To compare and sort multiple fractions, they should either have the same denominator or the same numerator.
The operation of sorting fractions in ascending order:
- 48/34, - 48/25, - 82/33, - 52/16, - 62/24, - 121/35, - 126/18, - 263/23, - 500/33, - 554/24, - 1,190/37, - 2,720/28, - 5,251/2
Analyze the fractions to be compared and ordered, by category:
negative improper fractions: - 48/34, - 48/25, - 82/33, - 52/16, - 62/24, - 121/35, - 126/18, - 263/23, - 500/33, - 554/24, - 1,190/37, - 2,720/28, - 5,251/2
Calculate the expanding number of each fraction:
Divide the LCM by the denominator of each fraction.
- 24/17 : 334,187,700 ÷ 17 = (22 × 3 × 52 × 7 × 11 × 17 × 23 × 37) ÷ 17 = 19,658,100
- 48/25 : 334,187,700 ÷ 25 = (22 × 3 × 52 × 7 × 11 × 17 × 23 × 37) ÷ 52 = 13,367,508
- 82/33 : 334,187,700 ÷ 33 = (22 × 3 × 52 × 7 × 11 × 17 × 23 × 37) ÷ (3 × 11) = 10,126,900
- 13/4 : 334,187,700 ÷ 4 = (22 × 3 × 52 × 7 × 11 × 17 × 23 × 37) ÷ 22 = 83,546,925
- 31/12 : 334,187,700 ÷ 12 = (22 × 3 × 52 × 7 × 11 × 17 × 23 × 37) ÷ (22 × 3) = 27,848,975
- 121/35 : 334,187,700 ÷ 35 = (22 × 3 × 52 × 7 × 11 × 17 × 23 × 37) ÷ (5 × 7) = 9,548,220
- 7 : 334,187,700 ÷ 1 = (22 × 3 × 52 × 7 × 11 × 17 × 23 × 37) ÷ 1 = 334,187,700
- 263/23 : 334,187,700 ÷ 23 = (22 × 3 × 52 × 7 × 11 × 17 × 23 × 37) ÷ 23 = 14,529,900
- 500/33 : 334,187,700 ÷ 33 = (22 × 3 × 52 × 7 × 11 × 17 × 23 × 37) ÷ (3 × 11) = 10,126,900
- 277/12 : 334,187,700 ÷ 12 = (22 × 3 × 52 × 7 × 11 × 17 × 23 × 37) ÷ (22 × 3) = 27,848,975
- 1,190/37 : 334,187,700 ÷ 37 = (22 × 3 × 52 × 7 × 11 × 17 × 23 × 37) ÷ 37 = 9,032,100
- 680/7 : 334,187,700 ÷ 7 = (22 × 3 × 52 × 7 × 11 × 17 × 23 × 37) ÷ 7 = 47,741,100
- 5,251/2 : 334,187,700 ÷ 2 = (22 × 3 × 52 × 7 × 11 × 17 × 23 × 37) ÷ 2 = 167,093,850
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:
- 24/17 = - (19,658,100 × 24)/(19,658,100 × 17) = - 471,794,400/334,187,700
- 48/25 = - (13,367,508 × 48)/(13,367,508 × 25) = - 641,640,384/334,187,700
- 82/33 = - (10,126,900 × 82)/(10,126,900 × 33) = - 830,405,800/334,187,700
- 13/4 = - (83,546,925 × 13)/(83,546,925 × 4) = - 1,086,110,025/334,187,700
- 31/12 = - (27,848,975 × 31)/(27,848,975 × 12) = - 863,318,225/334,187,700
- 121/35 = - (9,548,220 × 121)/(9,548,220 × 35) = - 1,155,334,620/334,187,700
- 7/1 = - (334,187,700 × 7)/(334,187,700 × 1) = - 2,339,313,900/334,187,700
- 263/23 = - (14,529,900 × 263)/(14,529,900 × 23) = - 3,821,363,700/334,187,700
- 500/33 = - (10,126,900 × 500)/(10,126,900 × 33) = - 5,063,450,000/334,187,700
- 277/12 = - (27,848,975 × 277)/(27,848,975 × 12) = - 7,714,166,075/334,187,700
- 1,190/37 = - (9,032,100 × 1,190)/(9,032,100 × 37) = - 10,748,199,000/334,187,700
- 680/7 = - (47,741,100 × 680)/(47,741,100 × 7) = - 32,463,948,000/334,187,700
- 5,251/2 = - (167,093,850 × 5,251)/(167,093,850 × 2) = - 877,409,806,350/334,187,700