Sort the Common Fractions String - 39/78, - 59/81, - 32/64 in Ascending Order. Online Calculator

The operation of sorting fractions in ascending order:
- 39/78, - 59/81, - 32/64

Analyze the fractions to be compared and ordered, by category:

negative proper fractions: - 39/78, - 59/81, - 32/64

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


The fraction: - 39/78

  • The prime factorizations of the numerator and denominator:
  • 39 = 3 × 13
  • 78 = 2 × 3 × 13
  • 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 (39; 78) = 3 × 13 = 39

- 39/78 = - (39 ÷ 39)/(78 ÷ 39) = - 1/2


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


- 39/78 = - (3 × 13)/(2 × 3 × 13) = - ((3 × 13) ÷ (3 × 13))/((2 × 3 × 13) ÷ (3 × 13)) = - 1/2



The fraction: - 59/81

- 59/81 is already reduced to the lowest terms.

The numerator and denominator have no common prime factors:


  • 59 is a prime number.
  • 81 = 34
  • GCF (59; 81) = 1


The fraction: - 32/64

  • 32 = 25
  • 64 = 26
  • GCF (32; 64) = 25 = 32

- 32/64 = - (32 ÷ 32)/(64 ÷ 32) = - 1/2


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


- 32/64 = - 25/26 = - (25 ÷ 25)/(26 ÷ 25) = - 1/2




To compare and sort the fractions, make their numerators the same.

Expand the fractions that have 1 as a numerator.

Multiply the numerator and denominator by the same number:

- 1/2 = - (59 × 1)/(59 × 2) = - 59/118

The fractions have the same numerator, compare their denominators.

The larger the denominator the larger the negative fraction.

The larger the denominator the smaller the positive fraction.


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

The fractions sorted in ascending order:
- 59/81 < - 59/118 = - 59/118

The initial fractions sorted in ascending order:
- 59/81 < - 39/78 = - 32/64

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:
- 43/90, - 67/87, - 40/73

» 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: