From: Tom Hibbs
To: Teacher2Teacher Public Discussion
Subject: Re: metric conversions
I would go a bit further. 1km/1000m = 8.32km/X m then the units seem to cancel(divide out, divide to 1, etc)just like the numbers and solves to X = 8320 m. Your method of ratios and the previous teacher's method of unit fractions can fit together. The idea in teaching conversion of units of measurement is to give the student a basis for unit conversions in physics, chemistry, business, and other applications without having to unlearn a method that was not general enough. We are constantly looking at km/h, miles/hour, ft/sec, and m/s and trying to see what a rate with one combination of units equals using the other combination of units. The units are dictated by the application. 8 miles/hr = X ft/sec is solved with unit fractions as (8 miles/1 hr)(1hr/60 min)(1 min/60sec)(5280 ft/1mile) = X ft/sec This is visualized better with numerator over denominator type style. The units "cancel" in numerators and denominators except ft/sec and the resulting "rate" is 8x1x1x5280 ft / 1x60x60x1 sec. The decision to multiply or divide is decided by the unit fractions.
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