Clever Manipulations in Math

Problem Level: 2?

This is a set of numbers.

Starting with ½ , add 1 to both the numerator and denominator and you get a set of numbers.  Multiply these numbers and find the final value.

Solution:

First we should list the ways we could use to solve the problem

We could multiply everything out but that would take a long time.  Instead, we can solve the problem in a faster way.

Notice that the denominators cancel out the numerators:

2 cancels with 2

3 cancels with 3... all the way too 99.

The end result is clearly: 1/100

Clever manipulation, such as canceling out numbers can greatly help a problem becomes easier.