78/87 Additive Inverse :
The additive inverse of 78/87 is -78/87.
This means that when we add 78/87 and -78/87, the result is zero:
78/87 + (-78/87) = 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: 78/87
- Additive inverse: -78/87
To verify: 78/87 + (-78/87) = 0
Extended Mathematical Exploration of 78/87
Let's explore various mathematical operations and concepts related to 78/87 and its additive inverse -78/87.
Basic Operations and Properties
- Square of 78/87: 0.8038049940547
- Cube of 78/87: 0.72065275329042
- Square root of |78/87|: 0.946864152948
- Reciprocal of 78/87: 1.1153846153846
- Double of 78/87: 1.7931034482759
- Half of 78/87: 0.44827586206897
- Absolute value of 78/87: 0.89655172413793
Trigonometric Functions
- Sine of 78/87: 0.78117877411478
- Cosine of 78/87: 0.62430739453616
- Tangent of 78/87: 1.2512726598332
Exponential and Logarithmic Functions
- e^78/87: 2.4511363274111
- Natural log of 78/87: -0.10919929196499
Floor and Ceiling Functions
- Floor of 78/87: 0
- Ceiling of 78/87: 1
Interesting Properties and Relationships
- The sum of 78/87 and its additive inverse (-78/87) is always 0.
- The product of 78/87 and its additive inverse is: -6084
- The average of 78/87 and its additive inverse is always 0.
- The distance between 78/87 and its additive inverse on a number line is: 156
Applications in Algebra
Consider the equation: x + 78/87 = 0
The solution to this equation is x = -78/87, which is the additive inverse of 78/87.
Graphical Representation
On a coordinate plane:
- The point (78/87, 0) is reflected across the y-axis to (-78/87, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 78/87 and Its Additive Inverse
Consider the alternating series: 78/87 + (-78/87) + 78/87 + (-78/87) + ...
The sum of this series oscillates between 0 and 78/87, never converging unless 78/87 is 0.
In Number Theory
For integer values:
- If 78/87 is even, its additive inverse is also even.
- If 78/87 is odd, its additive inverse is also odd.
- The sum of the digits of 78/87 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: