Question Video: Subtraction of Rational Numbers into Simplest Form

Calculate (9 3/12) − (2 8/12). Give your answer as a mixed number.

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Video Transcript

Calculate nine and three twelfths minus two and eight twelfths. Give your answer as a mixed number.

We’re trying to subtract a mixed number from a mixed number. And in order to do that, there are a few things we should think about. First of all, for the fraction portions of our mixed number, do they have a common denominator? In this case, they do; both have a denominator of 12. After that, we could convert both of these mixed numbers into improper fractions. However, since our final answer needs to be written in the form of a mixed number, there’s also another strategy we could use.

We could try and subtract eight twelfths from three twelfths, but we’ve run into a problem because eight twelfths is larger than three twelfths. So, we’ll need to rewrite at least the nine and three twelfths. One way to do that is to take one away from our whole number nine and make that eight. And when we do that, we can add 12 to our numerator. This is because we’ve taken one from our whole number, which is equal to twelve twelfths. And twelve twelfths plus three twelfths equal fifteen twelfths. Eight and fifteen twelfths is equal to nine and three twelfths. It’s just written in a different format.

Then, we can say eight and fifteen twelfths minus two and eight twelfths. In this case, we can subtract the whole numbers and the mixed number pieces. To subtract eight twelfths from fifteen twelfths, we say 15 minus eight equals seven. And the denominator stays the same, 12. And now, we work on the whole number pieces. Eight minus two equals six. And that means nine and three twelfths minus two and eight twelfths will equal six and seven twelfths. This is already in the form of a mixed number. And seven twelfths cannot be reduced any further, making six and seven twelfths our final answer.

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