Divide 9000 by 125 without dividing

Question

Solve in your head, no long division. What is 9000 \div 125? Aim: under 6 seconds.

Accepted Answer

Dividing by 125 is the same as multiplying by 8 and dividing by 1000 (because 125 = 1000/8): \frac{9000}{125} = \frac{9000 	imes 8}{1000} = \frac{72000}{1000} = 72. Multiplying by 8 is three quick doublings (9000 	o 18000 	o 36000 	o 72000), and dividing by 1000 is a three-place decimal shift. Takeaway. The reciprocal-of-a-power-of-ten family is worth memorizing: \div 125 	o 	imes 8 / 1000, \div 25 	o 	imes 4 / 100, \div 5 	o 	imes 2 / 10. Each turns a hard division into a few doublings plus a decimal shift.

Divide 9000 by 125 without dividing

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