Question

What is the reciprocal of 1 and 2/3?

Answer 1

Answer: 3/5

Step-by-step explanation: To find the reciprocal of 1 and 2/3, we first need to convert 1 and 2/3 to an improper fraction.

To write a mixed number as an improper fraction, first multiply the denominator times the whole number, then add the numerator.

So here, we multiply the denominator, 3, times the whole number, 1, then we add the numerator. So we have (3 x 1) + 2 or 3 + 2 which is 5.

Now we put our new number over our old denominator and we get 5/3.

However, we're not done yet. We still need to find the reciprocal.

The reciprocal describes a fraction so when we're asked to find the reciprocal of 5/3, we want to switch the numerator and denominator.

So if we switch 5/3, we get the proper fraction 3/5.

Therefore, the mixed number 1 and 2/3 is equivalent to the improper fraction 5/3, and if we switch the top and bottom numbers, we get 3/5.