Sort the Common Fractions String - 63/23, - 30/39, - 33/99 in Ascending Order. Online Calculator
The operation of sorting fractions in ascending order:
- 63/23, - 30/39, - 33/99
Analyze the fractions to be compared and ordered, by category:
1 negative improper fraction: - 63/23
negative proper fractions: - 30/39, - 33/99
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:
- 30/39 and - 33/99
Simplify the operation
Reduce (simplify) the fractions to their lowest terms equivalents:
- To reduce a fraction to the lowest terms equivalent: divide both the numerator and denominator by their greatest common factor, GCF.
The fraction: - 30/39
- The prime factorizations of the numerator and denominator:
- 30 = 2 × 3 × 5
- 39 = 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 (30; 39) = 3
- 30/39 = - (30 ÷ 3)/(39 ÷ 3) = - 10/13
The fraction can also be reduced without calculating GCF; factor the numerator and denominator and cross out all the common prime factors:
- 30/39 = - (2 × 3 × 5)/(3 × 13) = - ((2 × 3 × 5) ÷ 3)/((3 × 13) ÷ 3) = - 10/13
The fraction: - 33/99
- 33 = 3 × 11
- 99 = 32 × 11
- GCF (33; 99) = 3 × 11 = 33
- 33/99 = - (33 ÷ 33)/(99 ÷ 33) = - 1/3
The fraction can also be reduced without calculating GCF; factor the numerator and denominator and cross out all the common prime factors:
- 33/99 = - (3 × 11)/(32 × 11) = - ((3 × 11) ÷ (3 × 11))/((32 × 11) ÷ (3 × 11)) = - 1/3
To compare and sort the fractions, make their numerators the same.
Expand the fraction that has 1 as a numerator.
Multiply the numerator and denominator by the same number:
- 1/3 = - (10 × 1)/(10 × 3) = - 10/30
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 fractions sorted in ascending order:
- 10/13 < - 10/30
The initial fractions sorted in ascending order:
- 30/39 < - 33/99
::: The operation of comparing fractions :::
The final answer:
Sort the negative proper fractions in ascending order:
- 30/39 < - 33/99
All the fractions sorted in ascending order:
- 63/23 < - 30/39 < - 33/99
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.
Compare and sort common fractions, online calculator: