Divide 720 by 15 with a scaling trick

Question

Dividing by 15 is awkward until you notice doubling makes it a divide-by-30. Solve in your head. What is 720 \div 15? Aim: under 10 seconds.

Accepted Answer

Scale numerator and denominator by 2, the quotient is unchanged, to get a clean divisor: \frac{720}{15} = \frac{1440}{30} = \frac{144}{3} = 48. So 720 \div 15 = \mathbf{48}. The step 1440/30 = 144/3 = 48 is all easy pieces. Alternatively, 15 = 	frac{30}{2}, so 720/15 = 720 	imes 2 / 30 = 1440/30 = 48. Same route. Takeaway. Scaling top and bottom by the same factor leaves a quotient unchanged, use it to turn 15 into 30, or any awkward divisor into a round one.

Divide 720 by 15 with a scaling trick

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