Multiply 35 × 16 by doubling and halving

Question

You can shuffle factors between two numbers without changing the product. Use it to make the arithmetic trivial. Solve in your head. What is 35 	imes 16? Aim: under 10 seconds.

Accepted Answer

Double one factor while halving the other, the product is unchanged, until a nice pair appears: 35 	imes 16 = 70 	imes 8 = 560. So 35 	imes 16 = \mathbf{560}. One step turned an ugly 35 	imes 16 into a clean 70 	imes 8 = 560. Alternatively push further: 70 	imes 8 = 140 	imes 4 = 280 	imes 2 = 560. Or just note 35 	imes 16 = 35 	imes 10 + 35 	imes 6 = 350 + 210 = 560 as a check. Takeaway. Halving one factor and doubling the other keeps the product fixed. Steer toward a factor of 10, 100, or a single-digit multiplier.

Multiply 35 × 16 by doubling and halving

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