Compare and sort in ascending order the set of the ordinary fractions: - 7/3, - 18/12, - 15/12, - 44/55, - 90/150, 0, 10/18, 24/32, 9/12, 1, 14/12, 20/16, 22/20. Ordinary fractions compared and sorted in ascending order, result explained below

Sort: - 7/3, - 18/12, - 15/12, - 44/55, - 90/150, 0, 10/18, 24/32, 9/12, 1, 14/12, 20/16, 22/20

The operation of sorting fractions in ascending order:
- 7/3, - 18/12, - 15/12, - 44/55, - 90/150, 0, 10/18, 24/32, 9/12, 1, 14/12, 20/16, 22/20

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

negative improper fractions: - 7/3, - 18/12, - 15/12;


negative proper fractions: - 44/55, - 90/150;


zero: 0;


positive proper fractions: 10/18, 24/32, 9/12;


positive improper fractions: 1, 14/12, 20/16, 22/20;

How to sort and order fractions by categories:

Any negative improper fraction is smaller than


any negative proper fraction, which is smaller than


zero, which is smaller than


any positive proper fraction, which is smaller than


any positive improper fraction

We will sort the fractions of each of the above categories separately.

Sort the negative improper fractions:
- 7/3, - 18/12, - 15/12

Reduce (simplify) fractions to their lowest terms equivalents:

- 7/3 already reduced to the lowest terms;
the numerator and denominator have no common prime factors:
7 is a prime number;
3 is a prime number;


- 18/12 = - (2 × 32)/(22 × 3) = - ((2 × 32) ÷ (2 × 3))/((22 × 3) ÷ (2 × 3)) = - 3/2


- 15/12 = - (3 × 5)/(22 × 3) = - ((3 × 5) ÷ 3)/((22 × 3) ÷ 3) = - 5/4


>> Reduce (simplify) fractions to their simplest form, online calculator


To sort fractions in ascending order, build up their denominators the same.

Calculate LCM, the least common multiple of the denominators of the fractions.

LCM will be the common denominator of the compared fractions.
In this case, LCM is also called LCD, the least common denominator.

The prime factorization of the denominators:


3 is a prime number


2 is a prime number


4 = 22


Multiply all the unique prime factors, by the largest exponents:


LCM (3, 2, 4) = 22 × 3 = 12

Calculate LCM, the least common multiple, online calculator


Calculate the expanding number of each fraction

Divide LCM by the denominator of each fraction:


For fraction: - 7/3 is 12 ÷ 3 = (22 × 3) ÷ 3 = 4


For fraction: - 3/2 is 12 ÷ 2 = (22 × 3) ÷ 2 = 6


For fraction: - 5/4 is 12 ÷ 4 = (22 × 3) ÷ 22 = 3



Expand the fractions

Build up all the fractions to the same denominator (which is LCM).
Multiply the numerators and denominators by their expanding number:

- 7/3 = - (4 × 7)/(4 × 3) = - 28/12


- 3/2 = - (6 × 3)/(6 × 2) = - 18/12


- 5/4 = - (3 × 5)/(3 × 4) = - 15/12



The fractions have the same denominator, compare their numerators.

The larger the numerator the smaller the negative fraction.

The fractions sorted in ascending order:
- 28/12 < - 18/12 < - 15/12

The initial fractions in ascending order:
- 7/3 < - 18/12 < - 15/12


Sort the negative proper fractions:
- 44/55 and - 90/150

Reduce (simplify) fractions to their lowest terms equivalents:

- 44/55 = - (22 × 11)/(5 × 11) = - ((22 × 11) ÷ 11)/((5 × 11) ÷ 11) = - 4/5


- 90/150 = - (2 × 32 × 5)/(2 × 3 × 52) = - ((2 × 32 × 5) ÷ (2 × 3 × 5))/((2 × 3 × 52) ÷ (2 × 3 × 5)) = - 3/5


>> Reduce (simplify) fractions to their simplest form, online calculator


The fractions have the same denominator, compare their numerators.

The larger the numerator the smaller the negative fraction.

The fractions sorted in ascending order:
- 4/5 < - 3/5

The initial fractions in ascending order:
- 44/55 < - 90/150


Sort the positive proper fractions:
10/18, 24/32, 9/12

Reduce (simplify) fractions to their lowest terms equivalents:

10/18 = (2 × 5)/(2 × 32) = ((2 × 5) ÷ 2)/((2 × 32) ÷ 2) = 5/9


24/32 = (23 × 3)/25 = ((23 × 3) ÷ 23)/(25 ÷ 23) = 3/4


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


>> Reduce (simplify) fractions to their simplest form, online calculator


To sort fractions, build them up to the same numerator.

Calculate LCM, the least common multiple of the fractions' numerators

LCM will be the common numerator of the compared fractions.

The prime factorization of the numerators:


5 is a prime number


3 is a prime number


Multiply all the unique prime factors, by the largest exponents:


LCM (5, 3) = 3 × 5 = 15

Calculate LCM, the least common multiple, online calculator


Calculate the expanding number of each fraction

Divide LCM by the numerator of each fraction:


For fraction: 5/9 is 15 ÷ 5 = (3 × 5) ÷ 5 = 3


For fraction: 3/4 is 15 ÷ 3 = (3 × 5) ÷ 3 = 5



Expand the fractions

Build up all the fractions to the same numerator (which is LCM).
Multiply the numerators and denominators by their expanding number:

5/9 = (3 × 5)/(3 × 9) = 15/27


3/4 = (5 × 3)/(5 × 4) = 15/20


3/4 = (5 × 3)/(5 × 4) = 15/20



The fractions have the same numerator, compare their denominators.

The larger the denominator the smaller the positive fraction.

The fractions sorted in ascending order:
15/27 < 15/20 = 15/20

The initial fractions in ascending order:
10/18 < 24/32 = 9/12


Sort the positive improper fractions:
1, 14/12, 20/16, 22/20

Reduce (simplify) fractions to their lowest terms equivalents:

14/12 = (2 × 7)/(22 × 3) = ((2 × 7) ÷ 2)/((22 × 3) ÷ 2) = 7/6


20/16 = (22 × 5)/24 = ((22 × 5) ÷ 22)/(24 ÷ 22) = 5/4


22/20 = (2 × 11)/(22 × 5) = ((2 × 11) ÷ 2)/((22 × 5) ÷ 2) = 11/10


>> Reduce (simplify) fractions to their simplest form, online calculator


To sort fractions in ascending order, build up their denominators the same.

Calculate LCM, the least common multiple of the denominators of the fractions.

LCM will be the common denominator of the compared fractions.
In this case, LCM is also called LCD, the least common denominator.

The prime factorization of the denominators:


6 = 2 × 3


4 = 22


10 = 2 × 5


Multiply all the unique prime factors, by the largest exponents:


LCM (6, 4, 10) = 22 × 3 × 5 = 60

Calculate LCM, the least common multiple, online calculator


Calculate the expanding number of each fraction

Divide LCM by the denominator of each fraction:


For fraction: 1 is 60


For fraction: 7/6 is 60 ÷ 6 = (22 × 3 × 5) ÷ (2 × 3) = 10


For fraction: 5/4 is 60 ÷ 4 = (22 × 3 × 5) ÷ 22 = 15


For fraction: 11/10 is 60 ÷ 10 = (22 × 3 × 5) ÷ (2 × 5) = 6



Expand the fractions

Build up all the fractions to the same denominator (which is LCM).
Multiply the numerators and denominators by their expanding number:

1/1 = (60 × 1)/(60 × 1) = 60/60


7/6 = (10 × 7)/(10 × 6) = 70/60


5/4 = (15 × 5)/(15 × 4) = 75/60


11/10 = (6 × 11)/(6 × 10) = 66/60



The fractions have the same denominator, compare their numerators.

The larger the numerator the larger the positive fraction.

The fractions sorted in ascending order:
60/60 < 66/60 < 70/60 < 75/60

The initial fractions in ascending order:
1 < 22/20 < 14/12 < 20/16


::: Comparing operation :::
The final answer:

Negative improper fractions, in ascending order:
- 7/3 < - 18/12 < - 15/12

Negative proper fractions, in ascending order:
- 44/55 < - 90/150

Positive proper fractions, in ascending order:
10/18 < 24/32 = 9/12

Positive improper fractions, in ascending order:
1 < 22/20 < 14/12 < 20/16

All the fractions sorted in ascending order:
- 7/3 < - 18/12 < - 15/12 < - 44/55 < - 90/150 < 0 < 10/18 < 9/12 = 24/32 < 1 < 22/20 < 14/12 < 20/16

More operations of this kind:

Compare and sort the fractions in ascending order:
- 18/8, - 28/17, - 25/16, - 48/60, - 98/155, - 2/11, - 15/25, - 16/22, - 27/44, - 3/7, - 27/28, - 25/21, - 25/19


Symbols: / fraction bar; ÷ divide; × multiply; + plus; - minus; = equal; < less than;

Compare and sort ordinary fractions, online calculator

The latest fractions compared and sorted in ascending order

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see more... compared fractions
see more... sorted fractions

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) math fractions theory:

(1) What is a fraction? Fractions types. How do they compare?


(2) Fractions changing form, expand and reduce (simplify) fractions


(3) Reducing fractions. The greatest common factor, GCF


(4) How to, comparing two fractions with unlike (different) numerators and denominators


(5) Sorting fractions in ascending order


(6) Adding ordinary (common, simple) fractions


(7) Subtracting ordinary (common, simple) fractions


(8) Multiplying ordinary (common, simple) fractions


(9) Fractions, theory: rational numbers