Sort the Common Fractions String - 30/10, - 51/16, - 64/16 in Ascending Order. Online Calculator

The operation of sorting fractions in ascending order:
- 30/10, - 51/16, - 64/16

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

negative improper fractions: - 30/10, - 51/16, - 64/16

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


The fraction: - 30/10

  • The prime factorizations of the numerator and denominator:
  • 30 = 2 × 3 × 5
  • 10 = 2 × 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 (30; 10) = 2 × 5 = 10

- 30/10 = - (30 ÷ 10)/(10 ÷ 10) = - 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:


- 30/10 = - (2 × 3 × 5)/(2 × 5) = - ((2 × 3 × 5) ÷ (2 × 5))/((2 × 5) ÷ (2 × 5)) = - 3/1 = - 3



The fraction: - 51/16

- 51/16 is already reduced to the lowest terms.

The numerator and denominator have no common prime factors:


  • 51 = 3 × 17
  • 16 = 24
  • GCF (51; 16) = 1


The fraction: - 64/16

  • 64 = 26
  • 16 = 24
  • GCF (64; 16) = 24 = 16

- 64/16 = - (64 ÷ 16)/(16 ÷ 16) = - 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:


- 64/16 = - 26/24 = - (26 ÷ 24)/(24 ÷ 24) = - 4/1 = - 4




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

Expand the fractions that have 1 as a denominator.

Multiply the numerator and denominator by the same number:

- 3 = - (16 × 3)/(16 × 1) = - 48/16

- 4 = - (16 × 4)/(16 × 1) = - 64/16

The fractions have the same denominator, compare their numerators.

The larger the numerator the smaller the negative fraction.

The larger the numerator the larger the positive fraction.


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

The fractions sorted in ascending order:
- 64/16 < - 51/16 < - 48/16

The initial fractions sorted in ascending order:
- 64/16 < - 51/16 < - 30/10

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:
- 38/15, - 59/20, - 75/24

» 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: