Compare the Two Common Fractions 76/114 and 82/123, Which One is Larger? Online Calculator

The operation of comparing fractions:
76/114 and 82/123

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


The fraction: 76/114

  • The prime factorizations of the numerator and denominator:
  • 76 = 22 × 19
  • 114 = 2 × 3 × 19
  • 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 (76; 114) = 2 × 19 = 38

76/114 = (76 ÷ 38)/(114 ÷ 38) = 2/3


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


76/114 = (22 × 19)/(2 × 3 × 19) = ((22 × 19) ÷ (2 × 19))/((2 × 3 × 19) ÷ (2 × 19)) = 2/3



The fraction: 82/123

  • 82 = 2 × 41
  • 123 = 3 × 41
  • GCF (82; 123) = 41

82/123 = (82 ÷ 41)/(123 ÷ 41) = 2/3


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


82/123 = (2 × 41)/(3 × 41) = ((2 × 41) ÷ 41)/((3 × 41) ÷ 41) = 2/3




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:
2/3 = 2/3

The initial fractions sorted in ascending order:
76/114 = 82/123

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:
- 76/114 and - 79/123

» 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: