Compare and sort in ascending order the set of the ordinary fractions: 1/10, 20/2, 3/7, 7/5. Ordinary fractions compared and sorted in ascending order, result explained below

The operation of sorting fractions in ascending order:
1/10, 20/2, 3/7, 7/5

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

positive proper fractions: 1/10, 3/7;


positive improper fractions: 20/2, 7/5;

How to sort and order fractions by categories:

Any positive proper fraction is smaller than


any positive improper fraction

We will sort the fractions of each of the above categories separately.

Sort the positive proper fractions:
1/10 vs. 3/7

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:


1/10 = (3 × 1)/(3 × 10) = 3/30;


The fractions have the same numerator, compare their denominators.

The larger the denominator the smaller the positive fraction.

The fractions sorted in ascending order:
3/30 < 3/7

The initial fractions in ascending order:
1/10 < 3/7


Sort the positive improper fractions:
20/2 vs. 7/5

Reduce (simplify) fractions to their lowest terms equivalents:

20/2 = (22 × 5)/2 = ((22 × 5) ÷ 2)/(2 ÷ 2) = 10/1 = 10;


7/5 already reduced to the lowest terms;
the numerator and the denominator have no common prime factors:
7 is a prime number;
5 is a prime number;


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:


10 = (5 × 10)/(5 × 1) = 50/5;


The fractions have the same denominator, compare their numerators.

The larger the numerator the larger the positive fraction.

The fractions sorted in ascending order:
7/5 < 50/5

The initial fractions in ascending order:
7/5 < 20/2


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

Positive proper fractions, in ascending order:
1/10 < 3/7

Positive improper fractions, in ascending order:
7/5 < 20/2

All the fractions sorted in ascending order:
1/10 < 3/7 < 7/5 < 20/2

Compare and sort the fractions in ascending order:
3/15, 10/17, 13/7, 31/4


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

1/10 < 3/7 < 7/5 < 20/2 Jul 02 20:58 UTC (GMT)
71/95 < 67/79 Jul 02 20:58 UTC (GMT)
1/4 < 11/32 Jul 02 20:58 UTC (GMT)
16/28 < 24/36 Jul 02 20:58 UTC (GMT)
- 674/1007 < - 667/1000 Jul 02 20:58 UTC (GMT)
13/15 < 13/14 Jul 02 20:58 UTC (GMT)
6/16 < 10/19 Jul 02 20:58 UTC (GMT)
- 18/16 < - 10/10 Jul 02 20:58 UTC (GMT)
- 14/27 < - 16/31 Jul 02 20:58 UTC (GMT)
32/20 < 33/17 < 32/16 < 36/11 Jul 02 20:58 UTC (GMT)
7/10 = 70/100 Jul 02 20:58 UTC (GMT)
- 76/77 < - 68/70 Jul 02 20:58 UTC (GMT)
18/35 < 22/31 < 25/29 Jul 02 20:58 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: