70/75 Additive Inverse :
The additive inverse of 70/75 is -70/75.
This means that when we add 70/75 and -70/75, the result is zero:
70/75 + (-70/75) = 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: 70/75
- Additive inverse: -70/75
To verify: 70/75 + (-70/75) = 0
Extended Mathematical Exploration of 70/75
Let's explore various mathematical operations and concepts related to 70/75 and its additive inverse -70/75.
Basic Operations and Properties
- Square of 70/75: 0.87111111111111
- Cube of 70/75: 0.81303703703704
- Square root of |70/75|: 0.9660917830793
- Reciprocal of 70/75: 1.0714285714286
- Double of 70/75: 1.8666666666667
- Half of 70/75: 0.46666666666667
- Absolute value of 70/75: 0.93333333333333
Trigonometric Functions
- Sine of 70/75: 0.80360826369441
- Cosine of 70/75: 0.59515859946913
- Tangent of 70/75: 1.3502422117587
Exponential and Logarithmic Functions
- e^70/75: 2.542971637808
- Natural log of 70/75: -0.068992871486951
Floor and Ceiling Functions
- Floor of 70/75: 0
- Ceiling of 70/75: 1
Interesting Properties and Relationships
- The sum of 70/75 and its additive inverse (-70/75) is always 0.
- The product of 70/75 and its additive inverse is: -4900
- The average of 70/75 and its additive inverse is always 0.
- The distance between 70/75 and its additive inverse on a number line is: 140
Applications in Algebra
Consider the equation: x + 70/75 = 0
The solution to this equation is x = -70/75, which is the additive inverse of 70/75.
Graphical Representation
On a coordinate plane:
- The point (70/75, 0) is reflected across the y-axis to (-70/75, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 70/75 and Its Additive Inverse
Consider the alternating series: 70/75 + (-70/75) + 70/75 + (-70/75) + ...
The sum of this series oscillates between 0 and 70/75, never converging unless 70/75 is 0.
In Number Theory
For integer values:
- If 70/75 is even, its additive inverse is also even.
- If 70/75 is odd, its additive inverse is also odd.
- The sum of the digits of 70/75 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: