Compare the Two Common Fractions 72/18 and 78/26, Which One is Larger? Online Calculator

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


The fraction: 72/18

  • The prime factorizations of the numerator and denominator:
  • 72 = 23 × 32
  • 18 = 2 × 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 (72; 18) = 2 × 32 = 18

72/18 = (72 ÷ 18)/(18 ÷ 18) = 4/1 = 4


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


72/18 = (23 × 32)/(2 × 32) = ((23 × 32) ÷ (2 × 32))/((2 × 32) ÷ (2 × 32)) = 4/1 = 4



The fraction: 78/26

  • 78 = 2 × 3 × 13
  • 26 = 2 × 13
  • GCF (78; 26) = 2 × 13 = 26

78/26 = (78 ÷ 26)/(26 ÷ 26) = 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:


78/26 = (2 × 3 × 13)/(2 × 13) = ((2 × 3 × 13) ÷ (2 × 13))/((2 × 13) ÷ (2 × 13)) = 3/1 = 3




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:
3 < 4

The initial fractions sorted in ascending order:
78/26 < 72/18

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:
- 72/18 and - 81/22

» 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: