Compare and sort in ascending order the two ordinary fractions, which one is larger: 12/12 vs. 22/21. Ordinary fractions compared and sorted in ascending order, result explained below

The operation of comparing fractions:
12/12 vs. 22/21

Reduce (simplify) fractions to their lowest terms equivalents:

12/12 = (12 ÷ 12)/(12 ÷ 12) = 1/1 = 1;


22/21 already reduced to the lowest terms;
the numerator and the denominator have no common prime factors:
22 = 2 × 11;
21 = 3 × 7;


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


To sort fractions in ascending order, build up their denominators the same.

Expand the fraction that has 1 as a denominator


Multiply the numerator and the denominator by the same number:


1 = (21 × 1)/(21 × 1) = 21/21;


The fractions have the same denominator, compare their numerators.

The larger the numerator the larger the positive fraction.

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

The fractions sorted in ascending order:
21/21 < 22/21

The initial fractions in ascending order:
12/12 < 22/21

Compare and sort the fractions in ascending order:
- 12/12 vs. - 20/17


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

12/12 < 22/21 Jul 02 18:46 UTC (GMT)
- 11/16 < - 4/10 Jul 02 18:46 UTC (GMT)
18/35 < 20/38 Jul 02 18:46 UTC (GMT)
- 89/25 < - 95/29 Jul 02 18:45 UTC (GMT)
4/8 < 2/3 Jul 02 18:45 UTC (GMT)
- 61/33 < - 62/46 < - 52/61 Jul 02 18:45 UTC (GMT)
105/106 < 113/113 Jul 02 18:45 UTC (GMT)
13/30 < 7/15 < 1/2 < 8/15 < 17/30 Jul 02 18:45 UTC (GMT)
1/6 < 3/14 < 2/7 < 1/3 Jul 02 18:45 UTC (GMT)
35/41 < 43/44 Jul 02 18:45 UTC (GMT)
- 19/21 < - 9/14 Jul 02 18:45 UTC (GMT)
17/36 < 27/39 < 25/33 < 36/46 Jul 02 18:45 UTC (GMT)
7/16 < 5/9 Jul 02 18:45 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: