you want to change it to 1/2 times 2/1 which is 2/2 = 1

I would first recommend looking at the relevant Math is Fun page.

In your example 1/2 / 1/2, the answer is simply 1 because a number divided by itself is always 1.

In other cases you would find the recipricol of the second fraction, or the fraction flipped, so in that case 2, and multiply it by the first fraction. (1/2 / 1/2 = 1/2 * 2 = (1*2)/2 = 2/2 = 1)