Sort the Common Fractions String 223/21, 221/30, 721/172, 554/168, 59/27, 74/26, 466/162, 334/170, 276/142, 282/148, 287/158, 236/146 in Ascending Order. Online Calculator

Multiple fractions 223/21, 221/30, 721/172, 554/168, 59/27, 74/26, 466/162, 334/170, 276/142, 282/148, 287/158, 236/146 compared and then sorted in ascending order

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:
223/21, 221/30, 721/172, 554/168, 59/27, 74/26, 466/162, 334/170, 276/142, 282/148, 287/158, 236/146

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

positive improper fractions: 223/21, 221/30, 721/172, 554/168, 59/27, 74/26, 466/162, 334/170, 276/142, 282/148, 287/158, 236/146

Simplify the operation
Reduce (simplify) the fractions to their lowest terms equivalents:


The fraction: 223/21

223/21 is already reduced to the lowest terms.

The numerator and denominator have no common prime factors:


  • 223 is a prime number.
  • 21 = 3 × 7
  • GCF (223; 21) = 1


The fraction: 221/30

221/30 is already reduced to the lowest terms.

The numerator and denominator have no common prime factors:


  • 221 = 13 × 17
  • 30 = 2 × 3 × 5
  • GCF (221; 30) = 1


The fraction: 721/172

721/172 is already reduced to the lowest terms.

The numerator and denominator have no common prime factors:


  • 721 = 7 × 103
  • 172 = 22 × 43
  • GCF (721; 172) = 1


The fraction: 554/168

  • The prime factorizations of the numerator and denominator:
  • 554 = 2 × 277
  • 168 = 23 × 3 × 7
  • Multiply all the common prime factors: if there are repeating prime factors we only take them once, and only the ones having the lowest exponent (the lowest powers).
  • GCF (554; 168) = 2

554/168 = (554 ÷ 2)/(168 ÷ 2) = 277/84


The fraction can also be reduced without calculating GCF; factor the numerator and denominator and cross out all the common prime factors:


554/168 = (2 × 277)/(23 × 3 × 7) = ((2 × 277) ÷ 2)/((23 × 3 × 7) ÷ 2) = 277/84



The fraction: 59/27

59/27 is already reduced to the lowest terms.

The numerator and denominator have no common prime factors:


  • 59 is a prime number.
  • 27 = 33
  • GCF (59; 27) = 1


The fraction: 74/26

  • 74 = 2 × 37
  • 26 = 2 × 13
  • GCF (74; 26) = 2

74/26 = (74 ÷ 2)/(26 ÷ 2) = 37/13


The fraction can also be reduced without calculating GCF; factor the numerator and denominator and cross out all the common prime factors:


74/26 = (2 × 37)/(2 × 13) = ((2 × 37) ÷ 2)/((2 × 13) ÷ 2) = 37/13



The fraction: 466/162

  • 466 = 2 × 233
  • 162 = 2 × 34
  • GCF (466; 162) = 2

466/162 = (466 ÷ 2)/(162 ÷ 2) = 233/81


The fraction can also be reduced without calculating GCF; factor the numerator and denominator and cross out all the common prime factors:


466/162 = (2 × 233)/(2 × 34) = ((2 × 233) ÷ 2)/((2 × 34) ÷ 2) = 233/81



The fraction: 334/170

  • 334 = 2 × 167
  • 170 = 2 × 5 × 17
  • GCF (334; 170) = 2

334/170 = (334 ÷ 2)/(170 ÷ 2) = 167/85


The fraction can also be reduced without calculating GCF; factor the numerator and denominator and cross out all the common prime factors:


334/170 = (2 × 167)/(2 × 5 × 17) = ((2 × 167) ÷ 2)/((2 × 5 × 17) ÷ 2) = 167/85



The fraction: 276/142

  • 276 = 22 × 3 × 23
  • 142 = 2 × 71
  • GCF (276; 142) = 2

276/142 = (276 ÷ 2)/(142 ÷ 2) = 138/71


The fraction can also be reduced without calculating GCF; factor the numerator and denominator and cross out all the common prime factors:


276/142 = (22 × 3 × 23)/(2 × 71) = ((22 × 3 × 23) ÷ 2)/((2 × 71) ÷ 2) = 138/71



The fraction: 282/148

  • 282 = 2 × 3 × 47
  • 148 = 22 × 37
  • GCF (282; 148) = 2

282/148 = (282 ÷ 2)/(148 ÷ 2) = 141/74


The fraction can also be reduced without calculating GCF; factor the numerator and denominator and cross out all the common prime factors:


282/148 = (2 × 3 × 47)/(22 × 37) = ((2 × 3 × 47) ÷ 2)/((22 × 37) ÷ 2) = 141/74



The fraction: 287/158

287/158 is already reduced to the lowest terms.

The numerator and denominator have no common prime factors:


  • 287 = 7 × 41
  • 158 = 2 × 79
  • GCF (287; 158) = 1


The fraction: 236/146

  • 236 = 22 × 59
  • 146 = 2 × 73
  • GCF (236; 146) = 2

236/146 = (236 ÷ 2)/(146 ÷ 2) = 118/73


The fraction can also be reduced without calculating GCF; factor the numerator and denominator and cross out all the common prime factors:


236/146 = (22 × 59)/(2 × 73) = ((22 × 59) ÷ 2)/((2 × 73) ÷ 2) = 118/73




To compare and sort the fractions, make their denominators the same.

To make the fractions' denominators the same - we have to:

  • 1) calculate their common denominator
  • 2) then calculate the expanding number of each fraction
  • 3) expand the fractions to equivalent forms having the same denominator

Calculate the common denominator

The common denominator is nothing else than the least common multiple (LCM) of the denominators of the fractions.


To calculate the LCM, we need the prime factorization of the denominators:

21 = 3 × 7

30 = 2 × 3 × 5

172 = 22 × 43

84 = 22 × 3 × 7

27 = 33

13 is a prime number.

81 = 34

85 = 5 × 17

71 is a prime number.

74 = 2 × 37

158 = 2 × 79

73 is a prime number.


Multiply all the unique prime factors: if there are repeating prime factors we only take them once, and only the ones having the highest exponent (the highest powers).


External link » Calculate LCM, the least common multiple of numbers, online calculator

LCM (21, 30, 172, 84, 27, 13, 81, 85, 71, 74, 158, 73) = 22 × 34 × 5 × 7 × 13 × 17 × 37 × 43 × 71 × 73 × 79 = 1,632,615,096,474,180



Calculate the expanding number of each fraction:

Divide the LCM by the denominator of each fraction.

223/21 ⟶ 1,632,615,096,474,180 ÷ 21 = (22 × 34 × 5 × 7 × 13 × 17 × 37 × 43 × 71 × 73 × 79) ÷ (3 × 7) = 77,743,576,022,580

221/30 ⟶ 1,632,615,096,474,180 ÷ 30 = (22 × 34 × 5 × 7 × 13 × 17 × 37 × 43 × 71 × 73 × 79) ÷ (2 × 3 × 5) = 54,420,503,215,806

721/172 ⟶ 1,632,615,096,474,180 ÷ 172 = (22 × 34 × 5 × 7 × 13 × 17 × 37 × 43 × 71 × 73 × 79) ÷ (22 × 43) = 9,491,948,235,315

277/84 ⟶ 1,632,615,096,474,180 ÷ 84 = (22 × 34 × 5 × 7 × 13 × 17 × 37 × 43 × 71 × 73 × 79) ÷ (22 × 3 × 7) = 19,435,894,005,645

59/27 ⟶ 1,632,615,096,474,180 ÷ 27 = (22 × 34 × 5 × 7 × 13 × 17 × 37 × 43 × 71 × 73 × 79) ÷ 33 = 60,467,225,795,340

37/13 ⟶ 1,632,615,096,474,180 ÷ 13 = (22 × 34 × 5 × 7 × 13 × 17 × 37 × 43 × 71 × 73 × 79) ÷ 13 = 125,585,776,651,860

233/81 ⟶ 1,632,615,096,474,180 ÷ 81 = (22 × 34 × 5 × 7 × 13 × 17 × 37 × 43 × 71 × 73 × 79) ÷ 34 = 20,155,741,931,780

167/85 ⟶ 1,632,615,096,474,180 ÷ 85 = (22 × 34 × 5 × 7 × 13 × 17 × 37 × 43 × 71 × 73 × 79) ÷ (5 × 17) = 19,207,236,429,108

138/71 ⟶ 1,632,615,096,474,180 ÷ 71 = (22 × 34 × 5 × 7 × 13 × 17 × 37 × 43 × 71 × 73 × 79) ÷ 71 = 22,994,578,823,580

141/74 ⟶ 1,632,615,096,474,180 ÷ 74 = (22 × 34 × 5 × 7 × 13 × 17 × 37 × 43 × 71 × 73 × 79) ÷ (2 × 37) = 22,062,366,168,570

287/158 ⟶ 1,632,615,096,474,180 ÷ 158 = (22 × 34 × 5 × 7 × 13 × 17 × 37 × 43 × 71 × 73 × 79) ÷ (2 × 79) = 10,333,006,939,710

118/73 ⟶ 1,632,615,096,474,180 ÷ 73 = (22 × 34 × 5 × 7 × 13 × 17 × 37 × 43 × 71 × 73 × 79) ÷ 73 = 22,364,590,362,660



Make the denominators of the fractions the same:

  • Expand each fraction: multiply both its numerator and denominator by its corresponding expanding number, calculated above.
  • This way all the fractions will have the same denominator:

223/21 = (77,743,576,022,580 × 223)/(77,743,576,022,580 × 21) = 17,336,817,453,035,340/1,632,615,096,474,180

221/30 = (54,420,503,215,806 × 221)/(54,420,503,215,806 × 30) = 12,026,931,210,693,126/1,632,615,096,474,180

721/172 = (9,491,948,235,315 × 721)/(9,491,948,235,315 × 172) = 6,843,694,677,662,115/1,632,615,096,474,180

277/84 = (19,435,894,005,645 × 277)/(19,435,894,005,645 × 84) = 5,383,742,639,563,665/1,632,615,096,474,180

59/27 = (60,467,225,795,340 × 59)/(60,467,225,795,340 × 27) = 3,567,566,321,925,060/1,632,615,096,474,180

37/13 = (125,585,776,651,860 × 37)/(125,585,776,651,860 × 13) = 4,646,673,736,118,820/1,632,615,096,474,180

233/81 = (20,155,741,931,780 × 233)/(20,155,741,931,780 × 81) = 4,696,287,870,104,740/1,632,615,096,474,180

167/85 = (19,207,236,429,108 × 167)/(19,207,236,429,108 × 85) = 3,207,608,483,661,036/1,632,615,096,474,180

138/71 = (22,994,578,823,580 × 138)/(22,994,578,823,580 × 71) = 3,173,251,877,654,040/1,632,615,096,474,180

141/74 = (22,062,366,168,570 × 141)/(22,062,366,168,570 × 74) = 3,110,793,629,768,370/1,632,615,096,474,180

287/158 = (10,333,006,939,710 × 287)/(10,333,006,939,710 × 158) = 2,965,572,991,696,770/1,632,615,096,474,180

118/73 = (22,364,590,362,660 × 118)/(22,364,590,362,660 × 73) = 2,639,021,662,793,880/1,632,615,096,474,180



The fractions have the same denominator, compare their numerators.

The larger the numerator the larger the positive fraction.

The larger the numerator the smaller the negative fraction.


::: The operation of comparing fractions :::
The final answer:

The fractions sorted in ascending order:
2,639,021,662,793,880/1,632,615,096,474,180 < 2,965,572,991,696,770/1,632,615,096,474,180 < 3,110,793,629,768,370/1,632,615,096,474,180 < 3,173,251,877,654,040/1,632,615,096,474,180 < 3,207,608,483,661,036/1,632,615,096,474,180 < 3,567,566,321,925,060/1,632,615,096,474,180 < 4,646,673,736,118,820/1,632,615,096,474,180 < 4,696,287,870,104,740/1,632,615,096,474,180 < 5,383,742,639,563,665/1,632,615,096,474,180 < 6,843,694,677,662,115/1,632,615,096,474,180 < 12,026,931,210,693,126/1,632,615,096,474,180 < 17,336,817,453,035,340/1,632,615,096,474,180

The initial fractions sorted in ascending order:
236/146 < 287/158 < 282/148 < 276/142 < 334/170 < 59/27 < 74/26 < 466/162 < 554/168 < 721/172 < 221/30 < 223/21

How are the numbers written: comma ',' used as a thousands separator; point '.' as a decimal separator; numbers rounded off to max. 12 decimals (if the case). Used symbols: '/' the fraction bar; ÷ dividing; × multiplying; + plus (adding); - minus (subtracting); = equal; ≈ approximately equal.

Other similar operations

Compare and sort the fractions in ascending order:
230/26, 226/39, 726/181, 563/177, 70/31, 86/35, 471/168, 344/176, 287/145, 292/151, 297/166, 247/151

» New. All the Calculations Performed by Our Visitors: Common Fractions Compared and Sorted. Data organized on a Monthly Basis

Compare and sort common fractions, online calculator:

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) fractions / theory: