Compare and sort in ascending order the two ordinary fractions, which one is larger: 7/32 vs. 1/2. Ordinary fractions compared and sorted in ascending order, result explained below

The operation of comparing fractions:
7/32 vs. 1/2

Reduce (simplify) fractions to their lowest terms equivalents:

7/32 already reduced to the lowest terms;
the numerator and the denominator have no common prime factors:
7 is a prime number;
32 = 25;


1/2 already reduced to the lowest terms;
the numerator and the denominator have no common prime factors:
1 cannot be factored into other prime factors;
2 is a prime number;


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:


1/2 = (7 × 1)/(7 × 2) = 7/14;


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:
7/32 < 7/14

The initial fractions in ascending order:
7/32 < 1/2

Compare and sort the fractions in ascending order:
- 7/32 vs. - 15/36


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

7/32 < 1/2 Jul 02 22:42 UTC (GMT)
44/12 < 37/6 Jul 02 22:42 UTC (GMT)
8/22 < 11/28 Jul 02 22:42 UTC (GMT)
- 49/50 < - 47/48 Jul 02 22:42 UTC (GMT)
16/18 < 23/16 < 51/20 Jul 02 22:42 UTC (GMT)
9/76 < 12/85 Jul 02 22:42 UTC (GMT)
- 28/34 < - 32/40 < - 37/57 < - 16/35 Jul 02 22:42 UTC (GMT)
- 24/17 < - 18/24 < - 13/28 Jul 02 22:42 UTC (GMT)
6/9 < 5/6 < 8/8 < 39/9 < 53/10 < 47/5 < 40/4 < 407/5 Jul 02 22:42 UTC (GMT)
- 17/10 < - 6/16 < - 6/17 Jul 02 22:42 UTC (GMT)
- 97/107 < - 90/100 Jul 02 22:42 UTC (GMT)
- 1 < 1/7 Jul 02 22:42 UTC (GMT)
- 22/23 < - 13/15 Jul 02 22:42 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: