The reciprocal of a fraction less than 1 is always a fraction greater than 1. Why is this?

Answer 1

The above statement is not true!

-3/4 is a fraction which is less than 1. Its reciprocal is -4/3 which is also less than 1, NOT greater.

Answer 2

Let's see, an example of a reciprocal of a fraction less than 1 would be something like this: 1/8, after the reciprocal it will become 8/1.

8/1 equals 8 therefore is larger than 1.

This will always happen because as long as the denominator(the bottom) is larger than the numerator, the reciprocal(flipping the numbers) will make it larger than 1.

Here are some examples of reciprocals: 1/2 becomes 2/1. 1/3 becomes 3/1. 1/4 becomes 4/1. Just swap the two numbers and the number that it becomes will be automatically larger than 1.

Answer 3

Let's say you have 1/2. To equal one, you have to multiply by the reciprocal. The reciprocal is always greater than one because the fraction is less than one. If you have one, then you multiply by one to get one. If you have a fraction, then it's less than one, and it takes something greater than it to equal one. This might be confusing, so I'll provide a visual example.

1/2 < 1

1/2 * 1/2 = 1/4