Express seven and five-eighths as an improper fraction.
Well, the important information in this question is seven and five-eighths and we’ve got to express it as an improper fraction. Now, if we write seven and five-eighths out in numbers, it means seven whole ones and an additional five-eighths of a whole one. Now, a number in this format is called “a mixed number.” And that’s because it’s a mixture of a whole number and a fraction of a whole number. Now, we can visualize that as seven whole objects — in our case the whole objects are little circles — and five-eighths of a whole object. Well, if I take a circle and I split it into eight equal parts and then I color in five of them and delete the other three parts, then we’ve got seven whole objects plus five-eighths of a whole object. And we’ve got to convert that number — seven and five-eighths — into an improper fraction and that sometimes called “a top heavy fraction.” So, that’s not going to have a whole number part; it’s just going to be a number on top of another number.
Now, the easiest way to approach this is to use as a denominator the same number that we had as the denominator of the fractional part of our mixed number. So, our denominator is going to be eighths. So, the question is how many eighths have we got? Well, we had five of them here — in this fractional part of a whole. And then each of those seven whole ones have got eight-eighths each. So that whole one has got eight-eighths, so is that one, and that one, and all of the other whole ones.
So as one of the five-eighths, we’ve got seven times eight-eighths. And seven times eight is fifty-six. So in the whole numbers there, we got fifty-six eighths. And in the fractional part of our number, we had five-eights. So adding those two together, in total, we got sixty-one eighths. So, there’s our answer, sixty-one eighths.
Now, just to summarize that process, first of all we decided which denominator we were going to use. Then, we multiplied the whole number by that denominator to work out how many eighths we had in seven whole ones. And then, we added on the numerator from the original fractional part of the mixed number. And adding those two together gives us our numerator in our final answer.