Sort the Common Fractions String 2/6, 3/4, 2/8, 1/2 in Ascending Order. Online Calculator

The operation of sorting fractions in ascending order:
2/6, 3/4, 2/8, 1/2

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

positive proper fractions: 2/6, 3/4, 2/8, 1/2

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


The fraction: 2/6

  • The prime factorizations of the numerator and denominator:
  • 2 is a prime number.
  • 6 = 2 × 3
  • 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 (2; 6) = 2

2/6 = (2 ÷ 2)/(6 ÷ 2) = 1/3


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


2/6 = 2/(2 × 3) = (2 ÷ 2)/((2 × 3) ÷ 2) = 1/3



The fraction: 3/4

3/4 is already reduced to the lowest terms.

The numerator and denominator have no common prime factors:


  • 3 is a prime number.
  • 4 = 22
  • GCF (3; 4) = 1


The fraction: 2/8

  • 2 is a prime number.
  • 8 = 23
  • GCF (2; 8) = 2

2/8 = (2 ÷ 2)/(8 ÷ 2) = 1/4


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


2/8 = 2/23 = (2 ÷ 2)/(23 ÷ 2) = 1/4



The fraction: 1/2

1/2 is already reduced to the lowest terms.

The numerator and denominator have no common prime factors:


  • 1 cannot be factored into other prime factors.
  • 2 is a prime number.
  • GCF (1; 2) = 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:

1/3 = (3 × 1)/(3 × 3) = 3/9

1/4 = (3 × 1)/(3 × 4) = 3/12

1/2 = (3 × 1)/(3 × 2) = 3/6

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:
3/12 < 3/9 < 3/6 < 3/4

The initial fractions sorted in ascending order:
2/8 < 2/6 < 1/2 < 3/4

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:
10/17, 12/11, 4/20, 6/12

» 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: