70/85 Additive Inverse :
The additive inverse of 70/85 is -70/85.
This means that when we add 70/85 and -70/85, the result is zero:
70/85 + (-70/85) = 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: 70/85
- Additive inverse: -70/85
To verify: 70/85 + (-70/85) = 0
Extended Mathematical Exploration of 70/85
Let's explore various mathematical operations and concepts related to 70/85 and its additive inverse -70/85.
Basic Operations and Properties
- Square of 70/85: 0.67820069204152
- Cube of 70/85: 0.55851821697537
- Square root of |70/85|: 0.90748521297303
- Reciprocal of 70/85: 1.2142857142857
- Double of 70/85: 1.6470588235294
- Half of 70/85: 0.41176470588235
- Absolute value of 70/85: 0.82352941176471
Trigonometric Functions
- Sine of 70/85: 0.73354911043833
- Cosine of 70/85: 0.67963644882771
- Tangent of 70/85: 1.0793257361397
Exponential and Logarithmic Functions
- e^70/85: 2.278527524544
- Natural log of 70/85: -0.19415601444096
Floor and Ceiling Functions
- Floor of 70/85: 0
- Ceiling of 70/85: 1
Interesting Properties and Relationships
- The sum of 70/85 and its additive inverse (-70/85) is always 0.
- The product of 70/85 and its additive inverse is: -4900
- The average of 70/85 and its additive inverse is always 0.
- The distance between 70/85 and its additive inverse on a number line is: 140
Applications in Algebra
Consider the equation: x + 70/85 = 0
The solution to this equation is x = -70/85, which is the additive inverse of 70/85.
Graphical Representation
On a coordinate plane:
- The point (70/85, 0) is reflected across the y-axis to (-70/85, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 70/85 and Its Additive Inverse
Consider the alternating series: 70/85 + (-70/85) + 70/85 + (-70/85) + ...
The sum of this series oscillates between 0 and 70/85, never converging unless 70/85 is 0.
In Number Theory
For integer values:
- If 70/85 is even, its additive inverse is also even.
- If 70/85 is odd, its additive inverse is also odd.
- The sum of the digits of 70/85 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
Enter a number (whole number, decimal, or fraction) to find its additive inverse: