Round seventeen over thirty-six to the nearest quarter.
Now we’ve been given a number between zero and one, and we’ve got to round it to the nearest quarter. Well first, let’s imagine a scale from zero to one. Now if we mark that off in quarters, we’ve got zero, one quarter, two quarters, three quarters, or four quarters. Well zero is just zero, one quarter is just one quarter. But two quarters, we can simplify to a half. Three quarters doesn’t simplify, and four quarters is the same as one. So what we’ve got to do in this question is decide, which one of those seventeen thirty-sixths is nearest.
Now I’m just gonna think about how many thirty-sixths represent each of those fractions. Well no thirty-sixths is representing zero. And thirty-six thirty-sixths would represent one. And a half of thirty-six is eighteen, so eighteen thirty-sixths represents a half. And a quarter is half of a half, so half of eighteen is nine, so nine thirty-sixths represents one quarter. And that leaves us with three quarters. Well three times one quarter would be three quarters, so three lots of nine thirty-sixths are twenty-seven thirty-sixths.
So whereabouts on that scale would seventeen thirty-sixths sit? Well it would sit in here somewhere. It’s bigger than nine thirty-sixths, but it’s less than eighteen thirty-sixths. So which is it nearer to, eighteen thirty-sixths, or nine thirty-sixths? Well the difference between seventeen thirty-sixths and eighteen thirty-sixths is just one thirty-sixth. But the difference between nine thirty-sixths and seventeen thirty-sixths is eight thirty-sixths. So seventeen thirty-sixths is much closer to eighteen thirty-sixths than nine thirty-sixths.
And remember, eighteen thirty-sixths is the same as two quarters, which is equivalent to a half. So to the nearest quarter, we could say it’s two quarters, but we’d probably simplify that to a half.
So our answer is, rounded to the nearest quarter, seventeen thirty-sixths, is approximately equal to a half.