Lesson A shortcut to adding and subtracting fractions

Contrary to popular belief, there is a fast way to add and subtract fractions with unlike denominators, and it does not involve finding a common denominator. It uses the following formulas, provided that no denominator is ever zero:
+ =
and
- =
The steps are as follows:
1) Take the cross products and add/subtract them
2) Put the resulting sum or difference over the product of the denominators
3) Reduce if possible.
Some examples:
+
First, take the cross products. 2x8=16 and 5x3=15. Add 16 and 15 to get 31. This is your numerator. To get the denominator, multiply 5 and 8 to get 40, giving you , which is the exact same answer you would get with common denominators.

Now let's try a subtraction problem:
-
Again, take the cross products...2x5=10 and 3x3=9. Subtract 10 minus 9 to get 1. This is the numerator, To get the denominator, multiply the original denominators, 3 and 5, to get 15. So the answer to this one is .
Also, if you have numerators of 1, that makes the problem even easier because you're multiplying by 1 in your cross-products. In that case your answer would simply be the sum/difference of the denominators over the product of the denominators. For example, + = , and - = .