Rick B. answered • 11/21/13
Tutor
New to Wyzant
Most types of Math
Hi Conny,
The key to solving conversion problems like this is to chain cancelations until you reach the desired units in the proper layout for the outcome. In this case you are starting with yd/s, but you want to end up with mi/h.
Let's look at a simpler example to get the basic idea of conversion, and then we can extend the idea to as many links of the chain as necessary.
As you are aware, if you are multiplying 2 fractions and the units in the denominator of one fraction match the units of the numerator of the other, you can cancel those units.
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Example: How many feet are in 2 yards? Or, numerically: 2 yd = ? ft
This is a much simpler conversion, but follows the same principle we will use to
solve the much longer question you originally asked.
Since the idea is to convert feet to yards, and you know the much simpler problem of how many feet are in one yard,write the ratio of how many feet are in a yard, and multiply the fractions: 2 yd * 3 ft/1 yd = ? ft
Now, you have the same unit name ('yd') in the numerator of the first fraction, and denominator of the second fraction, so you can simply cancel them: 2 yd * 3 ft/1 yd = ? ft
*Note - You cannot cancel the numbers that belong
to the units; they lead to the proper numerical con-
version. Canceling them will take you right back where
you started.
You are now left with a much simpler equation: 2 * 3 ft = ? ft
All you have to do is multiply to get the answer 2 * 3 ft = 6 ft
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Now for the much longer problem you initially posted: 264 yd/s = mi/h
In this problem, you have 2 conversions to accomplish, but the problem will follow the same algorithm (method of solving).
To go from yards to miles, you can directly convert from yards
to miles, if you know how many yards are in a mile, or you can
convert from yards, to feet, to miles. I have a hard time
remembering how many feet are in a mile, but I do know that
there are 440 yards in a quarter mile (since I used to run it in
track), so I multiply that by 4 and get 1,760 yards in a mile.
I will convert directly from yards to miles:
264 yd/s * 1 mi/1,760 yd = mi/hr
That leaves only the seconds (s) to hours (h) conversion. Convert seconds, to minutes, to hours.
60 min/1 hr * 60 s/1 min * 264 yd/1s * 1 mi/1,760 yd = mi/hr
Cancel all units where appropriate:
60 min/1 hr * 60 s/1 min * 264 yd/1s * 1 mi/1,760 yd = mi/hr
We are now left with the numbers and desired units:
60/1 hr * 60/1 * 264/1 * 1 mi/1,760 = mi/hr
Multiplying these numbers yields:
60 * 60 * 264 mi/1,760 hr = 950,400 mi/1,760 hr
Finally, simplify (divide): 950,400 mi/1,760 hr = 540 mi/hr
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The cancellations are much more obvious when you can write the numerator directly over the denominator, instead of using a slash on a computer. I recommend that you write the problem out by hand in order to get a clearer visual sense of what is going on.
Some math problems can look scary until you break them down, so remember:
* stay calm
* and take small bites. ;-)
"Yard by yard, life is hard,
inch by inch, life is a cinch!"
