Divide 6120 by 9 the smart way

Question

Before dividing by 9, a quick digit-sum tells you it goes in cleanly. Solve in your head. What is 6120 \div 9? Aim: under 12 seconds.

Accepted Answer

Digit sum 6+1+2+0 = 9, divisible by 9, so expect a whole answer. Now divide by 9 via 10-minus-a-bit, or split 6120 = 5400 + 720: \frac{5400}{9} + \frac{720}{9} = 600 + 80 = 680. So 6120 \div 9 = \mathbf{680}. Check: 9 	imes 680 = 6120. Correct. Takeaway. A digit sum divisible by 9 guarantees clean division by 9. Then split the dividend into 9-friendly chunks (5400, 720) and add the quotients.

Divide 6120 by 9 the smart way

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