First, we put those mixed numbers into an improper form. 4 1/6 will become 25/6. Then to find the reciprocal, we flip the numbers, as well as if they’re positive or negative. 25 being the numerator, 6 being denominator. We switch it up. So 6/25 is when you switch the fraction. Then, since it is positive, you will make it negative since negative is the opposite of positive. So -6/25 is the reciprocal of 25/6. Reciprocals are simply the opposite of the given (improper) number.
The next problem: 5 5/6. We put it into an improper fraction. 35/6. Then we flip the numerator and denominator. 6/35. Since it’s positive, let’s make it the opposite. Negative. -6/35 is your answer.
Final problem: 1 5/6. Make it an improper fraction. 11/6. Now flip it. 6/11. Now it’s positive so, the opposite is negative. -6/11 is your answer. If you don’t know how to find an improper fraction, this is how. Let’s take the first problem, 4 1/6. Multiply the whole number by the denominator and then add the numerator. You’re welcome.