Compare and sort in ascending order the two ordinary fractions, which one is larger: 100/30 vs. 3. Ordinary fractions compared and sorted in ascending order, result explained below

The operation of comparing fractions:
100/30 vs. 3

Reduce (simplify) fractions to their lowest terms equivalents:

100/30 = (22 × 52)/(2 × 3 × 5) = ((22 × 52) ÷ (2 × 5))/((2 × 3 × 5) ÷ (2 × 5)) = 10/3;


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:


3 = (3 × 3)/(3 × 1) = 9/3;


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:
9/3 < 10/3

The initial fractions in ascending order:
3 < 100/30

Compare and sort the fractions in ascending order:
- 3 vs. - 7/3


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

3 < 100/30 Jul 10 16:04 UTC (GMT)
- 6/14 < - 8/19 < - 10/30 Jul 10 16:04 UTC (GMT)
29/32 < 15/16 Jul 10 16:04 UTC (GMT)
8/13 < 6/4 Jul 10 16:04 UTC (GMT)
22/32 < 31/37 Jul 10 16:04 UTC (GMT)
- 11/15 < - 8/12 < - 63/109 Jul 10 16:04 UTC (GMT)
1/20 < 1/15 < 1/14 < 1/10 < 1/7 < 1/5 < 1/3 < 1/2 < 1 Jul 10 16:03 UTC (GMT)
8/18 < 17/27 Jul 10 16:03 UTC (GMT)
42/600 < 9/100 = 45/500 < 64/200 < 99/300 < 8/10 Jul 10 16:03 UTC (GMT)
1/8 < 4/8 Jul 10 16:03 UTC (GMT)
16/19 < 11/13 Jul 10 16:03 UTC (GMT)
- 6/7 < - 8/15 Jul 10 16:03 UTC (GMT)
1/4 < 1/3 < 2/5 Jul 10 16:03 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: