Question

Some fractions have a denominator that is greater than the numerator. Some fractions have a numerator that is greater than the denominator. Can you find one of each type of fraction that have an equal value to each other?

Answer 1

No, you can't. If the denominator is greater than the numerator, that fraction's absolute value is always less than 1. If the numerator is greater than the denominator, that fraction's absolute value is always more than 1. Therefore, for both of them to be equal to each other, you are saying that a fraction that is less than 1 is equal to the fraction more than one. However, you can have a fraction with a larger denominator actually be of greater value than the one with the larger numerator. For example, -(9/8) vs -(8/9). -(9/8) has a greater numerator, yet -(8/9) is greater than it, despite having a larger denominator. Of course, this case can be written off as having the negative factored in with either the numerator with denominator, so it is easier to remember the rule above without the negative mumbo jumbo.