Daniel’s room is 173 inches long. Express, in feet, his room’s length as a mixed number in simplest form.
Before we began any calculations, we have to remember that one foot equals 12 inches. And if we want to convert 173 inches into feet, we have to divide 173 by 12. There are a few different ways to do this. But let’s start with long division.
We need to divide 173 by 12. We know that 12 can divide into 17 one time. And then, we need to subtract 12 from 17 which is five. From there, we bring down our three. And we’ll ask, how many times does 12 go into 53? I know that 12 times four equals 48. And then, we need to subtract 48 from 53. We’ll borrow one from the five and we’ll subtract eight from 13, which gives us a remainder of five. 12 goes into 173 14 times with five left over.
To write this as a mixed number, we’ll have the whole number portion 14. And then, we’ll take our remainder and write it as a fraction out of our divisor. And so, that will become five 12ths. 173 inches is equal to 14 and five 12ths feet.
I did say that long division was only one way to solve this. We could write 173 as a fraction out of 12 and then simplify from there. To do that, we might break up 173 over 12 into smaller pieces that are still fractions out of 12. 144 plus 29 equals 173. So 173 over 12 is equal to 144 over 12 plus 29 over 12. But I know that 12 times 12 equals 144. And that means 144 divided by 12 will be equal to 12. So now, we have 12 and 29 12ths. But 29 12ths is still an improper fraction. So it’s not a mixed number in simplest form. Can we break 29 12ths up?
29 12ths could be written as 24 12ths plus five 12ths. And we know that 12 times two equals 24. And that means 24 over 12. 24 divided by 12 is two. And now, we have 12 plus two plus five 12ths. 12 plus two is 14 and we can’t simplify five 12ths any further. So it’s the fraction piece of our mixed number. And this confirms that the length of Daniel’s room in feet as a mixed number is 14 and five 12ths feet.