Divide 4836 by 12.5 in your head, then give the same reciprocal shortcut for dividing by 25 and by 6.25.

Divide 4836 by 12.5 in your head, then give the same reciprocal shortcut for dividing by 25 and by 6.25.

Approach: Replace the awkward divisor with a power of two over a power of ten, so the division becomes repeated doubling and a shift of the decimal point.

386.88. Dividing by 12.5 is multiplying by 8 and dividing by 100, since 12.5 is 100/8. So 4836 * 8 is 38688 and the answer is 386.88, where the multiplication by 8 is three doublings: 9672, 19344, 38688. The same reciprocal trick covers the rest of the desk divisors, since 1/25 = 4/100, 1/6.25 = 16/100, 1/5 = 2/10 and 1/2.5 = 4/10. Every one of them turns division into doubling, which is the operation least likely to break under a clock. The only step where errors happen is the decimal placement, so fix the order of magnitude first: 4836/12.5 sits near 4800/12, which is 400, so the answer carries three digits before the point.

Follow-up: What is 4836 divided by 3.125, and how many doublings does that take?

Key concepts: reciprocal trick, doubling, decimal placement.