_____ is the only rational number that is equal to its reciprocal.a)2b...
1 because the reciprocal of 1 is 1/1 which is equal to 1.
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_____ is the only rational number that is equal to its reciprocal.a)2b...
**Reciprocal of a Rational Number**
The reciprocal of a rational number is obtained by interchanging the numerator and the denominator. For example, the reciprocal of 3/4 is 4/3.
**Finding the Rational Number that is equal to its Reciprocal**
To find a rational number that is equal to its reciprocal, we need to find a number x such that x = 1/x.
Let's solve this equation to find the value of x:
x = 1/x
Multiplying both sides of the equation by x gives us:
x * x = 1
This equation can be written as:
x^2 = 1
Taking the square root of both sides, we get:
x = ±√1
Simplifying the square root of 1 gives us two possible values for x:
x = ±1
Therefore, the rational number that is equal to its reciprocal is 1.
**Explanation of the Correct Answer (Option B)**
Option B states that the only rational number that is equal to its reciprocal is 1. This is indeed correct because, as we derived earlier, the solution to the equation x = 1/x is x = ±1. Since we are looking for a rational number, the only valid solution is x = 1.
Option A (2), Option C (1/2), and Option D (0) are not correct because these numbers do not satisfy the equation x = 1/x. For example, if we substitute A = 2 in the equation, we get 2 = 1/2, which is not true. Similarly, if we substitute C = 1/2, we get 1/2 = 1/(1/2) = 2, which is also not true.
Therefore, the correct answer is Option B (1), as it is the only rational number that is equal to its reciprocal.
_____ is the only rational number that is equal to its reciprocal.a)2b...
1 because when there is no denominator we consider it to be 1. so in this case the fraction would be 1/1 which is= to its reciprocal.
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