Video: Arranging Given Fractions and Mixed Numbers with Unlike Denominators in Descending Order

Arrange the elements in the set {1 2/3, −1/8, 1 1/9, −1/2} in descending order.


Video Transcript

Arrange the elements in the set one and two-thirds, negative one-eighth, one and one-ninth, and negative one-half in descending order.

Descending order is from greatest to least. And so we notice about all of these values that they do not have a common denominator. But if we think about them in terms of the number line, we know that negative one-half needs to go to the left of zero and one and two-thirds needs to go to the right of zero. At this point, we’ll need to compare negative one-half and negative one-eighth and one and one-ninth and one and two-thirds.

Starting with the negatives, we have negative one-half and negative one-eighth. If we multiply the numerator and the denominator by four, for negative one-half, it becomes negative four over eight. Now, because these values are negative, we need to be very careful how we compare them. Negative one-eighth will be closer to zero on a number line than negative four-eighths. So they belong on the number line like this. If we’re going in descending order, from greatest to least, negative one-eighth would belong on the list before negative one-half.

But now we need to compare the two positive values. One and one-ninth and one and two-thirds both have the whole-number portion of one. And that means to compare them, we’ll simply need to compare their fractions. These two fractions do not have a common denominator. But if we multiply two-thirds by three in the numerator and the denominator, this mixed number becomes one and six-ninths. One and six-ninths is larger than one and one-ninth. And so we could place them on our number line like this. And we’re ready to write them in descending order.

Descending order is greatest to least. We want to again write it in the set notation, so we’ll open the brackets. The largest of the values is one and two-thirds, then one and one-ninth, then negative one-eighth, and negative one-half. We’ll close the brackets. And we’ve rearranged this set into descending order.

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