Multiply 84 by 25 without multiplying

Question

Solve in your head, no columns. What is 84 	imes 25? Aim: under 5 seconds.

Accepted Answer

Since 25 = 100/4, multiplying by 25 means multiplying by 100 and dividing by 4: 84 	imes 25 = \frac{84 	imes 100}{4} = \frac{8400}{4} = 2100. Dividing by 4 is halving twice: 8400 	o 4200 	o 2100. Equivalently, halve 84 to get 42 first, then attach the two zeros: 42 	imes 100 = 4200... but the cleaner route is 84/4 = 21, then times 100 is 2100. Takeaway. Times 25 is "append two zeros, then halve twice." Reversing it, division by 25 is "double twice, drop two zeros," the exact same fact read backwards.

Multiply 84 by 25 without multiplying

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