Compare and sort the fractions in ascending order: - 334/559, - 3,039/5,051, - 30,034/50,044, - 38/62, - 61/108. Common ordinary fractions compared and sorted in ascending order, result explained below
Sort: - 334/559, - 3,039/5,051, - 30,034/50,044, - 38/62, - 61/108
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:
- 334/559, - 3,039/5,051, - 30,034/50,044, - 38/62, - 61/108
Analyze the fractions to be compared and ordered, by category:
negative proper fractions: - 334/559, - 3,039/5,051, - 30,034/50,044, - 38/62, - 61/108
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.
- 334/559 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors:
334 = 2 × 167
559 = 13 × 43
- 3,039/5,051 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors:
3,039 = 3 × 1,013
5,051 is a prime number.
- 30,034/50,044 = - (2 × 15,017)/(22 × 12,511) = - ((2 × 15,017) ÷ 2)/((22 × 12,511) ÷ 2) = - 15,017/25,022
- 38/62 = - (2 × 19)/(2 × 31) = - ((2 × 19) ÷ 2)/((2 × 31) ÷ 2) = - 19/31
- 61/108 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors:
61 is a prime number.
108 = 22 × 33
To compare and sort the fractions, make their numerators the same.
To make the fractions' numerators the same - we have to:
1) calculate their common numerator
2) then calculate the expanding number of each fraction
3) then make their numerators the same by expanding the fractions to equivalent forms, which all have equal numerators
Calculate the common numerator
The common numerator is nothing else than the least common multiple (LCM) of the numerators of the fractions.
The LCM will be the common numerator of the compared fractions.
To calculate the LCM, we need the prime factorization of the numerators:
334 = 2 × 167
3,039 = 3 × 1,013
15,017 is a prime number.
19 is a prime number.
61 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 (334, 3039, 15017, 19, 61) = 2 × 3 × 19 × 61 × 167 × 1,013 × 15,017 = 17,666,226,067,278
Calculate the expanding number of each fraction:
Divide the LCM by the numerator of each fraction.
- 334/559 : 17,666,226,067,278 ÷ 334 = (2 × 3 × 19 × 61 × 167 × 1,013 × 15,017) ÷ (2 × 167) = 52,892,892,417
- 3,039/5,051 : 17,666,226,067,278 ÷ 3,039 = (2 × 3 × 19 × 61 × 167 × 1,013 × 15,017) ÷ (3 × 1,013) = 5,813,170,802
- 15,017/25,022 : 17,666,226,067,278 ÷ 15,017 = (2 × 3 × 19 × 61 × 167 × 1,013 × 15,017) ÷ 15,017 = 1,176,415,134
- 19/31 : 17,666,226,067,278 ÷ 19 = (2 × 3 × 19 × 61 × 167 × 1,013 × 15,017) ÷ 19 = 929,801,371,962
- 61/108 : 17,666,226,067,278 ÷ 61 = (2 × 3 × 19 × 61 × 167 × 1,013 × 15,017) ÷ 61 = 289,610,263,398
Make the fractions' numerators the same:
Expand each fraction: multiply both its numerator and denominator by its corresponding expanding number, calculated at the step 2, above.
This way all the fractions will have the same numerator:
- 334/559 = - (52,892,892,417 × 334)/(52,892,892,417 × 559) = - 17,666,226,067,278/29,567,126,861,103
- 3,039/5,051 = - (5,813,170,802 × 3,039)/(5,813,170,802 × 5,051) = - 17,666,226,067,278/29,362,325,720,902
- 15,017/25,022 = - (1,176,415,134 × 15,017)/(1,176,415,134 × 25,022) = - 17,666,226,067,278/29,436,259,482,948
- 19/31 = - (929,801,371,962 × 19)/(929,801,371,962 × 31) = - 17,666,226,067,278/28,823,842,530,822
- 61/108 = - (289,610,263,398 × 61)/(289,610,263,398 × 108) = - 17,666,226,067,278/31,277,908,446,984
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 operation of comparing fractions :::
The final answer:
The fractions sorted in ascending order:
- 17,666,226,067,278/28,823,842,530,822 < - 17,666,226,067,278/29,362,325,720,902 < - 17,666,226,067,278/29,436,259,482,948 < - 17,666,226,067,278/29,567,126,861,103 < - 17,666,226,067,278/31,277,908,446,984
The initial fractions sorted in ascending order:
- 38/62 < - 3,039/5,051 < - 30,034/50,044 < - 334/559 < - 61/108
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.
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