Compare and sort in ascending order the set of the ordinary fractions: 8/32, 8/15, 16/54. Ordinary fractions compared and sorted in ascending order, result explained below

The operation of sorting fractions in ascending order:
8/32, 8/15, 16/54

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

positive proper fractions: 8/32, 8/15, 16/54;

Reduce (simplify) fractions to their lowest terms equivalents:

8/32 = 23/25 = (23 ÷ 23)/(25 ÷ 23) = 1/4;


8/15 already reduced to the lowest terms;
the numerator and the denominator have no common prime factors:
8 = 23;
15 = 3 × 5;


16/54 = 24/(2 × 33) = (24 ÷ 2)/((2 × 33) ÷ 2) = 8/27;


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


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

Expand the fractions that have 1 as a numerator


Multiply the numerator and the denominator by the same number:


1/4 = (8 × 1)/(8 × 4) = 8/32;


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:
8/32 < 8/27 < 8/15

The initial fractions in ascending order:
8/32 < 16/54 < 8/15

Compare and sort the fractions in ascending order:
15/41, 23/66, 16/23


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

8/32 < 16/54 < 8/15 Jul 04 02:48 UTC (GMT)
1/8 < 1/4 < 3/8 < 1/2 < 5/8 < 3/4 < 7/8 < 1 Jul 04 02:48 UTC (GMT)
5/29 < 7/34 Jul 04 02:48 UTC (GMT)
13/12 < 8/3 Jul 04 02:48 UTC (GMT)
4/15 < 1/3 Jul 04 02:48 UTC (GMT)
1/40 < 1/4 Jul 04 02:48 UTC (GMT)
11/36 < 18/40 Jul 04 02:48 UTC (GMT)
9/13 < 9/10 Jul 04 02:48 UTC (GMT)
17/43 < 18/40 < 16/30 < 14/23 < 17/21 Jul 04 02:48 UTC (GMT)
3/109 < 10025/1005 < 100300/10007 < 100 Jul 04 02:48 UTC (GMT)
5/20 < 9/25 Jul 04 02:48 UTC (GMT)
13/32 < 7/16 Jul 04 02:48 UTC (GMT)
9/20 < 8/15 Jul 04 02:48 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: