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# How would I order this from least to greatest.. -8/9, -7/8, -22/25.. Thanks!

brandih | eNotes Employee

Posted September 5, 2013 at 2:32 AM via web

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How would I order this from least to greatest.. -8/9, -7/8, -22/25..

Thanks!

Tagged with math, order

tjbrewer | Elementary School Teacher | (Level 2) Associate Educator

Posted September 5, 2013 at 2:55 AM (Answer #1)

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I understand how this can be confusing.  First let's ignore the negative (-) signs for a moment and focus on the fractions themselves.  We need to know which one is greatest (i.e. closest to one).  Since they all have different numerators and different denominators, we have to find equivalent fractions with a common denominator.  An easy way to a common denominator, is to find the product of all the denominators.  8x9x25=1800.  So we convert all our fractions to 1800s

`(8 xx 200)/(9 xx 200)=1600/1800`` `

`(7 xx 225)/(8 xx 225)=1575/1800`

`(22 xx 72)/(25 xx 72)= 1584/1800` Now it is clear that from least to greatest the order is `1575/1800` or `7/8` , `1584/1800` or `22/25` and `1600/1800` or `8/9`

Now we take into account that they are all negatives.  An easy way to remember negative patterns is, "Less is more."  So the order would be reversed, from least to greatest the fractions would be:

`-8/9, -22/25, -7/8`

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