Compare the Two Common Fractions 12/9 and 20/15, Which One is Larger? Online Calculator

The operation of comparing fractions:
12/9 and 20/15

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


The fraction: 12/9

  • The prime factorizations of the numerator and denominator:
  • 12 = 22 × 3
  • 9 = 32
  • 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 (12; 9) = 3

12/9 = (12 ÷ 3)/(9 ÷ 3) = 4/3


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


12/9 = (22 × 3)/32 = ((22 × 3) ÷ 3)/(32 ÷ 3) = 4/3



The fraction: 20/15

  • 20 = 22 × 5
  • 15 = 3 × 5
  • GCF (20; 15) = 5

20/15 = (20 ÷ 5)/(15 ÷ 5) = 4/3


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


20/15 = (22 × 5)/(3 × 5) = ((22 × 5) ÷ 5)/((3 × 5) ÷ 5) = 4/3




The fractions are equal.

This is one of the simplest cases when comparing two fractions.

Not only are the numerators of the fractions equal but their denominators are also equal.


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

The fractions sorted in ascending order:
4/3 = 4/3

The initial fractions sorted in ascending order:
12/9 = 20/15

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:
- 12/9 and - 17/14

» 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: