Sort the Common Fractions String 13/20, 13/20, 10/30 in Ascending Order. Online Calculator

The operation of sorting fractions in ascending order:
13/20, 13/20, 10/30

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

positive proper fractions: 13/20, 10/30

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


The fraction: 13/20

13/20 is already reduced to the lowest terms.

The numerator and denominator have no common prime factors:


  • 13 is a prime number.
  • 20 = 22 × 5
  • GCF (13; 20) = 1


The fraction: 10/30

  • The prime factorizations of the numerator and denominator:
  • 10 = 2 × 5
  • 30 = 2 × 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 (10; 30) = 2 × 5 = 10

10/30 = (10 ÷ 10)/(30 ÷ 10) = 1/3


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


10/30 = (2 × 5)/(2 × 3 × 5) = ((2 × 5) ÷ (2 × 5))/((2 × 3 × 5) ÷ (2 × 5)) = 1/3




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:

1/3 = (13 × 1)/(13 × 3) = 13/39

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:
13/39 < 13/20 = 13/20

The initial fractions sorted in ascending order:
10/30 < 13/20 = 13/20

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:
22/27, 16/28, 12/38

» 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: