Compare the Two Common Fractions - 108/3 and - 117/9, Which One is Larger? Online Calculator

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


The fraction: - 108/3

  • The prime factorizations of the numerator and denominator:
  • 108 = 22 × 33
  • 3 is a prime number.
  • Multiply all the common prime factors: if there are repeating prime factors we only take them once, and only the ones having the lowest exponent (the lowest powers).
  • GCF (108; 3) = 3

- 108/3 = - (108 ÷ 3)/(3 ÷ 3) = - 36/1 = - 36


The fraction can also be reduced without calculating GCF; factor the numerator and denominator and cross out all the common prime factors:


- 108/3 = - (22 × 33)/3 = - ((22 × 33) ÷ 3)/(3 ÷ 3) = - 36/1 = - 36



The fraction: - 117/9

  • 117 = 32 × 13
  • 9 = 32
  • GCF (117; 9) = 32 = 9

- 117/9 = - (117 ÷ 9)/(9 ÷ 9) = - 13/1 = - 13


The fraction can also be reduced without calculating GCF; factor the numerator and denominator and cross out all the common prime factors:


- 117/9 = - (32 × 13)/32 = - ((32 × 13) ÷ 32)/(32 ÷ 32) = - 13/1 = - 13




Sort the integer numbers in ascending order.

This is a simple case of comparing and sorting integer numbers.

The integer numbers are a particular case of those fractions that have a denominator equal to 1.


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

The integer numbers sorted in ascending order:
- 36 < - 13

The initial fractions sorted in ascending order:
- 108/3 < - 117/9

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:
117/9 and 122/19

» New. All the Calculations Performed by Our Visitors: Common Fractions Compared and Sorted. Data organized on a Monthly Basis

Compare and sort common fractions, online calculator:

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: