Compare and sort in ascending order the two common ordinary fractions, which one is larger: 6/10 and 3/5. Common ordinary fractions compared and sorted in ascending order, result explained below

Compare: 6/10 and 3/5

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

The operation of comparing fractions:
6/10 and 3/5

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



6/10 = (2 × 3)/(2 × 5) = ((2 × 3) ÷ 2)/((2 × 5) ÷ 2) = 3/5

3/5 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors:
3 is a prime number.
5 is a prime number.

The fractions are equal.

This is one of the simplest cases when comparing two fractions.


Not only are the numerators of the fractions equal but their denominators are also equal.


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

The fractions sorted in ascending order:
3/5 = 3/5

The initial fractions sorted in ascending order:
6/10 = 3/5

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:
- 6/10 and - 11/19

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: