In the case where digits in one column add up to more than 10, here’s what happens:

Let’s say you’re adding 87+56. Adding individually would be 8+7+5+6=26; 2+6=8. If you first add them as 87+56=143, 1+4+3=8, what you’re doing is adding the 1’s (7+6=13) and then taking that 1 from 13 and adding it to the 10’s (8+5+1=14) and then adding that to the 3 from the 1’s (14+3=17=8). The effect, no matter what you do, is that when you add individual digits and they make more than 10, the amount in the 10’s column ends up getting added back to them. The order in which it gets added back makes no difference:

8+7=15, 5+6=11, 11+15=26 or (1+1=2) and (1+5=6), 2+6=8

8+6=14, 5+7=12, 12+14=26 or (1+1=2) and (2+4=6), 2+6=8

So the two principles at operation here are:

1) The order in which you add numbers makes no difference. This is a universal principle in arithmetic.

2) Any time the sum adds a 1 in the 10’s column, you just add that 1 back in the 1’s column. This is a rule specific to this kind of addition.

Since the order in which you add makes no difference, the same number of 1’s will be added in the 10’s column no matter how you do it. Think of numbers as poker chips that you’re putting in stacks of 10. (If you make a stack of 10, you take the remainder and start a new stack. Not sure if you play poker but this is standard chip handling. ðŸ™‚ ) You can try as many different ways as you want of piling them and it will still make a new stack of 10 exactly as many times. In this kind of addition, you get an extra chip for every stack of 10 you make. So you will always end up with the same number no matter the order you do it in.

]]>Wowâ€¦thanks for your research and detail again! It gives me a new appreciation of the phrase and the reading.

I enjoy your â€˜dailyâ€™sâ€™â€¦ but seldom tell you.

Regards

Lawrence Buehler

]]>