**Front-end addition and subtraction **

Most formal written algorithms for addition and subtraction work from right to left, starting with the units. In mental calculations it is much more common to work from left to right. This makes more sense, because you deal with the biggest and most significant bits of the numbers first.

*partitioning into hundreds, tens and ones.* We would then use the freedom granted to us by the associative and commutative laws to add these bits in any order we like. The ‘front-end approach’ would deal with the hundreds first (400 + 300 = 700), then the tens (50 + 40 = 90, making 790 so far), then the ones (for example, 790 + 9 = 799; 799 + 7 = 799 + 1 + 6 = 806). Notice that I have used 800 as a stepping stone for the last step here.

Writing this out in full, in a way which might explain my thinking to someone else:

459 + 347 = (400 + 50 + 9) + (300 + 40 + 7)

= (400 + 300) + (50 + 40) + (9 + 7)

= 700 + 90 + 9 + 7

= 799 + 7 = 799 + 1 + 6 = 800 + 6 = 806