Compare and sort in ascending order the two ordinary fractions, which one is larger: - 190/119 and - 196/123. Ordinary fractions compared and sorted in ascending order, result explained below

Compare: - 190/119 and - 196/123

The operation of comparing fractions:
- 190/119 and - 196/123

Reduce (simplify) fractions to their lowest terms equivalents:

- 190/119 already reduced to the lowest terms;
the numerator and denominator have no common prime factors:
190 = 2 × 5 × 19;
119 = 7 × 17;


- 196/123 already reduced to the lowest terms;
the numerator and denominator have no common prime factors:
196 = 22 × 72;
123 = 3 × 41;


>> 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:


119 = 7 × 17


123 = 3 × 41


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


LCM (119, 123) = 3 × 7 × 17 × 41 = 14,637

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: - 190/119 is 14,637 ÷ 119 = (3 × 7 × 17 × 41) ÷ (7 × 17) = 123


For fraction: - 196/123 is 14,637 ÷ 123 = (3 × 7 × 17 × 41) ÷ (3 × 41) = 119



Expand the fractions

Build up all the fractions to the same denominator (which is LCM).
Multiply the numerators and denominators by their expanding number:

- 190/119 = - (123 × 190)/(123 × 119) = - 23,370/14,637


- 196/123 = - (119 × 196)/(119 × 123) = - 23,324/14,637



The fractions have the same denominator, compare their numerators.

The larger the numerator the smaller the negative fraction.

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

The fractions sorted in ascending order:
- 23,370/14,637 < - 23,324/14,637

The initial fractions in ascending order:
- 190/119 < - 196/123

More operations of this kind:

Compare and sort the fractions in ascending order:
196/123 and 204/132


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

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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:

(1) What is a fraction? Fractions types. How do they compare?


(2) Fractions changing form, expand and reduce (simplify) fractions


(3) Reducing fractions. The greatest common factor, GCF


(4) How to, comparing two fractions with unlike (different) numerators and denominators


(5) Sorting fractions in ascending order


(6) Adding ordinary (common, simple) fractions


(7) Subtracting ordinary (common, simple) fractions


(8) Multiplying ordinary (common, simple) fractions


(9) Fractions, theory: rational numbers