Estimate ten-elevenths plus one-seventh by rounding each fraction to the nearest half.
What does it mean to the nearest half? For this problem, we’ll have three main choices if we’re gonna estimate to the nearest half: we could have zero halves or just zero; we could have one-half or two halves. And what we wanna do is to see where the fractions we’re working with fall on a number line like this.
Whichever number they’re closest to — whichever half they’re closest to — zero, one-half, or two halves; that’s what we’ll use for rounding. Ten-elevenths is nearly eleven-elevenths; it is almost one. So for rounding purposes, we’ll consider ten-elevenths one. Ten-elevenths is about one. One-seventh is actually closest to zero.
I know that three and a half sevenths would be equal to one-half. One-seventh is much closer to zero than it is to one-half. So for rounding, we round one-seventh to zero. And then we estimate. So we add the two together: one plus zero equals one. This is the estimation for ten-elevenths plus one-seventh.