Compare and sort the fractions in ascending order: - 8/13, - 4/13, - 12/6, - 15/5. Common ordinary fractions compared and sorted in ascending order, result explained below

Sort: - 8/13, - 4/13, - 12/6, - 15/5

To compare and sort multiple fractions, they should either have the same denominator or the same numerator.

The operation of sorting fractions in ascending order:
- 8/13, - 4/13, - 12/6, - 15/5

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

negative improper fractions: - 12/6, - 15/5


negative proper fractions with equal denominators: - 8/13, - 4/13

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

- any negative improper fraction is smaller than...


- any negative proper fraction.



How do we compare and sort all the fractions?

It is clear that there is no point in comparing fractions from different categories.


We will compare and sort the fractions in each of the above categories, separately.


Sort the negative improper fractions in ascending order:
- 12/6 and - 15/5

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

By reducing the values of the numerators and denominators of the fractions, further calculations with these fractions become easier to do.


To reduce a fraction to the lowest terms equivalent: divide both the numerator and denominator by their greatest common factor, GCF.


Internal link » Reduce (simplify) common (ordinary) fractions to the lowest terms (to their simplest form equivalent), online calculator



- 12/6 = - (22 × 3)/(2 × 3) = - ((22 × 3) ÷ (2 × 3))/((2 × 3) ÷ (2 × 3)) = - 2/1 = - 2


- 15/5 = - (3 × 5)/5 = - ((3 × 5) ÷ 5)/(5 ÷ 5) = - 3/1 = - 3

Sort the integer numbers in ascending order.

This is a simple case of comparing and sorting integer numbers.


The integer numbers are a particular case of those fractions that have a denominator equal to 1.


Any integer number 'n' can be written as a fraction with a denominator of 1. Starting from here, by multiplying both the numerator and the denominator by the same number, an integer number can be written as a multitude of equivalent fractions:


n = n/1 = (2 × n)/2 = (3 × n)/3 = ...


Example: 3 = 3/1 = (2 × 3)/2 = 6/2 = (3 × 3)/3 = 9/3 = ...


The integer numbers sorted in ascending order:
- 3 < - 2

The initial fractions sorted in ascending order:
- 15/5 < - 12/6


Sort the negative proper fractions in ascending order:
- 8/13 and - 4/13

The fractions have the same denominator, compare their numerators.

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


The larger the numerator the smaller the negative fraction.


The larger the numerator the larger the positive fraction.


The fractions sorted in ascending order:
- 8/13 < - 4/13


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

Sort the negative improper fractions in ascending order:
- 15/5 < - 12/6

Sort the negative proper fractions in ascending order:
- 8/13 < - 4/13

All the fractions sorted in ascending order:
- 15/5 < - 12/6 < - 8/13 < - 4/13

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:
- 12/21, - 6/25, - 19/13, - 23/9

Compare and sort common ordinary fractions, online calculator:

The latest common ordinary fractions compared and sorted in ascending order

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: