Compare the Two Common Fractions - 75/30 and - 85/34, Which One is Larger? Online Calculator

The operation of comparing fractions:
- 75/30 and - 85/34

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


The fraction: - 75/30

  • The prime factorizations of the numerator and denominator:
  • 75 = 3 × 52
  • 30 = 2 × 3 × 5
  • 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 (75; 30) = 3 × 5 = 15

- 75/30 = - (75 ÷ 15)/(30 ÷ 15) = - 5/2


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


- 75/30 = - (3 × 52)/(2 × 3 × 5) = - ((3 × 52) ÷ (3 × 5))/((2 × 3 × 5) ÷ (3 × 5)) = - 5/2



The fraction: - 85/34

  • 85 = 5 × 17
  • 34 = 2 × 17
  • GCF (85; 34) = 17

- 85/34 = - (85 ÷ 17)/(34 ÷ 17) = - 5/2


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


- 85/34 = - (5 × 17)/(2 × 17) = - ((5 × 17) ÷ 17)/((2 × 17) ÷ 17) = - 5/2




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:
- 5/2 = - 5/2

The initial fractions sorted in ascending order:
- 75/30 = - 85/34

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:
85/34 and 91/41

» 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: