Answer:
-7/9, -4/9, 1/9, 1/2
There's no change as this list is already from smallest to largest
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Explanation:
We can get each denominator to 18 as this is the LCD (lowest common denominator)
-7/9 = -14/18 ... multiply top and bottom by 2
-4/9 = -8/18 ... multiply top and bottom by 2
1/9 = 2/18 ... multiply top and bottom by 2
1/2 = 9/18 ... multiply top and bottom by 9
We now have to sort this list {-14/18, -8/18, 2/18, 9/18}
Which is the same as sorting {-14, -8, 2, 9} since we can focus solely on the numerators. This only applies when the denominators are the same.
The list {-14, -8, 2, 9} is already sorted from smallest to largest. Think of a number line. We would have -14 as the left most value, then -8 is next, followed by 2 and then 9.
So the original list of fractions {-7/9, -4/9, 1/9, 1/2} is already sorted from smallest to largest.
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An alternative is to use your calculator to see that
-7/9 = -0.78 approximately
-4/9 = -0.44 approximately
1/9 = 0.11 approximately
1/2 = 0.50
The order from least to greatest is
-0.78, -0.44, 0.11, 0.50
The -0.78 is smaller than -0.44 since its further away from 0
So the order would be
-7/9, -4/9, 1/9, 1/2
and there's no change from the original order your teacher gave you.
