Compare the Two Common Fractions - 207/69 and - 216/72, Which One is Larger? Online Calculator

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


The fraction: - 207/69

  • The prime factorizations of the numerator and denominator:
  • 207 = 32 × 23
  • 69 = 3 × 23
  • 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 (207; 69) = 3 × 23 = 69

- 207/69 = - (207 ÷ 69)/(69 ÷ 69) = - 3/1 = - 3


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


- 207/69 = - (32 × 23)/(3 × 23) = - ((32 × 23) ÷ (3 × 23))/((3 × 23) ÷ (3 × 23)) = - 3/1 = - 3



The fraction: - 216/72

  • 216 = 23 × 33
  • 72 = 23 × 32
  • GCF (216; 72) = 23 × 32 = 72

- 216/72 = - (216 ÷ 72)/(72 ÷ 72) = - 3/1 = - 3


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


- 216/72 = - (23 × 33)/(23 × 32) = - ((23 × 33) ÷ (23 × 32))/((23 × 32) ÷ (23 × 32)) = - 3/1 = - 3




The numbers are equal.

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:
- 3 = - 3

The initial fractions sorted in ascending order:
- 207/69 = - 216/72

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:
216/72 and 225/78

» 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: