Analyze the fractions to be compared and ordered, by category:
positive improper fractions: 359/15, 350/10, 337/19, 252/18, 189/18, 204/21, 113/17, 69/21, 41/21
Calculate the expanding number of each fraction:
Divide the LCM by the denominator of each fraction.
359/15 : 67,830 ÷ 15 = (2 × 3 × 5 × 7 × 17 × 19) ÷ (3 × 5) = 4,522
35 : 67,830 ÷ 1 = (2 × 3 × 5 × 7 × 17 × 19) ÷ 1 = 67,830
337/19 : 67,830 ÷ 19 = (2 × 3 × 5 × 7 × 17 × 19) ÷ 19 = 3,570
14 : 67,830 ÷ 1 = (2 × 3 × 5 × 7 × 17 × 19) ÷ 1 = 67,830
21/2 : 67,830 ÷ 2 = (2 × 3 × 5 × 7 × 17 × 19) ÷ 2 = 33,915
68/7 : 67,830 ÷ 7 = (2 × 3 × 5 × 7 × 17 × 19) ÷ 7 = 9,690
113/17 : 67,830 ÷ 17 = (2 × 3 × 5 × 7 × 17 × 19) ÷ 17 = 3,990
23/7 : 67,830 ÷ 7 = (2 × 3 × 5 × 7 × 17 × 19) ÷ 7 = 9,690
41/21 : 67,830 ÷ 21 = (2 × 3 × 5 × 7 × 17 × 19) ÷ (3 × 7) = 3,230
Make the fractions' denominators the same:
Expand each fraction: multiply both its numerator and denominator by its corresponding expanding number, calculated at the step 2, above.
This way all the fractions will have the same denominator:
359/15 = (4,522 × 359)/(4,522 × 15) = 1,623,398/67,830
35/1 = (67,830 × 35)/(67,830 × 1) = 2,374,050/67,830
337/19 = (3,570 × 337)/(3,570 × 19) = 1,203,090/67,830
14/1 = (67,830 × 14)/(67,830 × 1) = 949,620/67,830
21/2 = (33,915 × 21)/(33,915 × 2) = 712,215/67,830
68/7 = (9,690 × 68)/(9,690 × 7) = 658,920/67,830
113/17 = (3,990 × 113)/(3,990 × 17) = 450,870/67,830
23/7 = (9,690 × 23)/(9,690 × 7) = 222,870/67,830
41/21 = (3,230 × 41)/(3,230 × 21) = 132,430/67,830