7/8 Additive Inverse :
The additive inverse of 7/8 is -7/8.
This means that when we add 7/8 and -7/8, the result is zero:
7/8 + (-7/8) = 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: 7/8
- Additive inverse: -7/8
To verify: 7/8 + (-7/8) = 0
Extended Mathematical Exploration of 7/8
Let's explore various mathematical operations and concepts related to 7/8 and its additive inverse -7/8.
Basic Operations and Properties
- Square of 7/8: 0.765625
- Cube of 7/8: 0.669921875
- Square root of |7/8|: 0.93541434669349
- Reciprocal of 7/8: 1.1428571428571
- Double of 7/8: 1.75
- Half of 7/8: 0.4375
- Absolute value of 7/8: 0.875
Trigonometric Functions
- Sine of 7/8: 0.76754350223603
- Cosine of 7/8: 0.64099685816333
- Tangent of 7/8: 1.1974216292343
Exponential and Logarithmic Functions
- e^7/8: 2.3988752939671
- Natural log of 7/8: -0.13353139262452
Floor and Ceiling Functions
- Floor of 7/8: 0
- Ceiling of 7/8: 1
Interesting Properties and Relationships
- The sum of 7/8 and its additive inverse (-7/8) is always 0.
- The product of 7/8 and its additive inverse is: -49
- The average of 7/8 and its additive inverse is always 0.
- The distance between 7/8 and its additive inverse on a number line is: 14
Applications in Algebra
Consider the equation: x + 7/8 = 0
The solution to this equation is x = -7/8, which is the additive inverse of 7/8.
Graphical Representation
On a coordinate plane:
- The point (7/8, 0) is reflected across the y-axis to (-7/8, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 7/8 and Its Additive Inverse
Consider the alternating series: 7/8 + (-7/8) + 7/8 + (-7/8) + ...
The sum of this series oscillates between 0 and 7/8, never converging unless 7/8 is 0.
In Number Theory
For integer values:
- If 7/8 is even, its additive inverse is also even.
- If 7/8 is odd, its additive inverse is also odd.
- The sum of the digits of 7/8 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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