This is something we do on a fairly regular basis. I need 3 feet of a certain material, but it’s only sold by the inch, how many inches do I need? To be able to do this, we first need to know the basic unit rates.
12 inches / 1 foot
3 feet / 1 yard
36 inches / 1 yard
5280 feet / 1 mile
1760 yards / 1 mile
We may also be asked to do this with times as well.
60 seconds / 1 minute
60 minutes / 1 hour
24 hours / 1 day
365 days / 1 year
From there it’s just a matter of setting up a proportion. Let’s say I need 8 feet of a material, but the material is sold by inches. The proportion would be set up like this:
Notice how I have set up the proportion. I know I want to convert feet to inches, so I put the unit rate for the conversion I want on the left. On the other side, I have my unknown over how many feet I need. Note, I have the same units on top and bottom. Like all proportions, I have to have the same units on the top of both rations, and the same units on the bottom of both ratios, otherwise it will not work. From there, I can solve it as any proportion, by cross multiplying and solving the equation.
So, there are 96 inches in 8 feet. Here is another example.
How many seconds are there in 4.5 minutes?
So, there are 270 seconds in 4.6 minutes.