Answer

Factor all the denominators.

10 = 2 × 5

15 = 3 × 5

       20 = 2 × 2 × 5

25 = 5 × 5

       30 = 2 × 3 × 5
 

The least common multiple of 10, 15, 20, 25, and 30 is
 

2 × 2 × 3 × 3 × 5 × 5 = 300

So, 300 is the common denominator. Divide 300 by each denominator.
 

300 ÷ 10 = 30
300 ÷ 15 = 20
300 ÷ 20 = 15
300 ÷ 25 = 12
300 ÷ 30 = 10

Multiply the denominators and numerators of the numbers by 30, 20, 15, 12, and 10 as below.

 

=
 

=
 

– =
 

– =
 

=
 

Then,

=
 

=
 

– =
 

– =
 

=
 

Now, all numbers have the same denominator. Order the numerators from smaller to larger. You can also order them from larger to the smaller. Here is their order.
 

–255, –252, 210, 220, 230.
 

Now, order the fractions corresponding to the order of the numerators above.
 

– < – < < < .

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