# How to Use Proportional Relationships for Conversions

When converting between two different units, you will need to use a proportional relationship. For instance, when converting 12 hours to minutes, take the variable and put it over the unit you want to convert. In this case m/12 hours. Then set this equal to another ratio, which will be 60 minutes/1 hour. The multiply each side by 12 hours and you will get 12×60=720 minutes.

## Conversions Using Proportional Relationships

When converting between two different units, it is very simple just to use a proportional relationship to do that conversion. A proportion is two ratios set equal to each other. What we’re going to do with this first ratio is take our variable, which we’re going to use m this time, (actually going to scoot this over a little bit so we have some more room) we’re going to do the variable on top, (it could be m, could be x, could be y) in this case just put m because we’re looking for minutes (we’re converting from 12 hours to minutes).

If someone says they got 12 hours of sleep last night, you’re like, “Wow, how many minutes is that?” You’re trying to figure that out. We put what we already know, 12 hours, on the bottom, and then we set it equal to another ratio. In this case, it’s going to be the conversion ratio of 60 minutes over 1 hour, (so 60 minutes equals 1 hour) and then we want to know how many minutes equals 12 hours.

We have two ratios set equal to each other, and since we know all this other information, except for how many minutes equals 12 hours, we’re going to be able to find out what that variable is. We multiply each side by the denominator 12 hours, so 12 hours and 12 hours cross out, so m is only left over there.

Then multiply this side by 12 hours, so hours and hours cross out because those are like units, so 12 times 60 you need to figure out what that is. We multiply here and we find out that’s 720, (so we get 720) but then we notice there’s a 1 down here, so we need to divide that 720 divided by 1. It’s still 720, so we get 720 minutes.

Remember we had m left over here, so the variable m equals 720 minutes. Now over here, we’re trying to convert 8 weeks to days, so we could use any type of variable, (d to stand for days) I’m just going to use x, over 8 weeks. Then we’re going to set it equal to our conversion ratio, which is 7 days equals 1 week.

We multiply each side by 8 weeks, those cross out, multiply this side, these units cross out, so we get 7 times 8 is 56, and the unit we have left right here is days, so we do 56 days, and we take our variable x, x equals 56 days. Now, say we want to convert 96 inches to feet, so we’re converting two different units of measurement—two different ways to measure length.

We’re going to put f over here, to stand for feet. We’re going to put 96 inches on the bottom because that’s what we already know. Then we’re going to do the conversion ratio, so 1 foot equals 12 inches. We multiply both sides by 96.

If we do like we did earlier, we just multiply by the numerator, 96 times 1 is still 96, but look we have to divide by 12, so these units cross out but that number’s still there, so 96 divided by 12 is 8, so f equals 8, and we need to know which units to use. Well, inches have crossed out but we still have feet, so the answer here is 8 feet.

Now you may be wondering how to set up the **conversion ratios**, or both these ratios actually, as far as what to put on top. Well just remember this, when you’re converting from a smaller unit to a larger unit you’re going to use division, like inches to feet, you’re going to need to use division like we did here, (from smaller to larger) but when we convert from something larger to smaller, we need to use multiplication.

This may seem kind of opposite, but the reason is because when you’re converting from a larger unit to a smaller unit, the number is going to have to get bigger because you’re now using a smaller number, so you’re going to need multiplication.

When you’re converting from the smaller unit to this larger unit the number’s going to get smaller because you’re using a bigger unit, so you’re going to need to use division. Hopefully, that helps guide you when you’re setting up these proportional relationships.