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:
- 73/660, - 78/552, - 51/143, - 142/346, - 107/252, - 38/53
Analyze the fractions to be compared and ordered, by category:
negative proper fractions: - 73/660, - 78/552, - 51/143, - 142/346, - 107/252, - 38/53
Calculate the expanding number of each fraction:
Divide the LCM by the numerator of each fraction.
- 73/660 : 13,972,113,714 ÷ 73 = (2 × 3 × 13 × 17 × 19 × 71 × 73 × 107) ÷ 73 = 191,398,818
- 13/92 : 13,972,113,714 ÷ 13 = (2 × 3 × 13 × 17 × 19 × 71 × 73 × 107) ÷ 13 = 1,074,777,978
- 51/143 : 13,972,113,714 ÷ 51 = (2 × 3 × 13 × 17 × 19 × 71 × 73 × 107) ÷ (3 × 17) = 273,963,014
- 71/173 : 13,972,113,714 ÷ 71 = (2 × 3 × 13 × 17 × 19 × 71 × 73 × 107) ÷ 71 = 196,790,334
- 107/252 : 13,972,113,714 ÷ 107 = (2 × 3 × 13 × 17 × 19 × 71 × 73 × 107) ÷ 107 = 130,580,502
- 38/53 : 13,972,113,714 ÷ 38 = (2 × 3 × 13 × 17 × 19 × 71 × 73 × 107) ÷ (2 × 19) = 367,687,203
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:
- 73/660 = - (191,398,818 × 73)/(191,398,818 × 660) = - 13,972,113,714/126,323,219,880
- 13/92 = - (1,074,777,978 × 13)/(1,074,777,978 × 92) = - 13,972,113,714/98,879,573,976
- 51/143 = - (273,963,014 × 51)/(273,963,014 × 143) = - 13,972,113,714/39,176,711,002
- 71/173 = - (196,790,334 × 71)/(196,790,334 × 173) = - 13,972,113,714/34,044,727,782
- 107/252 = - (130,580,502 × 107)/(130,580,502 × 252) = - 13,972,113,714/32,906,286,504
- 38/53 = - (367,687,203 × 38)/(367,687,203 × 53) = - 13,972,113,714/19,487,421,759