Mental math practice

You cover 5 kilometres in 27 minutes at a steady effort.

What is your pace per kilometre, in minutes?

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Pace over five kilometres

You cover 5 kilometres in 27 minutes at a steady effort.

What is your pace per kilometre, in minutes?

5.4 minutes

Dividing by five means doubling and then moving the decimal point. Twenty seven doubles to 54, and 54 shifted one place is 5.4 minutes.

Dividing by 5 is the same as multiplying by 2 and dividing by 10, because 5 is 10 over 2. Twenty seven doubles to 54, and moving the decimal point one place gives 5.4 minutes per kilometre. In minutes and seconds that is 5 minutes and 24 seconds, since 0.4 of a minute is 24 seconds. The conversion between decimal minutes and seconds trips people constantly.

A pace of 5.5 is 5 minutes 30 seconds, and a pace of 5.25 is 5 minutes 15 seconds. Multiply the decimal part by 60 rather than reading it as seconds directly, or a 5.45 pace gets mistaken for 5 minutes 45 seconds when it is really 5 minutes 27. The reverse direction is just as useful for planning a race. A target pace of 5 minutes a kilometre over 10 kilometres is 50 minutes.

Over 21.1 kilometres it is 105.5 minutes, so 1 hour 45 and a half. Multiply the pace by the distance and convert once at the end. The same doubling shortcut handles other divisors that hide a 10. Dividing by 50 is doubling and moving the point twice. Dividing by 25 is multiplying by 4 and moving the point twice. Dividing by 20 is halving and moving the point once.

Every divisor that divides a power of ten has a version of this, and it is faster than long division in all of them. For runners there is one more piece worth carrying. Pace per kilometre times 1.61 gives pace per mile, so 5.4 becomes about 8 minutes 42 seconds. Multiplying by 1.6 and adding a touch is close enough at conversational speed.

Technique: Divide by 5: double, move the point

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