Compare and sort in ascending order the two common ordinary fractions, which one is larger: 13/36 and 1/3. Common ordinary fractions compared and sorted in ascending order, result explained below

Compare: 13/36 and 1/3

To compare and sort multiple fractions, they should either have the same denominator or the same numerator.

The operation of comparing fractions:
13/36 and 1/3

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

By reducing the values of the numerators and denominators of the fractions, further calculations with these fractions become easier to do.


To reduce a fraction to the lowest terms equivalent: divide both the numerator and denominator by their greatest common factor, GCF.


Internal link » Reduce (simplify) common (ordinary) fractions to the lowest terms (to their simplest form equivalent), online calculator


13/36 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors:
13 is a prime number.
36 = 22 × 32

1/3 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors:
1 cannot be factored into other prime factors.
3 is a prime number.

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

Expand the fraction that has 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 < 13/36

The initial fractions sorted in ascending order:
1/3 < 13/36

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:
1/3 and 11/9

Compare and sort common ordinary fractions, online calculator:

The latest common ordinary fractions compared and sorted in ascending order

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: