# Converting between Inches, Feet, Yards and Miles 128-2.4

This video is provided as supplementary material for courses taught at Howard Community College and in this video I’m going to show how to convert between inches, feet, yards and miles. Now before we can actually do a problem, we have to understand how these four units of measure relate to each other. So let’s start with that. One foot is equal to 12 inches. Another way to say this would be that there are 12 inches in one foot. One yard is equal to 3 feet. Now very often yards are expressed in terms of inches. So we can find what one yard equals in inches.

We can do it this way: if one yard equals 3 feet and each of those 3 feet has 12 inches, if we multiply 3 times 12 inches, we should get the number ofinches in a yard. So 3 times 12 is 36. That’s going to be 36 inches. We’ve also got miles. One mile is equal to 5280 feet. So these are some facts that you should have memorized. So when you get a chance, make sure you commit them to memory. Now let’s go on to a problem. Convert 4 yards to inches. Here’s how I’m going to do this.

I’ll write 4 yards. I can abbreviate yards as yds, and just to make this clear, I’m go to make that into a fraction has a one as its denominator. And now I’ll multiply it by another fraction. What I’m going to multiply it by is the fraction 36 inches — and I’m going to keep that unit of measure — 36 inches over one yard. Now this fraction equals one, because 36 inches is the same as one yard. When my numerator and denominator are the same, then the fraction equals one. So all I’m doing is taking 4 yards and multiplying it by one.

Now when I do this, the next step I’ll do is cancel out anything I have in common in the numerator and denominator, and both have yards. So I’ll cross our the yards the numerator, cross it out from the denominator, and now my denominators are just ones, which means I can just multiply the numerators. That’s going to be 4 times 36 inches. 4 times 36 is 144, and the unit of measure was inches. Now let’s do this is second way.

Let’s convert the yards first into feet and then the feet into inches. Let’s see if we come up with the same answer. So once again, I’ll write 4 yards as a fraction. It’s not absolutely necessary. And now I want to convert this into feet. So the unit I want to convert into its going to be unit I put in the numerator. So let’s see: one yards is 3 feet. So I’ll have three feet as the numerator. I’m converting out of yards, so I’ll have one yard in the denominator. So I’m multiplying 4 yards times times feet over one yard. 3 feet is the same as one yard, some I’m just multiplying by one. But after I do that I’ll want to convert feet to inches. Now there are 12 inches in every foot. So 12 inches equals one foot. So 12 inches over one foot is a fraction equal to one.

Now I’ve got my multiplication problem. I can cross out things that I have in common. So I’ve got yards in the numerator and yards in the denominator, feet in the numerator, feet in the denominator. All of my denominators are now one, so I just have to multiply the numerators. I’ve got 4 times 3, that’s 12, times 12 again is 144, and the unit of measure is inches. So that’s 144 inches.

It’s the same thing I got the first time. Let’s do one more. Let’s convert 48 inches into miles. So I’ll start out with 48 inches. I’ll make that into a fraction and I don’t know how many inches are in a mile, so I’ll have to convert 48 inches first into feet. So let’s see. One foot is the equivalent of 12 inches. So I’ll make a fraction with one foot as the numerator, because that’s what I want to turn my number into, into feet, and 12 inches is the denominator, that’s what I want to cancel out, the inches, and that fraction, again, equals one because one foot is the same as 12 inches.

So it’s a fraction with the numerator and denominator the same. Once I get the number feet, I’m going to want to convert that into miles. So one mile — I’ll make that the numerator — is equivalent to 5280 feet, and that’ll be the denominator. Now let’s get rid of inches, which I have in both the numerator and denominator. So I can cancel them out. We’ll get rid of feet, which I have in the numerator and denominator. We can simplify this a bit more. I’ve got 48 as a numerator and 12 as a denominator. So I can divide both of those numbers by 12. 48 divided by 12 is 4, and 12 divided by 12 is one. And now when I multiply this, I get 4 times one times one mile. Let’s put that down here. So that’s 4. Mile is the unit of measure I have left. And that’s going to be divided by one times one times 5,280. So I’ve got 4 over 5,280 with miles as the unit of measure. So let’s see if we can simplify this. I can divide 4 by 4, and I know I can divide 5,280 by 4. Let’s see what I get.

4 divided by 4 is 1. Dividing 4 into 5280… 4 goes into 5 one time with a one remainder. 4 goes into 12 3 times with no remainder, it goes into 8 2 times, and it goes into zero zero times. So I’m going to have one over 1320. I’ll have that faction of a mile. Okay, so that’s basically how this works. As I said, you have to know the conversion facts before you can do this. Once you know those facts, it’s a fairly simple and straightforward process. Okay, take care. I’ll see you next time..

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