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:
59/82, 64/102, 46/82, 48/74, 49/89, 67/128
Analyze the fractions to be compared and ordered, by category:
positive proper fractions: 59/82, 64/102, 46/82, 48/74, 49/89, 67/128
Calculate the expanding number of each fraction:
Divide the LCM by the numerator of each fraction.
59/82 : 427,682,976 ÷ 59 = (25 × 3 × 72 × 23 × 59 × 67) ÷ 59 = 7,248,864
32/51 : 427,682,976 ÷ 32 = (25 × 3 × 72 × 23 × 59 × 67) ÷ 25 = 13,365,093
23/41 : 427,682,976 ÷ 23 = (25 × 3 × 72 × 23 × 59 × 67) ÷ 23 = 18,594,912
24/37 : 427,682,976 ÷ 24 = (25 × 3 × 72 × 23 × 59 × 67) ÷ (23 × 3) = 17,820,124
49/89 : 427,682,976 ÷ 49 = (25 × 3 × 72 × 23 × 59 × 67) ÷ 72 = 8,728,224
67/128 : 427,682,976 ÷ 67 = (25 × 3 × 72 × 23 × 59 × 67) ÷ 67 = 6,383,328
Make the fractions' numerators 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 numerator:
59/82 = (7,248,864 × 59)/(7,248,864 × 82) = 427,682,976/594,406,848
32/51 = (13,365,093 × 32)/(13,365,093 × 51) = 427,682,976/681,619,743
23/41 = (18,594,912 × 23)/(18,594,912 × 41) = 427,682,976/762,391,392
24/37 = (17,820,124 × 24)/(17,820,124 × 37) = 427,682,976/659,344,588
49/89 = (8,728,224 × 49)/(8,728,224 × 89) = 427,682,976/776,811,936
67/128 = (6,383,328 × 67)/(6,383,328 × 128) = 427,682,976/817,065,984