MathBench > Measurement

Follow the Units

Doing the two-step

angry chickenDeep Throat: You'll have to figure that on your own.

Bob Woodward: Look, I'm tired of your chicken sh** games! I don't want hints! I need to know what you know!

Deep Throat: [reluctantly] ... the money... everything. ... It leads everywhere. Get out your notebook. There's more. I think your lives are in danger.

dance patternSo far we've only done one conversion -- we changed miles to feet. On this page, we're going to tackle the whole problem -- changing miles/hr to feet/minute. Ready? Strap on your seatbelt, cuz 4.5 mph is suddenly gonna sound a whole lot faster...

Our basic strategy is going to be, take the whole fraction (4.5 miles/hr), and run it through one conversion for each unit that needs to change.

conversion #1

In this case, we have 2 units that need to change -- miles and hours. So we'll have to go through 2 conversions.

conversion #2

Above is a sort of intermediate result -- the miles have been converted, but the hours haven't, yet. So let's fix that. First, make a fraction-that-equals-1 using minutes and hours...

So which one is it? Let's give them each a test drive:

The moral of the story is the same as it was before -- follow the units! The first fraction didn't work out because we couldn't cancel the units. The second fraction works because we CAN cancel. And so we have our answer.

The faster 2-step

You don't need to do two separate equations for this. Instead, you can simply chain both conversions onto the starting value, like this: