# Converting yards into inches | Ratios, proportions, units, and rates | Pre-Algebra | Khan Academy

How many inches are there in 4 whole and 1/2 yards? Let me write the task on the board. 4 whole and 1/2 yard. When we have fractions and will we multiply and divide by fractions, really complicates the matter if there are mixed numbers. So from the very beginning I want to turn this into irregular liver. Let me do it here in the upper right corner. What is equal to 4 whole 1/2 as an irregular fraction? We will still have 2 as the denominator. So 2 over 4 is 8. 8/2 is the same 4.

Let’s rewrite this, just for the sake of clarity. 4 is the same thing as 8/2. This is the same thing as 4. And then you have this plus 1/2. This will give you 9/2. The quickest way to do it: 2 over 4 is 8, 8 plus 1 is 9. 4 and 1/2 is the same as 9/2. 4 whole and 1/2 yards is the same thing as … Let me write it up here – 9/2, 9/2 yards. Now we want to convert it to inches.

We can take this little by little, maybe we transform this in feet first and then after we have it in feet, we can turn it into inches. To turn it into feet, we just have to remember that there are 3 feet in every 1 yard. So, let me write this down. There are 3 feet in one yard. And if we had multiplied 9/2 yards by 3 feet, that yard it would be in the numerator. It would be divided into this yard and they would be shortened, and we would just be left with feet. So, we know we have to multiply by 3. You could say it’s 3 feet for every 1 yard if it does simpler, or just 3 feet per yard. Another way to look at this is the more yards you have, you will have more feet, right? There are 3 feet in one yard. So if I have 1 yard, I will have 3 feet. If I have 2 yards, I will have 6 feet. You should always keep this in mind, well yes, we multiply by 3. This also makes sense. If we multiply by 3 here up here – 9 by 3 is 27/2.

Let’s write it. Let’s take it step by step, not skip it. This is equal to 9/2 by 3/1 yards. These yards here, I’ll make them in orange. Yards by feet to yards. Yards by feet to yards. The yards are shrinking and we are left with 9 by 3 equal to 27/2 feet. We learned that 4 whole and 1/2 yards is 27/2 feet. And that makes sense, because we have to have more feet than yards. Actually three times as much, so everything makes sense. 27/2 is 3 by 9/2. We now have 27/2 feet and we want to turn that into inches. We just have to keep in mind that there are 12 inches in one yard. We will multiply by 12 because no matter how many feet we have, we will have 12 times more inches. If we have 1 foot, we will have 12 inches, 2 feet – 24 inches. 27/2 feet, we will multiply them by 12 to get inches. Since this will be 12, we will make sure that stick to the measure: 12 inches per foot. A feet and a foot is just a plural and singular of the same word.

This is the same measure. This will be shortened. This will be… If we just rearrange the multiplication, to look at it as if everything is multiplying and when you multiply a bunch of things, the order doesn’t matter. So that’s equal to 27/2 by 12 feet. I’m just swapping orders. Feet by inch, divided by feet. Feet or feet, just the same word. Feet and feet are shortened, they are the same unit. And you have 27 by 12 divided by 2 inches. What we can do here is that our final answer will be 27 by 12/2 inches. And before we multiply 27 by 12, and then divide by 2, we immediately see: Okay, I can divide 12 by 2 and 2 at 2 and this makes our calculations easier. 12 divided by 2 is 6, 2 divided by 2 is 1. This is 27 by 6 inches and let’s find out what is this. 27 to 6. 7 by 6 is 42. 2 over 6 is 12, plus 4 is 16. That’s equal to 162 inches, which makes sense. 4 whole and 1/2 yards, which brings us to this number here: 27 divided by 2 is 13 whole and 1/2 feet. you multiply that by 12 and that makes sense. You will have many inches.

162 inches. 162 inches.

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