Sort the Common Fractions String 137/2,703, 135/2,694, 204/112, 207/141, 195/113, 302/118, 313/111, 313/130, 310/109, 298/142, 304/128, 319/35 in Ascending Order. Online Calculator

Multiple fractions 137/2,703, 135/2,694, 204/112, 207/141, 195/113, 302/118, 313/111, 313/130, 310/109, 298/142, 304/128, 319/35 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:
137/2,703, 135/2,694, 204/112, 207/141, 195/113, 302/118, 313/111, 313/130, 310/109, 298/142, 304/128, 319/35

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

positive proper fractions: 137/2,703, 135/2,694

positive improper fractions: 204/112, 207/141, 195/113, 302/118, 313/111, 313/130, 310/109, 298/142, 304/128, 319/35

How to compare and sort the fractions in ascending order, by categories:

- any positive proper fraction is smaller than...

- any positive improper fraction.


How do we compare and sort all the fractions?

It is clear that there is no point in comparing fractions from different categories.

We will compare and sort the fractions in each of the above categories, separately.


Sort the positive proper fractions in ascending order:
137/2,703 and 135/2,694

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


The fraction: 137/2,703

137/2,703 is already reduced to the lowest terms.

The numerator and denominator have no common prime factors:


  • 137 is a prime number.
  • 2,703 = 3 × 17 × 53
  • GCF (137; 2,703) = 1


The fraction: 135/2,694

  • The prime factorizations of the numerator and denominator:
  • 135 = 33 × 5
  • 2,694 = 2 × 3 × 449
  • 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 (135; 2,694) = 3

135/2,694 = (135 ÷ 3)/(2,694 ÷ 3) = 45/898


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


135/2,694 = (33 × 5)/(2 × 3 × 449) = ((33 × 5) ÷ 3)/((2 × 3 × 449) ÷ 3) = 45/898




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

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

  • 1) calculate their common numerator
  • 2) calculate the expanding number of each fraction
  • 3) expand the fractions to equivalent forms having equal numerators

Calculate the common numerator

The common numerator is nothing else than the least common multiple (LCM) of the numerators of the fractions.


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

137 is a prime number.

45 = 32 × 5


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 (137, 45) = 32 × 5 × 137 = 6,165



Calculate the expanding number of each fraction:

Divide the LCM by the numerator of each fraction.

137/2,703 ⟶ 6,165 ÷ 137 = (32 × 5 × 137) ÷ 137 = 45

45/898 ⟶ 6,165 ÷ 45 = (32 × 5 × 137) ÷ (32 × 5) = 137



Make the numerators 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 numerator:

137/2,703 = (45 × 137)/(45 × 2,703) = 6,165/121,635

45/898 = (137 × 45)/(137 × 898) = 6,165/123,026



The fractions have the same numerator, compare their denominators.

The larger the denominator the smaller the positive fraction.

The larger the denominator the larger the negative fraction.


The fractions sorted in ascending order:
6,165/123,026 < 6,165/121,635

The initial fractions sorted in ascending order:
135/2,694 < 137/2,703

Sort the positive improper fractions in ascending order:
204/112, 207/141, 195/113, 302/118, 313/111, 313/130, 310/109, 298/142, 304/128, 319/35

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


The fraction: 204/112

  • The prime factorizations of the numerator and denominator:
  • 204 = 22 × 3 × 17
  • 112 = 24 × 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 (204; 112) = 22 = 4

204/112 = (204 ÷ 4)/(112 ÷ 4) = 51/28


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


204/112 = (22 × 3 × 17)/(24 × 7) = ((22 × 3 × 17) ÷ 22)/((24 × 7) ÷ 22) = 51/28



The fraction: 207/141

  • 207 = 32 × 23
  • 141 = 3 × 47
  • GCF (207; 141) = 3

207/141 = (207 ÷ 3)/(141 ÷ 3) = 69/47


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


207/141 = (32 × 23)/(3 × 47) = ((32 × 23) ÷ 3)/((3 × 47) ÷ 3) = 69/47



The fraction: 195/113

195/113 is already reduced to the lowest terms.

The numerator and denominator have no common prime factors:


  • 195 = 3 × 5 × 13
  • 113 is a prime number.
  • GCF (195; 113) = 1


The fraction: 302/118

  • 302 = 2 × 151
  • 118 = 2 × 59
  • GCF (302; 118) = 2

302/118 = (302 ÷ 2)/(118 ÷ 2) = 151/59


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


302/118 = (2 × 151)/(2 × 59) = ((2 × 151) ÷ 2)/((2 × 59) ÷ 2) = 151/59



The fraction: 313/111

313/111 is already reduced to the lowest terms.

The numerator and denominator have no common prime factors:


  • 313 is a prime number.
  • 111 = 3 × 37
  • GCF (313; 111) = 1


The fraction: 313/130

313/130 is already reduced to the lowest terms.

The numerator and denominator have no common prime factors:


  • 313 is a prime number.
  • 130 = 2 × 5 × 13
  • GCF (313; 130) = 1


The fraction: 310/109

310/109 is already reduced to the lowest terms.

The numerator and denominator have no common prime factors:


  • 310 = 2 × 5 × 31
  • 109 is a prime number.
  • GCF (310; 109) = 1


The fraction: 298/142

  • 298 = 2 × 149
  • 142 = 2 × 71
  • GCF (298; 142) = 2

298/142 = (298 ÷ 2)/(142 ÷ 2) = 149/71


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


298/142 = (2 × 149)/(2 × 71) = ((2 × 149) ÷ 2)/((2 × 71) ÷ 2) = 149/71



The fraction: 304/128

  • 304 = 24 × 19
  • 128 = 27
  • GCF (304; 128) = 24 = 16

304/128 = (304 ÷ 16)/(128 ÷ 16) = 19/8


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


304/128 = (24 × 19)/27 = ((24 × 19) ÷ 24)/(27 ÷ 24) = 19/8



The fraction: 319/35

319/35 is already reduced to the lowest terms.

The numerator and denominator have no common prime factors:


  • 319 = 11 × 29
  • 35 = 5 × 7
  • GCF (319; 35) = 1



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:

28 = 22 × 7

47 is a prime number.

113 is a prime number.

59 is a prime number.

111 = 3 × 37

130 = 2 × 5 × 13

109 is a prime number.

71 is a prime number.

8 = 23

35 = 5 × 7


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 (28, 47, 113, 59, 111, 130, 109, 71, 8, 35) = 23 × 3 × 5 × 7 × 13 × 37 × 47 × 59 × 71 × 109 × 113 = 979,800,196,360,440



Calculate the expanding number of each fraction:

Divide the LCM by the denominator of each fraction.

51/28 ⟶ 979,800,196,360,440 ÷ 28 = (23 × 3 × 5 × 7 × 13 × 37 × 47 × 59 × 71 × 109 × 113) ÷ (22 × 7) = 34,992,864,155,730

69/47 ⟶ 979,800,196,360,440 ÷ 47 = (23 × 3 × 5 × 7 × 13 × 37 × 47 × 59 × 71 × 109 × 113) ÷ 47 = 20,846,812,688,520

195/113 ⟶ 979,800,196,360,440 ÷ 113 = (23 × 3 × 5 × 7 × 13 × 37 × 47 × 59 × 71 × 109 × 113) ÷ 113 = 8,670,798,197,880

151/59 ⟶ 979,800,196,360,440 ÷ 59 = (23 × 3 × 5 × 7 × 13 × 37 × 47 × 59 × 71 × 109 × 113) ÷ 59 = 16,606,782,989,160

313/111 ⟶ 979,800,196,360,440 ÷ 111 = (23 × 3 × 5 × 7 × 13 × 37 × 47 × 59 × 71 × 109 × 113) ÷ (3 × 37) = 8,827,028,796,040

313/130 ⟶ 979,800,196,360,440 ÷ 130 = (23 × 3 × 5 × 7 × 13 × 37 × 47 × 59 × 71 × 109 × 113) ÷ (2 × 5 × 13) = 7,536,924,587,388

310/109 ⟶ 979,800,196,360,440 ÷ 109 = (23 × 3 × 5 × 7 × 13 × 37 × 47 × 59 × 71 × 109 × 113) ÷ 109 = 8,988,992,627,160

149/71 ⟶ 979,800,196,360,440 ÷ 71 = (23 × 3 × 5 × 7 × 13 × 37 × 47 × 59 × 71 × 109 × 113) ÷ 71 = 13,800,002,765,640

19/8 ⟶ 979,800,196,360,440 ÷ 8 = (23 × 3 × 5 × 7 × 13 × 37 × 47 × 59 × 71 × 109 × 113) ÷ 23 = 122,475,024,545,055

319/35 ⟶ 979,800,196,360,440 ÷ 35 = (23 × 3 × 5 × 7 × 13 × 37 × 47 × 59 × 71 × 109 × 113) ÷ (5 × 7) = 27,994,291,324,584



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:

51/28 = (34,992,864,155,730 × 51)/(34,992,864,155,730 × 28) = 1,784,636,071,942,230/979,800,196,360,440

69/47 = (20,846,812,688,520 × 69)/(20,846,812,688,520 × 47) = 1,438,430,075,507,880/979,800,196,360,440

195/113 = (8,670,798,197,880 × 195)/(8,670,798,197,880 × 113) = 1,690,805,648,586,600/979,800,196,360,440

151/59 = (16,606,782,989,160 × 151)/(16,606,782,989,160 × 59) = 2,507,624,231,363,160/979,800,196,360,440

313/111 = (8,827,028,796,040 × 313)/(8,827,028,796,040 × 111) = 2,762,860,013,160,520/979,800,196,360,440

313/130 = (7,536,924,587,388 × 313)/(7,536,924,587,388 × 130) = 2,359,057,395,852,444/979,800,196,360,440

310/109 = (8,988,992,627,160 × 310)/(8,988,992,627,160 × 109) = 2,786,587,714,419,600/979,800,196,360,440

149/71 = (13,800,002,765,640 × 149)/(13,800,002,765,640 × 71) = 2,056,200,412,080,360/979,800,196,360,440

19/8 = (122,475,024,545,055 × 19)/(122,475,024,545,055 × 8) = 2,327,025,466,356,045/979,800,196,360,440

319/35 = (27,994,291,324,584 × 319)/(27,994,291,324,584 × 35) = 8,930,178,932,542,296/979,800,196,360,440



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 fractions sorted in ascending order:
1,438,430,075,507,880/979,800,196,360,440 < 1,690,805,648,586,600/979,800,196,360,440 < 1,784,636,071,942,230/979,800,196,360,440 < 2,056,200,412,080,360/979,800,196,360,440 < 2,327,025,466,356,045/979,800,196,360,440 < 2,359,057,395,852,444/979,800,196,360,440 < 2,507,624,231,363,160/979,800,196,360,440 < 2,762,860,013,160,520/979,800,196,360,440 < 2,786,587,714,419,600/979,800,196,360,440 < 8,930,178,932,542,296/979,800,196,360,440

The initial fractions sorted in ascending order:
207/141 < 195/113 < 204/112 < 298/142 < 304/128 < 313/130 < 302/118 < 313/111 < 310/109 < 319/35

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

Sort the positive proper fractions in ascending order:
135/2,694 < 137/2,703

Sort the positive improper fractions in ascending order:
207/141 < 195/113 < 204/112 < 298/142 < 304/128 < 313/130 < 302/118 < 313/111 < 310/109 < 319/35

All the fractions sorted in ascending order:
135/2,694 < 137/2,703 < 207/141 < 195/113 < 204/112 < 298/142 < 304/128 < 313/130 < 302/118 < 313/111 < 310/109 < 319/35

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:
144/2,708, 139/2,704, 216/116, 216/143, 206/115, 310/123, 323/116, 322/138, 319/118, 306/144, 311/134, 331/42

» 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: