The height of a building is sixty-five over seven meters. Write that height as a mixed number.
So we’ve been given our measurement, our height, in meters. And that, in this case, is a top heavy or an improper fraction. And the question is asking us to convert that into a height as a mixed number. Now a mixed number is a number that’s got a whole part and then to that we add a fractional part, which is less than one. So we need to analyse sixty-five over seven and split it down into a whole number plus a fractional number.
So we can visualize this as some whole meters plus a fraction of a meter. Now each of these whole meters are gonna be split into sevenths, because our denominator on our improper fraction is seven. So each of those whole meters could be split into seven. And then we’ll have some of the sevenths of a meter left over which are going to make up our fractional part. Now at this stage, I don’t know how many whole meters we’re gonna have, but each whole meter is seven seven seven meter. So we’ve got seven seventh of a meter, plus another seven seven seventh of a meter, plus another seven seven seventh of a meter and so on, and finally another seven seven seventh of a meter. And then we’re gonna have some number of other sevenths left over. So the first thing we need to address is how many of these seven seven sevenths of a meter are we gonna get out of our sixty-five sevenths of a meter.
So for the whole part, how many times does seven go into sixty-five? Well seven times nine is sixty-three, so I could have nine lots of seven. Seven times ten is seventy, so that would be too many. Seventy is bigger than sixty-five. So the largest whole number that I can multiply seven by and get an answer of sixty-five or less is nine, so nine is gonna be the whole part of our answer. So the whole number accounts for sixty-three sevenths, but I want sixty-five sevenths. So to work out the fractional part, I need to find the difference between these two. So that’s sixty-five minus sixty-three sevenths, which is two-sevenths. So to get our mixed number, all I have to do is add the nine for the whole number to the two-seventh we’ve got here. And that gives us our answer of nine and two-sevenths meters.