: 0
- Ceiling of 70/83: 1
Interesting Properties and Relationships
- The sum of 70/83 and its additive inverse (-70/83) is always 0.
- The product of 70/83 and its additive inverse is: -4900
- The average of 70/83 and its additive inverse is always 0.
- The distance between 70/83 and its additive inverse on a number line is: 140
Applications in Algebra
Consider the equation: x + 70/83 = 0
The solution to this equation is x = -70/83, which is the additive inverse of 70/83.
Graphical Representation
On a coordinate plane:
- The point (70/83, 0) is reflected across the y-axis to (-70/83, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 70/83 and Its Additive Inverse
Consider the alternating series: 70/83 + (-70/83) + 70/83 + (-70/83) + ...
The sum of this series oscillates between 0 and 70/83, never converging unless 70/83 is 0.
In Number Theory
For integer values:
- If 70/83 is even, its additive inverse is also even.
- If 70/83 is odd, its additive inverse is also odd.
- The sum of the digits of 70/83 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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