Compare and sort in ascending order the set of the ordinary fractions: 62/39, 45/52, 41/59, 31/53, 31/57, 33/60, 37/64. Ordinary fractions compared and sorted in ascending order, result explained below

Sort: 62/39, 45/52, 41/59, 31/53, 31/57, 33/60, 37/64

The operation of sorting fractions in ascending order:
62/39, 45/52, 41/59, 31/53, 31/57, 33/60, 37/64

Analyze the fractions to be compared and ordered, by category:

positive proper fractions: 45/52, 41/59, 31/53, 31/57, 33/60, 37/64;


1 positive improper fraction: 62/39;

How to sort and order fractions by categories:

Any positive proper fraction is smaller than


any positive improper fraction

Sort the positive proper fractions:
45/52, 41/59, 31/53, 31/57, 33/60, 37/64

Reduce (simplify) fractions to their lowest terms equivalents:

45/52 already reduced to the lowest terms;
the numerator and denominator have no common prime factors:
45 = 32 × 5;
52 = 22 × 13;


41/59 already reduced to the lowest terms;
the numerator and denominator have no common prime factors:
41 is a prime number;
59 is a prime number;


31/53 already reduced to the lowest terms;
the numerator and denominator have no common prime factors:
31 is a prime number;
53 is a prime number;


31/57 already reduced to the lowest terms;
the numerator and denominator have no common prime factors:
31 is a prime number;
57 = 3 × 19;


33/60 = (3 × 11)/(22 × 3 × 5) = ((3 × 11) ÷ 3)/((22 × 3 × 5) ÷ 3) = 11/20


37/64 already reduced to the lowest terms;
the numerator and denominator have no common prime factors:
37 is a prime number;
64 = 26;


>> Reduce (simplify) fractions to their simplest form, online calculator


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:


45 = 32 × 5


41 is a prime number


31 is a prime number


11 is a prime number


37 is a prime number


Multiply all the unique prime factors, by the largest exponents:


LCM (45, 41, 31, 11, 37) = 32 × 5 × 11 × 31 × 37 × 41 = 23,278,365

Calculate LCM, the least common multiple, online calculator


Calculate the expanding number of each fraction

Divide LCM by the numerator of each fraction:


For fraction: 45/52 is 23,278,365 ÷ 45 = (32 × 5 × 11 × 31 × 37 × 41) ÷ (32 × 5) = 517,297


For fraction: 41/59 is 23,278,365 ÷ 41 = (32 × 5 × 11 × 31 × 37 × 41) ÷ 41 = 567,765


For fraction: 31/53 is 23,278,365 ÷ 31 = (32 × 5 × 11 × 31 × 37 × 41) ÷ 31 = 750,915


For fraction: 31/57 is 23,278,365 ÷ 31 = (32 × 5 × 11 × 31 × 37 × 41) ÷ 31 = 750,915


For fraction: 11/20 is 23,278,365 ÷ 11 = (32 × 5 × 11 × 31 × 37 × 41) ÷ 11 = 2,116,215


For fraction: 37/64 is 23,278,365 ÷ 37 = (32 × 5 × 11 × 31 × 37 × 41) ÷ 37 = 629,145



Expand the fractions

Build up all the fractions to the same numerator (which is LCM).
Multiply the numerators and denominators by their expanding number:

45/52 = (517,297 × 45)/(517,297 × 52) = 23,278,365/26,899,444


41/59 = (567,765 × 41)/(567,765 × 59) = 23,278,365/33,498,135


31/53 = (750,915 × 31)/(750,915 × 53) = 23,278,365/39,798,495


31/57 = (750,915 × 31)/(750,915 × 57) = 23,278,365/42,802,155


11/20 = (2,116,215 × 11)/(2,116,215 × 20) = 23,278,365/42,324,300


37/64 = (629,145 × 37)/(629,145 × 64) = 23,278,365/40,265,280



The fractions have the same numerator, compare their denominators.

The larger the denominator the smaller the positive fraction.

The fractions sorted in ascending order:
23,278,365/42,802,155 < 23,278,365/42,324,300 < 23,278,365/40,265,280 < 23,278,365/39,798,495 < 23,278,365/33,498,135 < 23,278,365/26,899,444

The initial fractions in ascending order:
31/57 < 33/60 < 37/64 < 31/53 < 41/59 < 45/52


::: Comparing operation :::
The final answer:

Positive proper fractions, in ascending order:
31/57 < 33/60 < 37/64 < 31/53 < 41/59 < 45/52

All the fractions sorted in ascending order:
31/57 < 33/60 < 37/64 < 31/53 < 41/59 < 45/52 < 62/39

More operations of this kind:

Compare and sort the fractions in ascending order:
- 38/68, - 36/72, - 41/72, - 35/59, - 43/71, - 48/64, - 73/48


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

62/39, 45/52, 41/59, 31/53, 31/57, 33/60, 37/64? Sep 19 08:03 UTC (GMT)
60/137 and 65/144? Sep 19 08:03 UTC (GMT)
42/156 and 50/166? Sep 19 08:03 UTC (GMT)
- 89/816 and - 99/824? Sep 19 08:03 UTC (GMT)
3/4 and 14/15? Sep 19 08:03 UTC (GMT)
110/7, 100/16, 92/20, 232/53, 157/53, 168/64, 166/63, 169/67, 144/63, 134/60, 99/50, 42/26, 104/56, 90/53? Sep 19 08:03 UTC (GMT)
4/20 and 12/28? Sep 19 08:03 UTC (GMT)
14/76 and 16/83? Sep 19 08:03 UTC (GMT)
- 49/68, - 91/122, - 37/60? Sep 19 08:03 UTC (GMT)
116/21 and 120/25? Sep 19 08:03 UTC (GMT)
1/10, 5/6, 2/6, 1/3? Sep 19 08:03 UTC (GMT)
- 154/170 and - 161/176? Sep 19 08:03 UTC (GMT)
- 49/68, - 91/122, - 37/60? Sep 19 08:03 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).

More on ordinary (common) math fractions theory:

(1) What is a fraction? Fractions types. How do they compare?


(2) Fractions changing form, expand and reduce (simplify) fractions


(3) Reducing fractions. The greatest common factor, GCF


(4) How to, comparing two fractions with unlike (different) numerators and denominators


(5) Sorting fractions in ascending order


(6) Adding ordinary (common, simple) fractions


(7) Subtracting ordinary (common, simple) fractions


(8) Multiplying ordinary (common, simple) fractions


(9) Fractions, theory: rational numbers