Compare and sort in ascending order the two common ordinary fractions, which one is larger: - 363/1,028 and - 373/1,035. Common ordinary fractions compared and sorted in ascending order, result explained below

Compare: - 363/1,028 and - 373/1,035

To compare and sort multiple fractions, they should either have the same denominator or the same numerator.

The operation of comparing fractions:
- 363/1,028 and - 373/1,035

Simplify the operation
Reduce (simplify) the fractions to their lowest terms equivalents:

By reducing the values of the numerators and denominators of the fractions, further calculations with these fractions become easier to do.


To reduce a fraction to the lowest terms equivalent: divide both the numerator and denominator by their greatest common factor, GCF.


Internal link » Reduce (simplify) common (ordinary) fractions to the lowest terms (to their simplest form equivalent), online calculator


- 363/1,028 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors:
363 = 3 × 112
1,028 = 22 × 257

- 373/1,035 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors:
373 is a prime number.
1,035 = 32 × 5 × 23

To compare and sort the fractions, make their numerators the same.

To make the fractions' numerators the same - we have to:

1) calculate their common numerator


2) then calculate the expanding number of each fraction


3) then make their numerators the same by expanding the fractions to equivalent forms, which all have equal numerators

Calculate the common numerator

The common numerator is nothing else than the least common multiple (LCM) of the numerators of the fractions.


The LCM will be the common numerator of the compared fractions.


To calculate the LCM, we need the prime factorization of the numerators:


363 = 3 × 112


373 is a prime number.


Multiply all the unique prime factors: if there are repeating prime factors we only take them once, and only the ones having the highest exponent (the highest powers).


External link » Calculate LCM, the least common multiple of numbers, online calculator


LCM (363, 373) = 3 × 112 × 373 = 135,399


Calculate the expanding number of each fraction:

Divide the LCM by the numerator of each fraction.


- 363/1,028 : 135,399 ÷ 363 = (3 × 112 × 373) ÷ (3 × 112) = 373


- 373/1,035 : 135,399 ÷ 373 = (3 × 112 × 373) ÷ 373 = 363



Make the fractions' numerators the same:

Expand each fraction: multiply both its numerator and denominator by its corresponding expanding number, calculated at the step 2, above.


This way all the fractions will have the same numerator:



- 363/1,028 = - (373 × 363)/(373 × 1,028) = - 135,399/383,444


- 373/1,035 = - (363 × 373)/(363 × 1,035) = - 135,399/375,705


The fractions have the same numerator, compare their denominators.

The larger the denominator the larger the negative fraction.


The larger the denominator the smaller the positive fraction.


::: The operation of comparing fractions :::
The final answer:

The fractions sorted in ascending order:
- 135,399/375,705 < - 135,399/383,444

The initial fractions sorted in ascending order:
- 373/1,035 < - 363/1,028

How are the numbers written: comma ',' used as a thousands separator; point '.' as a decimal separator; numbers rounded off to max. 12 decimals (if the case). Used symbols: '/' the fraction bar; ÷ dividing; × multiplying; + plus (adding); - minus (subtracting); = equal; ≈ approximately equal.

Other similar operations

Compare and sort the fractions in ascending order:
373/1,035 and 377/1,039

Compare and sort common ordinary fractions, online calculator:

The latest common ordinary fractions compared and sorted in ascending order

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) fractions / theory: