How to add or subtract fractions easily

Students are often taught that, to add and subtract fractions, they should find the GCD (Greatest Common Denominator) to end up with a new denominator.
A denominator is the bottom number of a fraction.

However there is a much simpler way.
Look at these fractions

a   c
- + -
b   d

The schooltaught way would be to multiply the first fraction by (d/d) and the second fraction by (b/b), because bd is the GCD) and then combine them.

However all you need to do is Criss-Cross Over.
Criss is multipling the first diagonal: the top number of the 1st fraction to the bottom of the 2nd fraction (a to d).
Cross is multiplying the 2nd diagonal: the top number of the 2nd fraction to the bottom of the 1st fraction (c to b)

Criss and Cross get added (or subtracted if you have a subtraction)

and Over is multiplying both denominators (b and d).

So you get

a*d + c*b
------------
b*d

The same result in 3 very short steps. True, in this example it doesn't seem much faster. However if you're using long algebraic fractions, this makes all the difference and will save you a lot of time.

Be careful when subtracting! The criss MUST start with the top number of the first fraction.

Simplify the resulting fraction if you must, but you don't have to.

What happens if you have more than two fractions? Do the first two, then use the result and add it to the next, etc..