Sort the Common Fractions String - 143/12, - 140/23, - 83/14, - 94/19, - 61/103, - 61/119 in Ascending Order. Online Calculator
The operation of sorting fractions in ascending order:
- 143/12, - 140/23, - 83/14, - 94/19, - 61/103, - 61/119
Analyze the fractions to be compared and ordered, by category:
negative improper fractions: - 143/12, - 140/23, - 83/14, - 94/19
negative proper fractions with equal numerators: - 61/103, - 61/119
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:
- 143/12, - 140/23, - 83/14, - 94/19
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: - 143/12
- 143/12 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors:
- 143 = 11 × 13
- 12 = 22 × 3
- GCF (143; 12) = 1
The fraction: - 140/23
- 140/23 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors:
- 140 = 22 × 5 × 7
- 23 is a prime number.
- GCF (140; 23) = 1
The fraction: - 83/14
- 83/14 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors:
- 83 is a prime number.
- 14 = 2 × 7
- GCF (83; 14) = 1
The fraction: - 94/19
- 94/19 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors:
- 94 = 2 × 47
- 19 is a prime number.
- GCF (94; 19) = 1
To compare and sort the fractions, make their denominators the same.
To make the fractions' denominators the same - we have to:
- 1) calculate their common denominator
- 2) then calculate the expanding number of each fraction
- 3) expand the fractions to equivalent forms having the same denominator
Calculate the common denominator
The common denominator is nothing else than the least common multiple (LCM) of the denominators of the fractions.
To calculate the LCM, we need the prime factorization of the denominators:
12 = 22 × 3
23 is a prime number.
14 = 2 × 7
19 is a prime number.
Multiply all the unique prime factors: if there are repeating prime factors we only take them once, and only the ones having the highest exponent (the highest powers).
LCM (12, 23, 14, 19) = 22 × 3 × 7 × 19 × 23 = 36,708
Calculate the expanding number of each fraction:
Divide the LCM by the denominator of each fraction.
- 143/12 ⟶ 36,708 ÷ 12 = (22 × 3 × 7 × 19 × 23) ÷ (22 × 3) = 3,059
- 140/23 ⟶ 36,708 ÷ 23 = (22 × 3 × 7 × 19 × 23) ÷ 23 = 1,596
- 83/14 ⟶ 36,708 ÷ 14 = (22 × 3 × 7 × 19 × 23) ÷ (2 × 7) = 2,622
- 94/19 ⟶ 36,708 ÷ 19 = (22 × 3 × 7 × 19 × 23) ÷ 19 = 1,932
Make the denominators of the fractions the same:
- Expand each fraction: multiply both its numerator and denominator by its corresponding expanding number, calculated above.
- This way all the fractions will have the same denominator:
- 143/12 = - (3,059 × 143)/(3,059 × 12) = - 437,437/36,708
- 140/23 = - (1,596 × 140)/(1,596 × 23) = - 223,440/36,708
- 83/14 = - (2,622 × 83)/(2,622 × 14) = - 217,626/36,708
- 94/19 = - (1,932 × 94)/(1,932 × 19) = - 181,608/36,708
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 fractions sorted in ascending order:
- 437,437/36,708 < - 223,440/36,708 < - 217,626/36,708 < - 181,608/36,708
The initial fractions sorted in ascending order:
- 143/12 < - 140/23 < - 83/14 < - 94/19
Sort the negative proper fractions in ascending order:
- 61/103 and - 61/119
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:
- 61/103 < - 61/119
::: The operation of comparing fractions :::
The final answer:
Sort the negative improper fractions in ascending order:
- 143/12 < - 140/23 < - 83/14 < - 94/19
Sort the negative proper fractions in ascending order:
- 61/103 < - 61/119
All the fractions sorted in ascending order:
- 143/12 < - 140/23 < - 83/14 < - 94/19 < - 61/103 < - 61/119
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: