Compare and sort in ascending order the two ordinary fractions, which one is larger: - 338/1,002 vs. - 342/1,009. Ordinary fractions compared and sorted in ascending order, result explained below

The operation of comparing fractions:
- 338/1,002 vs. - 342/1,009

Reduce (simplify) fractions to their lowest terms equivalents:

- 338/1,002 = - (2 × 132)/(2 × 3 × 167) = - ((2 × 132) ÷ 2)/((2 × 3 × 167) ÷ 2) = - 169/501;


- 342/1,009 already reduced to the lowest terms;
the numerator and the denominator have no common prime factors:
342 = 2 × 32 × 19;
1,009 is a prime number;


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


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

Calculate LCM, the least common multiple of the numerators of the fractions

LCM will be the common numerator of the compared fractions.

The prime factorization of the numerators:


169 = 132;


342 = 2 × 32 × 19;


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


LCM (169, 342) = 2 × 32 × 132 × 19 = 57,798

Calculate LCM, the least common multiple, online calculator


Calculate the expanding number of each fraction

Divide LCM by the numerator of each fraction:


For fraction: - 169/501 is 57,798 ÷ 169 = (2 × 32 × 132 × 19) ÷ 132 = 342;


For fraction: - 342/1,009 is 57,798 ÷ 342 = (2 × 32 × 132 × 19) ÷ (2 × 32 × 19) = 169;



Expand the fractions

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

Multiply the numerators and the denominators by their expanding number:


- 169/501 = - (342 × 169)/(342 × 501) = - 57,798/171,342;


- 342/1,009 = - (169 × 342)/(169 × 1,009) = - 57,798/170,521;



The fractions have the same numerator, compare their denominators.

The larger the denominator the larger the negative fraction.

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

The fractions sorted in ascending order:
- 57,798/170,521 < - 57,798/171,342

The initial fractions in ascending order:
- 342/1,009 < - 338/1,002

Compare and sort the fractions in ascending order:
338/1,002 vs. 346/1,005


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

- 342/1009 < - 338/1002 Jul 04 03:06 UTC (GMT)
8/127 < 8/100 < 8/17 < 8/6 < 8/3 < 8/2 < 8 Jul 04 03:06 UTC (GMT)
10/10 < 9/4 < 38/9 < 136/24 < 31/4 Jul 04 03:06 UTC (GMT)
34/7 < 36/7 Jul 04 03:06 UTC (GMT)
- 18/139 < - 16/135 Jul 04 03:06 UTC (GMT)
1/8 < 3/12 Jul 04 03:06 UTC (GMT)
- 42/24 < - 62/40 < - 48/32 < - 25/46 Jul 04 03:06 UTC (GMT)
338/1008 < 348/1018 Jul 04 03:06 UTC (GMT)
5/8 < 375/100 Jul 04 03:06 UTC (GMT)
1/8 < 9/64 Jul 04 03:06 UTC (GMT)
17/60 < 26/70 Jul 04 03:06 UTC (GMT)
21/12 < 11/6 Jul 04 03:06 UTC (GMT)
21/60 < 30/62 Jul 04 03:06 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: