By rounding each fraction to the nearest whole number, estimate the sum of three and one-third, four and one-twelfth, and nine and eight-elevenths.
We need to take each of these mixed numbers and round them to the nearest whole number. After that, we’ll be able to add these three rounded whole numbers together.
Let’s start with three and one-third. Three whole pieces plus one-third of a piece. You can visualise that one-third in this circle. Now in order for us to round this one-third up, it would need to be greater than or equal to fifty percent of our circle. It would need to be at least half of our circle.
But one-third is not half or more; one-third is a less than half of our circle, which means that three and one-third would round down to three. The nearest whole number to three and one third is three.
Next step, we have four and one-twelfth, four whole pieces and then one-twelfth of a piece. Again one-twelfth is less than half, and so the nearest whole number to four and one-twelfth is four. Four and one-twelfth rounds down to four. And our last piece, nine and eight-elevenths.
Here is our representation of nine wholes plus eight-elevenths of another one. We can recognize that eight-elevenths is more than half. So we want to round nine and eight-elevenths to the nearest whole number; it will round up to 10. Nine and eight-elevenths to the nearest whole number is 10.
We can’t forget that the original question is asking for the sum of these three values rounded to the nearest whole number. So now we need to add three plus four plus 10 equals 17. By rounding each fraction to the nearest whole number, we found that the sum would be 17.