Sort the Common Fractions String - 40/15, - 9/12, - 3/16 in Ascending Order. Online Calculator

The operation of sorting fractions in ascending order:
- 40/15, - 9/12, - 3/16

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

1 negative improper fraction: - 40/15

negative proper fractions: - 9/12, - 3/16

How to compare and sort the fractions in ascending order, by categories:

- any negative improper fraction is smaller than...

- any negative proper fraction.


Sort the negative proper fractions in ascending order:
- 9/12 and - 3/16

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


The fraction: - 9/12

  • The prime factorizations of the numerator and denominator:
  • 9 = 32
  • 12 = 22 × 3
  • 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 (9; 12) = 3

- 9/12 = - (9 ÷ 3)/(12 ÷ 3) = - 3/4


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


- 9/12 = - 32/(22 × 3) = - (32 ÷ 3)/((22 × 3) ÷ 3) = - 3/4



The fraction: - 3/16

- 3/16 is already reduced to the lowest terms.

The numerator and denominator have no common prime factors:


  • 3 is a prime number.
  • 16 = 24
  • GCF (3; 16) = 1



In fact, the two fractions have equal numerators

The numerator of one of the reduced fractions is equal to the numerator of the other initial fraction:

- 3/4 and - 3/16


The fractions have the same numerator, compare their denominators.

This is one of the simplest cases when it comes to comparing and sorting fractions.

The larger the denominator the larger the negative fraction.

The larger the denominator the smaller the positive fraction.


The fractions sorted in ascending order:
- 3/4 < - 3/16

The initial fractions sorted in ascending order:
- 9/12 < - 3/16

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

Sort the negative proper fractions in ascending order:
- 9/12 < - 3/16

All the fractions sorted in ascending order:
- 40/15 < - 9/12 < - 3/16

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:
47/24, 12/20, 5/26

» 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: