Sort the Common Fractions String 126/2,675, 113/2,672, 178/103, 177/127, 173/95, 274/103, 285/97, 285/120, 283/97, 278/126, 278/111, 296/18 in Ascending Order. Online Calculator

Multiple fractions 126/2,675, 113/2,672, 178/103, 177/127, 173/95, 274/103, 285/97, 285/120, 283/97, 278/126, 278/111, 296/18 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:
126/2,675, 113/2,672, 178/103, 177/127, 173/95, 274/103, 285/97, 285/120, 283/97, 278/126, 278/111, 296/18

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

positive proper fractions: 126/2,675, 113/2,672

positive improper fractions: 178/103, 177/127, 173/95, 274/103, 285/97, 285/120, 283/97, 278/126, 278/111, 296/18

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:
126/2,675 and 113/2,672

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


The fraction: 126/2,675

126/2,675 is already reduced to the lowest terms.

The numerator and denominator have no common prime factors:


  • 126 = 2 × 32 × 7
  • 2,675 = 52 × 107
  • GCF (126; 2,675) = 1


The fraction: 113/2,672

113/2,672 is already reduced to the lowest terms.

The numerator and denominator have no common prime factors:


  • 113 is a prime number.
  • 2,672 = 24 × 167
  • GCF (113; 2,672) = 1



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:

126 = 2 × 32 × 7

113 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 (126, 113) = 2 × 32 × 7 × 113 = 14,238



Calculate the expanding number of each fraction:

Divide the LCM by the numerator of each fraction.

126/2,675 ⟶ 14,238 ÷ 126 = (2 × 32 × 7 × 113) ÷ (2 × 32 × 7) = 113

113/2,672 ⟶ 14,238 ÷ 113 = (2 × 32 × 7 × 113) ÷ 113 = 126



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:

126/2,675 = (113 × 126)/(113 × 2,675) = 14,238/302,275

113/2,672 = (126 × 113)/(126 × 2,672) = 14,238/336,672



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:
14,238/336,672 < 14,238/302,275

The initial fractions sorted in ascending order:
113/2,672 < 126/2,675

Sort the positive improper fractions in ascending order:
178/103, 177/127, 173/95, 274/103, 285/97, 285/120, 283/97, 278/126, 278/111, 296/18

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


The fraction: 178/103

178/103 is already reduced to the lowest terms.

The numerator and denominator have no common prime factors:


  • 178 = 2 × 89
  • 103 is a prime number.
  • GCF (178; 103) = 1


The fraction: 177/127

177/127 is already reduced to the lowest terms.

The numerator and denominator have no common prime factors:


  • 177 = 3 × 59
  • 127 is a prime number.
  • GCF (177; 127) = 1


The fraction: 173/95

173/95 is already reduced to the lowest terms.

The numerator and denominator have no common prime factors:


  • 173 is a prime number.
  • 95 = 5 × 19
  • GCF (173; 95) = 1


The fraction: 274/103

274/103 is already reduced to the lowest terms.

The numerator and denominator have no common prime factors:


  • 274 = 2 × 137
  • 103 is a prime number.
  • GCF (274; 103) = 1


The fraction: 285/97

285/97 is already reduced to the lowest terms.

The numerator and denominator have no common prime factors:


  • 285 = 3 × 5 × 19
  • 97 is a prime number.
  • GCF (285; 97) = 1


The fraction: 285/120

  • The prime factorizations of the numerator and denominator:
  • 285 = 3 × 5 × 19
  • 120 = 23 × 3 × 5
  • 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 (285; 120) = 3 × 5 = 15

285/120 = (285 ÷ 15)/(120 ÷ 15) = 19/8


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


285/120 = (3 × 5 × 19)/(23 × 3 × 5) = ((3 × 5 × 19) ÷ (3 × 5))/((23 × 3 × 5) ÷ (3 × 5)) = 19/8



The fraction: 283/97

283/97 is already reduced to the lowest terms.

The numerator and denominator have no common prime factors:


  • 283 is a prime number.
  • 97 is a prime number.
  • GCF (283; 97) = 1


The fraction: 278/126

  • 278 = 2 × 139
  • 126 = 2 × 32 × 7
  • GCF (278; 126) = 2

278/126 = (278 ÷ 2)/(126 ÷ 2) = 139/63


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


278/126 = (2 × 139)/(2 × 32 × 7) = ((2 × 139) ÷ 2)/((2 × 32 × 7) ÷ 2) = 139/63



The fraction: 278/111

278/111 is already reduced to the lowest terms.

The numerator and denominator have no common prime factors:


  • 278 = 2 × 139
  • 111 = 3 × 37
  • GCF (278; 111) = 1


The fraction: 296/18

  • 296 = 23 × 37
  • 18 = 2 × 32
  • GCF (296; 18) = 2

296/18 = (296 ÷ 2)/(18 ÷ 2) = 148/9


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


296/18 = (23 × 37)/(2 × 32) = ((23 × 37) ÷ 2)/((2 × 32) ÷ 2) = 148/9




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:

103 is a prime number.

127 is a prime number.

95 = 5 × 19

97 is a prime number.

8 = 23

63 = 32 × 7

111 = 3 × 37

9 = 32


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 (103, 127, 95, 97, 8, 63, 111, 9) = 23 × 32 × 5 × 7 × 19 × 37 × 97 × 103 × 127 = 2,247,856,306,920



Calculate the expanding number of each fraction:

Divide the LCM by the denominator of each fraction.

178/103 ⟶ 2,247,856,306,920 ÷ 103 = (23 × 32 × 5 × 7 × 19 × 37 × 97 × 103 × 127) ÷ 103 = 21,823,847,640

177/127 ⟶ 2,247,856,306,920 ÷ 127 = (23 × 32 × 5 × 7 × 19 × 37 × 97 × 103 × 127) ÷ 127 = 17,699,655,960

173/95 ⟶ 2,247,856,306,920 ÷ 95 = (23 × 32 × 5 × 7 × 19 × 37 × 97 × 103 × 127) ÷ (5 × 19) = 23,661,645,336

274/103 ⟶ 2,247,856,306,920 ÷ 103 = (23 × 32 × 5 × 7 × 19 × 37 × 97 × 103 × 127) ÷ 103 = 21,823,847,640

285/97 ⟶ 2,247,856,306,920 ÷ 97 = (23 × 32 × 5 × 7 × 19 × 37 × 97 × 103 × 127) ÷ 97 = 23,173,776,360

19/8 ⟶ 2,247,856,306,920 ÷ 8 = (23 × 32 × 5 × 7 × 19 × 37 × 97 × 103 × 127) ÷ 23 = 280,982,038,365

283/97 ⟶ 2,247,856,306,920 ÷ 97 = (23 × 32 × 5 × 7 × 19 × 37 × 97 × 103 × 127) ÷ 97 = 23,173,776,360

139/63 ⟶ 2,247,856,306,920 ÷ 63 = (23 × 32 × 5 × 7 × 19 × 37 × 97 × 103 × 127) ÷ (32 × 7) = 35,680,258,840

278/111 ⟶ 2,247,856,306,920 ÷ 111 = (23 × 32 × 5 × 7 × 19 × 37 × 97 × 103 × 127) ÷ (3 × 37) = 20,250,957,720

148/9 ⟶ 2,247,856,306,920 ÷ 9 = (23 × 32 × 5 × 7 × 19 × 37 × 97 × 103 × 127) ÷ 32 = 249,761,811,880



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:

178/103 = (21,823,847,640 × 178)/(21,823,847,640 × 103) = 3,884,644,879,920/2,247,856,306,920

177/127 = (17,699,655,960 × 177)/(17,699,655,960 × 127) = 3,132,839,104,920/2,247,856,306,920

173/95 = (23,661,645,336 × 173)/(23,661,645,336 × 95) = 4,093,464,643,128/2,247,856,306,920

274/103 = (21,823,847,640 × 274)/(21,823,847,640 × 103) = 5,979,734,253,360/2,247,856,306,920

285/97 = (23,173,776,360 × 285)/(23,173,776,360 × 97) = 6,604,526,262,600/2,247,856,306,920

19/8 = (280,982,038,365 × 19)/(280,982,038,365 × 8) = 5,338,658,728,935/2,247,856,306,920

283/97 = (23,173,776,360 × 283)/(23,173,776,360 × 97) = 6,558,178,709,880/2,247,856,306,920

139/63 = (35,680,258,840 × 139)/(35,680,258,840 × 63) = 4,959,555,978,760/2,247,856,306,920

278/111 = (20,250,957,720 × 278)/(20,250,957,720 × 111) = 5,629,766,246,160/2,247,856,306,920

148/9 = (249,761,811,880 × 148)/(249,761,811,880 × 9) = 36,964,748,158,240/2,247,856,306,920



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:
3,132,839,104,920/2,247,856,306,920 < 3,884,644,879,920/2,247,856,306,920 < 4,093,464,643,128/2,247,856,306,920 < 4,959,555,978,760/2,247,856,306,920 < 5,338,658,728,935/2,247,856,306,920 < 5,629,766,246,160/2,247,856,306,920 < 5,979,734,253,360/2,247,856,306,920 < 6,558,178,709,880/2,247,856,306,920 < 6,604,526,262,600/2,247,856,306,920 < 36,964,748,158,240/2,247,856,306,920

The initial fractions sorted in ascending order:
177/127 < 178/103 < 173/95 < 278/126 < 285/120 < 278/111 < 274/103 < 283/97 < 285/97 < 296/18

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

Sort the positive proper fractions in ascending order:
113/2,672 < 126/2,675

Sort the positive improper fractions in ascending order:
177/127 < 178/103 < 173/95 < 278/126 < 285/120 < 278/111 < 274/103 < 283/97 < 285/97 < 296/18

All the fractions sorted in ascending order:
113/2,672 < 126/2,675 < 177/127 < 178/103 < 173/95 < 278/126 < 285/120 < 278/111 < 274/103 < 283/97 < 285/97 < 296/18

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:
128/2,684, 122/2,680, 185/105, 183/132, 181/102, 286/106, 295/101, 296/123, 291/100, 283/135, 285/120, 304/23

» 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: