Compare and sort in ascending order the set of the ordinary fractions: 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. Ordinary fractions compared and sorted in ascending order, result explained below

Sort: 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

The operation of sorting fractions in ascending order:
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

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

positive improper fractions: 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;

Reduce (simplify) fractions to their lowest terms equivalents:

110/7 already reduced to the lowest terms;
the numerator and denominator have no common prime factors:
110 = 2 × 5 × 11;
7 is a prime number;


100/16 = (22 × 52)/24 = ((22 × 52) ÷ 22)/(24 ÷ 22) = 25/4


92/20 = (22 × 23)/(22 × 5) = ((22 × 23) ÷ 22)/((22 × 5) ÷ 22) = 23/5


232/53 already reduced to the lowest terms;
the numerator and denominator have no common prime factors:
232 = 23 × 29;
53 is a prime number;


157/53 already reduced to the lowest terms;
the numerator and denominator have no common prime factors:
157 is a prime number;
53 is a prime number;


168/64 = (23 × 3 × 7)/26 = ((23 × 3 × 7) ÷ 23)/(26 ÷ 23) = 21/8


166/63 already reduced to the lowest terms;
the numerator and denominator have no common prime factors:
166 = 2 × 83;
63 = 32 × 7;


169/67 already reduced to the lowest terms;
the numerator and denominator have no common prime factors:
169 = 132;
67 is a prime number;


144/63 = (24 × 32)/(32 × 7) = ((24 × 32) ÷ 32)/((32 × 7) ÷ 32) = 16/7


134/60 = (2 × 67)/(22 × 3 × 5) = ((2 × 67) ÷ 2)/((22 × 3 × 5) ÷ 2) = 67/30


99/50 already reduced to the lowest terms;
the numerator and denominator have no common prime factors:
99 = 32 × 11;
50 = 2 × 52;


42/26 = (2 × 3 × 7)/(2 × 13) = ((2 × 3 × 7) ÷ 2)/((2 × 13) ÷ 2) = 21/13


104/56 = (23 × 13)/(23 × 7) = ((23 × 13) ÷ 23)/((23 × 7) ÷ 23) = 13/7


90/53 already reduced to the lowest terms;
the numerator and denominator have no common prime factors:
90 = 2 × 32 × 5;
53 is a prime number;


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


To sort fractions in ascending order, build up their denominators the same.

Calculate LCM, the least common multiple of the denominators of the fractions.

LCM will be the common denominator of the compared fractions.
In this case, LCM is also called LCD, the least common denominator.

The prime factorization of the denominators:


7 is a prime number


4 = 22


5 is a prime number


53 is a prime number


8 = 23


63 = 32 × 7


67 is a prime number


30 = 2 × 3 × 5


50 = 2 × 52


13 is a prime number


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


LCM (7, 4, 5, 53, 8, 63, 67, 30, 50, 13) = 23 × 32 × 52 × 7 × 13 × 53 × 67 = 581,653,800

Calculate LCM, the least common multiple, online calculator


Calculate the expanding number of each fraction

Divide LCM by the denominator of each fraction:


For fraction: 110/7 is 581,653,800 ÷ 7 = (23 × 32 × 52 × 7 × 13 × 53 × 67) ÷ 7 = 83,093,400


For fraction: 25/4 is 581,653,800 ÷ 4 = (23 × 32 × 52 × 7 × 13 × 53 × 67) ÷ 22 = 145,413,450


For fraction: 23/5 is 581,653,800 ÷ 5 = (23 × 32 × 52 × 7 × 13 × 53 × 67) ÷ 5 = 116,330,760


For fraction: 232/53 is 581,653,800 ÷ 53 = (23 × 32 × 52 × 7 × 13 × 53 × 67) ÷ 53 = 10,974,600


For fraction: 157/53 is 581,653,800 ÷ 53 = (23 × 32 × 52 × 7 × 13 × 53 × 67) ÷ 53 = 10,974,600


For fraction: 21/8 is 581,653,800 ÷ 8 = (23 × 32 × 52 × 7 × 13 × 53 × 67) ÷ 23 = 72,706,725


For fraction: 166/63 is 581,653,800 ÷ 63 = (23 × 32 × 52 × 7 × 13 × 53 × 67) ÷ (32 × 7) = 9,232,600


For fraction: 169/67 is 581,653,800 ÷ 67 = (23 × 32 × 52 × 7 × 13 × 53 × 67) ÷ 67 = 8,681,400


For fraction: 16/7 is 581,653,800 ÷ 7 = (23 × 32 × 52 × 7 × 13 × 53 × 67) ÷ 7 = 83,093,400


For fraction: 67/30 is 581,653,800 ÷ 30 = (23 × 32 × 52 × 7 × 13 × 53 × 67) ÷ (2 × 3 × 5) = 19,388,460


For fraction: 99/50 is 581,653,800 ÷ 50 = (23 × 32 × 52 × 7 × 13 × 53 × 67) ÷ (2 × 52) = 11,633,076


For fraction: 21/13 is 581,653,800 ÷ 13 = (23 × 32 × 52 × 7 × 13 × 53 × 67) ÷ 13 = 44,742,600


For fraction: 13/7 is 581,653,800 ÷ 7 = (23 × 32 × 52 × 7 × 13 × 53 × 67) ÷ 7 = 83,093,400


For fraction: 90/53 is 581,653,800 ÷ 53 = (23 × 32 × 52 × 7 × 13 × 53 × 67) ÷ 53 = 10,974,600



Expand the fractions

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

110/7 = (83,093,400 × 110)/(83,093,400 × 7) = 9,140,274,000/581,653,800


25/4 = (145,413,450 × 25)/(145,413,450 × 4) = 3,635,336,250/581,653,800


23/5 = (116,330,760 × 23)/(116,330,760 × 5) = 2,675,607,480/581,653,800


232/53 = (10,974,600 × 232)/(10,974,600 × 53) = 2,546,107,200/581,653,800


157/53 = (10,974,600 × 157)/(10,974,600 × 53) = 1,723,012,200/581,653,800


21/8 = (72,706,725 × 21)/(72,706,725 × 8) = 1,526,841,225/581,653,800


166/63 = (9,232,600 × 166)/(9,232,600 × 63) = 1,532,611,600/581,653,800


169/67 = (8,681,400 × 169)/(8,681,400 × 67) = 1,467,156,600/581,653,800


16/7 = (83,093,400 × 16)/(83,093,400 × 7) = 1,329,494,400/581,653,800


67/30 = (19,388,460 × 67)/(19,388,460 × 30) = 1,299,026,820/581,653,800


99/50 = (11,633,076 × 99)/(11,633,076 × 50) = 1,151,674,524/581,653,800


21/13 = (44,742,600 × 21)/(44,742,600 × 13) = 939,594,600/581,653,800


13/7 = (83,093,400 × 13)/(83,093,400 × 7) = 1,080,214,200/581,653,800


90/53 = (10,974,600 × 90)/(10,974,600 × 53) = 987,714,000/581,653,800



The fractions have the same denominator, compare their numerators.

The larger the numerator the larger the positive fraction.

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

The fractions sorted in ascending order:
939,594,600/581,653,800 < 987,714,000/581,653,800 < 1,080,214,200/581,653,800 < 1,151,674,524/581,653,800 < 1,299,026,820/581,653,800 < 1,329,494,400/581,653,800 < 1,467,156,600/581,653,800 < 1,526,841,225/581,653,800 < 1,532,611,600/581,653,800 < 1,723,012,200/581,653,800 < 2,546,107,200/581,653,800 < 2,675,607,480/581,653,800 < 3,635,336,250/581,653,800 < 9,140,274,000/581,653,800

The initial fractions in ascending order:
42/26 < 90/53 < 104/56 < 99/50 < 134/60 < 144/63 < 169/67 < 168/64 < 166/63 < 157/53 < 232/53 < 92/20 < 100/16 < 110/7

More operations of this kind:

Compare and sort the fractions in ascending order:
49/34, 101/55, 112/59, 109/56, 145/69, 150/72, 179/73, 178/69, 175/68, 164/61, 244/59, 100/24, 107/21, 115/10


Writing numbers: comma ',' used as a thousands separator;

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

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? Oct 25 07:26 UTC (GMT)
93/123 and 96/129? Oct 25 07:26 UTC (GMT)
2/100 and 1/50? Oct 25 07:26 UTC (GMT)
- 26/15 and - 36/21? Oct 25 07:26 UTC (GMT)
13/18 and 11/14? Oct 25 07:26 UTC (GMT)
11/32 and 19/37? Oct 25 07:26 UTC (GMT)
2, 2/5, 24/10? Oct 25 07:26 UTC (GMT)
29/47, 52/23, 56/20? Oct 25 07:26 UTC (GMT)
83/106 and 89/108? Oct 25 07:26 UTC (GMT)
13/18 and 11/14? Oct 25 07:26 UTC (GMT)
32/3 and 34/5? Oct 25 07:26 UTC (GMT)
12/15 and 20/19? Oct 25 07:26 UTC (GMT)
13/18 and 11/14? Oct 25 07:26 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