Video: Rounding Mixed Numbers to Whole Numbers to Estimate the Division of Integers by Mixed Numbers

12 pounds of oatmeal are going to be packaged in bags that hold 3 5/9 pounds each. By rounding to whole numbers, estimate the number of bags that will be used.

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Video Transcript

12 pounds of oatmeal are going to be packaged in bags that hold three and five-ninths pounds each. By rounding to whole numbers, estimate the number of bags that will be used.

12 pounds of oatmeal are going to be packaged into bags. And mathematically, we would represent that with division. Each bag can hold three and five-ninths pounds. By rounding to the nearest whole number, our job is to estimate 12 divided by three and five-ninths. 12 is already a whole number. And that means our first job will be to round three and five-ninths to its nearest whole number. Now, here is a visual representation of three and five-ninths. We have three whole bars. And one of the bars is divided into nine pieces, where five of them are shaded in. And we need to ask, is this fraction three and five-ninths closer to three or four on a number line.

To determine that, we first need to say, well, what is halfway between three and four. And then we ask the question, is three and five-ninths less than three and a half or greater than three and a half. If we take our denominator of nine and divide it by two, nine divided by two is four and a half. And so we could say that halfway between three and four is three and 4.5 ninths, because 4.5 over nine is one-half. But we have five out of nine. And five out of nine is greater than four and a half out of nine, which tells us that three and five-ninths is slightly more than three and a half. We can also see this in our figure, because we have slightly more shaded than half. And because three and five-ninths is a little bit closer to four, we round it, when we round to a nearest whole number, to four.

Back to the question at hand, 12 pounds of oatmeal, if they’re going to be packaged in three and five-ninths pounds bags, we round that three and five-ninths to four. Then we’ll say 12 divided by four equals three. About three bags will be used.

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