Compare and sort in ascending order the set of the ordinary fractions: 1,992/1,997, 1,993/1,997, 1,994/1,999, 1,995/2,000. Ordinary fractions compared and sorted in ascending order, result explained below

The operation of sorting fractions in ascending order:
1,992/1,997, 1,993/1,997, 1,994/1,999, 1,995/2,000

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

positive proper fractions: 1,992/1,997, 1,993/1,997, 1,994/1,999, 1,995/2,000;

Reduce (simplify) fractions to their lowest terms equivalents:

1,992/1,997 already reduced to the lowest terms;
the numerator and the denominator have no common prime factors:
1,992 = 23 × 3 × 83;
1,997 is a prime number;


1,993/1,997 already reduced to the lowest terms;
the numerator and the denominator have no common prime factors:
1,993 is a prime number;
1,997 is a prime number;


1,994/1,999 already reduced to the lowest terms;
the numerator and the denominator have no common prime factors:
1,994 = 2 × 997;
1,999 is a prime number;


1,995/2,000 = (3 × 5 × 7 × 19)/(24 × 53) = ((3 × 5 × 7 × 19) ÷ 5)/((24 × 53) ÷ 5) = 399/400;


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


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

Calculate LCM, the least common multiple of the denominators of the fractions.

LCM will be the common denominator of the compared fractions.
In this case, LCM is also called LCD, the least common denominator.

The prime factorization of the denominators:


1,997 is a prime number;


1,999 is a prime number;


400 = 24 × 52;


Multiply all the unique prime factors, by the largest exponents:


LCM (1997, 1999, 400) = 24 × 52 × 1,997 × 1,999 = 1,596,801,200

Calculate LCM, the least common multiple, online calculator


Calculate the expanding number of each fraction

Divide LCM by the denominator of each fraction:


For fraction: 1,992/1,997 is 1,596,801,200 ÷ 1,997 = (24 × 52 × 1,997 × 1,999) ÷ 1,997 = 799,600;


For fraction: 1,993/1,997 is 1,596,801,200 ÷ 1,997 = (24 × 52 × 1,997 × 1,999) ÷ 1,997 = 799,600;


For fraction: 1,994/1,999 is 1,596,801,200 ÷ 1,999 = (24 × 52 × 1,997 × 1,999) ÷ 1,999 = 798,800;


For fraction: 399/400 is 1,596,801,200 ÷ 400 = (24 × 52 × 1,997 × 1,999) ÷ (24 × 52) = 3,992,003;



Expand the fractions

Build up all the fractions to the same denominator (which is LCM).

Multiply the numerators and the denominators by their expanding number:


1,992/1,997 = (799,600 × 1,992)/(799,600 × 1,997) = 1,592,803,200/1,596,801,200;


1,993/1,997 = (799,600 × 1,993)/(799,600 × 1,997) = 1,593,602,800/1,596,801,200;


1,994/1,999 = (798,800 × 1,994)/(798,800 × 1,999) = 1,592,807,200/1,596,801,200;


399/400 = (3,992,003 × 399)/(3,992,003 × 400) = 1,592,809,197/1,596,801,200;



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:
1,592,803,200/1,596,801,200 < 1,592,807,200/1,596,801,200 < 1,592,809,197/1,596,801,200 < 1,593,602,800/1,596,801,200

The initial fractions in ascending order:
1,992/1,997 < 1,994/1,999 < 1,995/2,000 < 1,993/1,997

Compare and sort the fractions in ascending order:
1,995/2,003, 2,004/2,001, 1,999/2,006, 1,998/2,005


Writing numbers: comma ',' used as a thousands separator;

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

1992/1997 < 1994/1999 < 1995/2000 < 1993/1997 Jun 03 22:17 UTC (GMT)
2/9 < 3/12 Jun 03 22:16 UTC (GMT)
25/64 < 3/4 Jun 03 22:16 UTC (GMT)
17/15 < 15/6 Jun 03 22:16 UTC (GMT)
7/10 < 13/16 Jun 03 22:16 UTC (GMT)
17/24 < 6/7 Jun 03 22:16 UTC (GMT)
2/16 < 3/16 Jun 03 22:16 UTC (GMT)
1/8 < 1/7 < 1/6 Jun 03 22:16 UTC (GMT)
5/64 < 3/32 Jun 03 22:16 UTC (GMT)
7/32 < 1/4 Jun 03 22:16 UTC (GMT)
- 735/798 < - 730/796 Jun 03 22:16 UTC (GMT)
3/16 < 1/2 Jun 03 22:16 UTC (GMT)
1/10 < 3/16 Jun 03 22:16 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: