Dividing by 9 has always been an awkward one for the mathematical ninja - it ought to be a simple operation, but for some reason it’s never stuck.
However, there IS an easy way that involves not much more than adding up and (possibly) using your fingers to track a carry.
Allow me to show you how. Suppose you want to divide 23068 by 9.
You say the first number (2) - this is both the (provisional) first digit of the answer and the running total so far.
Add it to the next digit (2+3): 5 is the provisional next digit, so our answer so far is 25.
Repeat: (5 + 0) 5 is the provisional next digit; our answer so far is 255.
Then we hit a problem: 5 + 6 is 11, which isn’t a digit. Instead, we need to add one to our provisional answer (now it’s 256) and add the digits of 11 together (to make 2) as our new running total, and next digit. So far, we have 2562.
The last digit is when we get into decimal territory - and it works just the same. Our running total becomes 10 which is too large; we carry one onto the answer (2563) and the first digit after the dot will be (1+0 = 1). In fact, because we’re dealing with ninths, EVERY digit after the dot will be a 1, and our answer is 2563.1111…
Although handling the carry is a bit of a brainful at first, with a bit of practise, you can get very good at this - yet another way for the budding mathematical ninja to wow his or her classmates with seemingly impossible arithmetic skills.
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