Question

why does this work

3/4 + 2/7


2 | 7
3 | XXXX | 3 x 7 =21
---------------
4 | 2x4=8 | 4 x 7 = 28

add the diagonal answer is 29/28 or 1 1/28

Answer 1

What was the 2x4 used for?
I can't seem to figure that out...

Answer 2

Oh 8 +21... interesting :O

Answer 3

seems to work every time.... interesting way of adding fractions... eliminates the need for common denominators... or lowest common factors...

Answer 4

It is really just finding the common denominator and adding. Sure it moves the parts around to disguise what is going on, but it is exactly the same thing.

Answer 5

\[ \large {a \over b} + {c \over d} = {ad \over bd} + {cb \over bd}\]

You have put ad in the lower left corner, cb in the upper right corner, and bd in the lower right corner. The you add the lower left corner and the upper right corner and divide by the lower right corner. That is just exactly what the algebra does.

Answer 6

which is easier for a student to understand...?

Answer 7

it is evident that bd is a common multiple, and this system works every time. However - there may be a lower common multiple (In particular the Lowest Common Multiple). If so, then the resulting fraction can always be simplified..

I generally use @LarsEighner 's method - but your grid version is just a formalised way of notating it.

I think the student should be shown the way without the table, and in particular the LCM method.