Menu Compare and sort in ascending order the set of the ordinary fractions: ^{67} /_{121} , ^{20} /_{23} , ^{21} /_{20} . Ordinary fractions compared and sorted in ascending order, result explained below

Sort: ^{67} /_{121} , ^{20} /_{23} , ^{21} /_{20}

The operation of sorting fractions in ascending order: ^{67} /_{121} , ^{20} /_{23} , ^{21} /_{20} Analyze the fractions to be compared and ordered, by category:

positive proper fractions: ^{67} /_{121} , ^{20} /_{23} ; 1 positive improper fraction: ^{21} /_{20} ; How to sort and order fractions by categories:

Any positive proper fraction is smaller than any positive improper fraction Sort the positive proper fractions: ^{67} /_{121} and ^{20} /_{23}

Reduce (simplify) fractions to their lowest terms equivalents:

^{67} /_{121} already reduced to the lowest terms; the numerator and denominator have no common prime factors: 67 is a prime number; 121 = 11^{2} ; ^{20} /_{23} already reduced to the lowest terms; the numerator and denominator have no common prime factors: 20 = 2^{2} × 5; 23 is a prime number; To sort fractions, build them up to the same numerator. Calculate LCM, the least common multiple of the fractions' numerators LCM will be the common numerator of the compared fractions.

The prime factorization of the numerators: 67 is a prime number 20 = 2^{2} × 5 Multiply all the unique prime factors, by the largest exponents: LCM (67 , 20 ) = 2^{2} × 5 × 67 = 1,340

Calculate the expanding number of each fraction

Divide LCM by the numerator of each fraction: For fraction: ^{67} /_{121} is 1,340 ÷ 67 = (2^{2} × 5 × 67) ÷ 67 = 20 For fraction: ^{20} /_{23} is 1,340 ÷ 20 = (2^{2} × 5 × 67) ÷ (2^{2} × 5) = 67 Expand the fractions Build up all the fractions to the same numerator (which is LCM). Multiply the numerators and denominators by their expanding number:

^{67} /_{121} = ^{(20 × 67)} /_{(20 × 121)} = ^{1,340} /_{2,420} ^{20} /_{23} = ^{(67 × 20)} /_{(67 × 23)} = ^{1,340} /_{1,541} The fractions have the same numerator, compare their denominators. The larger the denominator the smaller the positive fraction. The fractions sorted in ascending order: ^{1,340} /_{2,420} < ^{1,340} /_{1,541} The initial fractions in ascending order: ^{67} /_{121} < ^{20} /_{23} ::: Comparing operation ::: The final answer:

Positive proper fractions, in ascending order: ^{67} /_{121} < ^{20} /_{23} All the fractions sorted in ascending order: ^{67} /_{121} < ^{20} /_{23} < ^{21} /_{20} More operations of this kind: Symbols: / fraction bar; ÷ divide; × multiply; + plus; - minus; = equal; < less than; Compare and sort ordinary fractions, online calculator

The latest fractions compared and sorted in ascending order ^{67} /_{121} , ^{20} /_{23} , ^{21} /_{20} ? Dec 03 15:41 UTC (GMT) - ^{79} /_{414} and - ^{81} /_{417} ? Dec 03 15:40 UTC (GMT) ^{2,065} /_{25} , ^{2,087} /_{40} , ^{69} /_{42} , ^{67} /_{35} , ^{67} /_{38} , ^{61} /_{38} , ^{60} /_{41} , ^{65} /_{46} , ^{61} /_{41} , ^{47} /_{72} , ^{43} /_{66} , ^{31} /_{68} ? Dec 03 15:40 UTC (GMT) ^{35} /_{34} , ^{34} /_{52} , ^{23} /_{46} , ^{28} /_{56} ? Dec 03 15:40 UTC (GMT) ^{3} /_{4} and ^{37} /_{50} ? Dec 03 15:40 UTC (GMT) ^{3} /_{4} and ^{13} /_{12} ? Dec 03 15:40 UTC (GMT) - ^{309} /_{420} and - ^{311} /_{424} ? Dec 03 15:40 UTC (GMT) ^{21} /_{32} and ^{1} /_{2} ? Dec 03 15:40 UTC (GMT) ^{1} /_{30} , ^{1} /_{4} , ^{1} /_{150} ? Dec 03 15:40 UTC (GMT) ^{7} /_{11} , ^{5} /_{8} , ^{3} /_{5} , ^{2} /_{3} ? Dec 03 15:40 UTC (GMT) - ^{773} /_{24} and - ^{778} /_{26} ? Dec 03 15:40 UTC (GMT) ^{11} /_{14} , ^{23} /_{27} , ^{105} /_{131} ? Dec 03 15:40 UTC (GMT) - ^{65} /_{15} and - ^{69} /_{21} ? Dec 03 15:40 UTC (GMT) see more... compared fractions see more... sorted fractions

Tutoring: Comparing ordinary fractions How to compare two fractions?
1. Fractions that have different signs: Any positive fraction is larger than any negative fraction: ie: ^{4} /_{25} > - ^{19} /_{2}
2. A proper and an improper fraction: Any positive improper fraction is larger than any positive proper fraction: ie: ^{44} /_{25} > 1 > ^{19} /_{200} Any negative improper fraction is smaller than any negative proper fraction: ie: - ^{44} /_{25} < -1 < - ^{19} /_{200}
3. Fractions that have both like numerators and denominators: The fractions are equal: ie: ^{89} /_{50} = ^{89} /_{50} 4. Fractions that have unlike (different) numerators but like (equal) denominators. Positive fractions : compare the numerators, the larger fraction is the one with the larger numerator: ie: ^{24} /_{25} > ^{19} /_{25} Negative fractions : compare the numerators, the larger fraction is the one with the smaller numerator: ie: - ^{19} /_{25} < - ^{17} /_{25}
5. Fractions that have unlike (different) denominators but like (equal) numerators.
Positive fractions : compare the denominators, the larger fraction is the one with the smaller denominator: ie: ^{24} /_{25} > ^{24} /_{26} Negative fractions : compare the denominators, the larger fraction is the one with the larger denominator: ie: - ^{17} /_{25} < - ^{17} /_{29}
6. Fractions that have different denominators and numerators (unlike denominators and numerators).
To compare them, fractions should be built up to the same denominator (or if it's easier, to the same numerator). More on ordinary (common) math fractions theory: