How to Convert Units of Capacity

Okay, now we’re going to look at conversion of units of capacity. So here, we have two problems to solve. In our first problem, we need to convert the measure of 48 quarts to gallons. So, we’re converting 48 quarts into gallons.

So here we have various conversions factors below, and we’re going to be looking at the quarts to gallons, so 1 gallon = 4 quarts, and this is going to be the conversion factor that is going to help us solve this problem, all right? So we know that 1 gallon = 4 quarts. And we also know that a quart is a smaller unit than a gallon. And anytime, you’re converting a smaller into a bigger unit, okay. So a smaller unit, in this case it will be quarts to a bigger unit in our case which will be gallons, we need to divide the smaller unit by the conversion factor which in this case 4 would be our conversion factor, okay?

So, we’re converting 48 quarts into gallons, right? So we know that 48 quarts would be equivalent to our smallest unit divided by our conversion factor. So our smallest is 48 divided by our conversion factor which is 4, and we’re converting into gallons. Okay, so 48/4 = 12 gallons. Okay? So 48 quarts is equal to 12 gallons.

We can also do the conversion using the method of proportion. So, let’s put 48 quarts equal, be expressed as n gallons. So that’s like 48 quarts be expressed as n gallons. So the ratio is 48 quarts / n gallons. And the conversion factor between a quart and a gallon is also a ratio, right? So we know that, so 4 quarts = 1 gallon. So the ratio is 4 quarts / 1 gallon. And here, that set up our proportion , right? So we equate our ratios, so 48 quarts is equivalent to how many gallons? Equals 4 quarts / 1 gallon, okay? And so we’re solving for n, all right?

So now we’re going to find our cross-product. So 48 x 1 = 4 x n. 48 x 1 = 48 and 4 x n = 4n and then we divide both sides by 4 and that gives us 48/4 = 12n, and we know that n is our number of gallons, so we have 12 gallons. Okay? So here we were able to convert quarts into gallons using two different methods. All right, so one method, we took our smallest unit, and divided it by the conversion factor. And then here we used the method of proportion.

Let’s move on to our second problem. So, now we’re converting two gallons into pints. Okay, so here we’re looking at gallons and pints. All right, so in this part of the problem, we’re converting gallons to pints. We want to know how many pints into gallons. But if we look at the table, it tells us that we know how many gallons equal quarts, right? So we need to know how many gallons equals pints. So we know, 1 gallon = 4 quarts and we know that 1 quart = 2 pints, okay? So, since 1 quart = 2 pints, then 4 quarts = 2 x 4 = 8 pints. All right, so now we know that 1 gallon = 8 pints, okay? Because we know that 4 quarts = 1 gallon. So 4 quarts = 8 pints, so that means 1 gallon = 8 pints, okay?

Now, we’re ready to convert our gallons into pints. So a gallon is a bigger unit than a pint. So when you’re converting a bigger unit, into a smaller unit, we need to multiply the bigger unit by the conversion factor. So in this case, our conversion factor will be 8 pints. So our bigger unit is 2 gallons, and our conversion unit is 8 pints, okay? So we’re taking 2 gallons = 2 x 8 pints, and this will give us our pints, so 2 gallons = 16 pints.

Again, we can solve this by using the method of proportion as well. So let’s let 2 gallons be expressed by n pints, so we know that the ratio is expressed 2 gallons / n pints. And the conversion factor between a gallon and a pint is also a ratio, right? And we said that 1 gallon = 8 pints. So that would mean 1 gallon = 8 pints. And we’re going to make these equal. So we set up the proportion and equate our two ratios, all right.

So now, we’re going to equate the cross-products. We go 2 x 8 = 1n and 2 x 8 = 16 and 1 x n = n and we know that n is pints, so it would be 16 pints. So here, we were able to solve, again, using two different methods. One we used the method of proportion and one we took our biggest unit and multiplied it by our conversion factor. Okay? So we used the following conversion factors to convert between the various units of capacity right? And to convert, remember to convert a smaller unit into a bigger unit, we divide the smaller unit by the conversion factor. And to convert a bigger unit into a smaller unit, we take our bigger unit and multiply it by the conversion factor, all right?

And we can also use our method of proportion just like we did in our two problems, right? We can use our method of proportion to convert one unit to another. And remember that one of the ratios used in the proportion is the conversion factor.