Divide 21400 by 50 without dividing

Question

Solve in your head, no long division. What is 21400 \div 50? Aim: under 5 seconds.

Accepted Answer

Dividing by 50 is the same as multiplying by 2 and dividing by 100 (because 50 = 100/2): \frac{21400}{50} = \frac{21400 	imes 2}{100} = \frac{42800}{100} = 428. Doubling is trivial and dividing by 100 is a two-place decimal shift, so the whole thing is nearly instant. Takeaway. Rewrite a divisor as "round number over small factor": 50 = 100/2, 25 = 100/4, 5 = 10/2, 125 = 1000/8. Then you multiply by the small factor and shift the decimal, which is always faster than dividing directly.

Divide 21400 by 50 without dividing

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