How to put -7/9 and -4/9 and 1/9 and 1/2 on a number line from least to greatest

Step-by-step explanation:

Take the LCM of the denominators:

=> LCM = 18

=> -7/9 x 2/2 = -14/18

=> -4/9 x 2/2 = -8/18

=> 1/9 x 2/2 = 2/18

=> 1/2 x 9/9 = 9/18

When the number is negative, the greater the number, the smaller it is.

So, -14 is smaller than -8.

< = smaller than

=> -14/18 < -8/18 < 2/18 < 9/18

=> -7/9 < -4/9 < 1/9 < 1/2

-7/9, -4/9, 1/9, 1/2

There's no change as this list is already from smallest to largest

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.

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.

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