Sort the Common Fractions String 16/32, 11/33, 19/25 in Ascending Order. Online Calculator

The operation of sorting fractions in ascending order:
16/32, 11/33, 19/25

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

positive proper fractions: 16/32, 11/33, 19/25

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


The fraction: 16/32

  • The prime factorizations of the numerator and denominator:
  • 16 = 24
  • 32 = 25
  • 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 (16; 32) = 24 = 16

16/32 = (16 ÷ 16)/(32 ÷ 16) = 1/2


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


16/32 = 24/25 = (24 ÷ 24)/(25 ÷ 24) = 1/2



The fraction: 11/33

  • 11 is a prime number.
  • 33 = 3 × 11
  • GCF (11; 33) = 11

11/33 = (11 ÷ 11)/(33 ÷ 11) = 1/3


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


11/33 = 11/(3 × 11) = (11 ÷ 11)/((3 × 11) ÷ 11) = 1/3



The fraction: 19/25

19/25 is already reduced to the lowest terms.

The numerator and denominator have no common prime factors:


  • 19 is a prime number.
  • 25 = 52
  • GCF (19; 25) = 1



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

Expand the fractions that have 1 as a numerator.

Multiply the numerator and denominator by the same number:

1/2 = (19 × 1)/(19 × 2) = 19/38

1/3 = (19 × 1)/(19 × 3) = 19/57

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 operation of comparing fractions :::
The final answer:

The fractions sorted in ascending order:
19/57 < 19/38 < 19/25

The initial fractions sorted in ascending order:
11/33 < 16/32 < 19/25

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:
20/41, 19/38, 26/30

» 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: