Originally Posted by

**topsquark** Think of it this way... if we have two fractions:

$\displaystyle \frac{3}{4} + \frac{1}{5}$

then we can add them by getting a common denominator. The common denominator in this case will be 4 x 5 = 20. So we need to multiply the fraction on the right to put it in the form (something)/20.

Now, we can't change the value of 1/5, but we must find a way to multiply the denominator by a factor of 4. How can we do this? Well if we multiply the fraction 1/5 by 1, then we still have 1/5. So I'm going to choose a particular kind of form of 1 to multiply the 1/5 by.

$\displaystyle \frac{1}{5} \times 1 = \frac{1}{5} \times \frac{4}{4} = \frac{1 \times 4}{5 \times 4} = \frac{4}{20}$.

We do the same thing with 3/4, but in this case we need to multiply the denominator by 5, thus

$\displaystyle \frac{3}{4} \times 1 = \frac{3}{4} \times \frac{5}{5} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}$

Why do we do all this? In order to add two fractions we need to have a common denominator, in this case 20.

$\displaystyle \frac{3}{4} + \frac{1}{5} = \frac{15}{20} + \frac{4}{20} = \frac{15 + 4}{20} = \frac{19}{20}$.

The problem you are being asked to do is very similar, except in this case I'm going to change the 1 into 1/1, so we can have the number 1 in fractional form. So how do you add

$\displaystyle 1 + \frac{1}{2} = \frac{1}{1} + \frac{1}{2}$