We are asked how many inches are in four and a half yards. We can do it in a couple of ways. One we could do is to see how many inches are in four yards and how many inches are there in half a yard. and this is really four plus one half yards. Or we could convert this into improper fraction first and then convert. But before I even do that, let us just think about how many inches are there in a yard. So, if I have one yard, We know that there are 3 feet for every one yard. Why am I multiplying by three? And the easiest way to think about is you are going to have a larger value over here and you are also going to want to have these units right over here cancel out. So yard is cancelling out with yard. So you have one yard is equal to three feet. Now how many inches are there in one foot? We know that there are twelve inches for every one foot. And same logic over here. Inches is a smaller unit of measurement. So it makes sense to multiply by twelve. Three feet is going to be more inches; so we multiply by twelve and also these units cancel out. Foot in the numerator, foot in the denominator. Three times twelve divided by one is thirty six inches You might have already known it, but it is nice to have the dimensions cancel out like this. We now know that one yard is equal to thirty six inches Or there are thirty six inches for every one yard. And now we can either break this down or convert this into an improper fraction. First I will break it down into four yards plus one half a yard. Four yards is going to be equal to four multiplied by thirty six inches per yard. Yard and yard cancel out. four times thirty six is a hundred and fourty four inches. That is just the four yards. And then if we do the half yard One half yard times 36 inches per yard yards cancel out. One half of thirty six is going to be eighteen inches. So four and half a yard is the same thing as four yards plus one half yard. Which is the same thing as One hundred and fourty four inches plus eighteen inches. Which is going to give us one hundred and sixty two inches. The other way to do this is: to convert this into an improper function and then multipy. If I have four and a half of anything Four is the same thing as eight halves. Four and a half is the same thing as four plus one half Four is the same thing as four over one. plus one half The common denominator is two So, four over one is the same thing as eight over two. plus one over two. This is equal to nine over two. A simple way to do is four times two is eight, and eight plus one is nine. So that gives the nine over two. So, we have nine half yards that we want to convert to inches. Nine half yards times thirty six inches per yard. Yard in the numerator, yard in the denominator. We are left with nine over two times thirty six over one inches. Divide both the numerator and the denominator by two. nine times thirty six over two inches. dividing gives nine times eighteen. Which is one hundred and sixty two inches. So, all of this simplifies to one hundred and sixty two inches. and we are done!