Compare and sort in ascending order the two ordinary fractions, which one is larger: 1/3 vs. 23/30. Ordinary fractions compared and sorted in ascending order, result explained below

The operation of comparing fractions:
1/3 vs. 23/30

Reduce (simplify) fractions to their lowest terms equivalents:

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


23/30 already reduced to the lowest terms;
the numerator and the denominator have no common prime factors:
23 is a prime number;
30 = 2 × 3 × 5;


Reduce (simplify) fractions to their simplest form, online calculator


To sort fractions, build them up to the same numerator.

Expand the fraction that has 1 as a numerator


Multiply the numerator and the denominator by the same number:


1/3 = (23 × 1)/(23 × 3) = 23/69;


The fractions have the same numerator, compare their denominators.

The larger the denominator the smaller the positive fraction.

::: Comparing operation :::
The final answer:

The fractions sorted in ascending order:
23/69 < 23/30

The initial fractions in ascending order:
1/3 < 23/30

Compare and sort the fractions in ascending order:
23/30 vs. 32/38


Symbols: / fraction bar; ÷ divide; × multiply; + plus; - minus; = equal; < less than;

Compare and sort ordinary fractions, online calculator

The latest fractions compared and sorted in ascending order

1/3 < 23/30 Jul 02 21:13 UTC (GMT)
5/40 < 3/8 Jul 02 21:13 UTC (GMT)
- 31/12 < - 30/13 < - 11/17 < - 13/22 Jul 02 21:13 UTC (GMT)
1/10 < 3/5 < 5/8 < 3/4 Jul 02 21:13 UTC (GMT)
- 23/24 < - 13/16 Jul 02 21:13 UTC (GMT)
- 53/40 < - 56/50 Jul 02 21:13 UTC (GMT)
- 64/104 < - 61/102 Jul 02 21:13 UTC (GMT)
- 87/44 < - 58/40 < - 46/61 Jul 02 21:13 UTC (GMT)
53/3 < 49 Jul 02 21:13 UTC (GMT)
7/64 < 1/4 Jul 02 21:13 UTC (GMT)
- 16/32 < - 13/29 < - 15/36 Jul 02 21:12 UTC (GMT)
- 10 < - 12/4 Jul 02 21:12 UTC (GMT)
- 9/13 < - 12/19 Jul 02 21:12 UTC (GMT)
see more... compared fractions
see more... sorted fractions

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) math fractions theory: