To compare and sort multiple fractions, they should either have the same denominator or the same numerator.
The operation of comparing fractions:
490/1,048 and 494/1,058
Simplify the operation
Reduce (simplify) the fractions to their lowest terms equivalents:
490/1,048 = (2 × 5 × 72)/(23 × 131) = ((2 × 5 × 72) ÷ 2)/((23 × 131) ÷ 2) = 245/524
494/1,058 = (2 × 13 × 19)/(2 × 232) = ((2 × 13 × 19) ÷ 2)/((2 × 232) ÷ 2) = 247/529
To compare and sort the fractions, build them up to the same numerator.
To build the fractions up to the same numerator we have to:
1) calculate their common numerator
2) then calculate the expanding number of each fraction
3) then build up 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:
245 = 5 × 72
247 = 13 × 19
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 (245, 247) = 5 × 72 × 13 × 19 = 60,515
Calculate the expanding number of each fraction:
Divide the LCM by the numerator of each fraction.
245/524 : 60,515 ÷ 245 = (5 × 72 × 13 × 19) ÷ (5 × 72) = 247
247/529 : 60,515 ÷ 247 = (5 × 72 × 13 × 19) ÷ (13 × 19) = 245
Build up the fractions to the same common numerator:
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:
245/524 = (247 × 245)/(247 × 524) = 60,515/129,428
247/529 = (245 × 247)/(245 × 529) = 60,515/129,605
The fractions have the same numerator, compare their denominators.
The larger the denominator the smaller the positive fraction.
The larger the denominator the larger the negative fraction.
::: The operation of comparing fractions :::
The final answer:
The fractions sorted in ascending order:
60,515/129,605 < 60,515/129,428
The initial fractions sorted in ascending order:
494/1,058 < 490/1,048
How are the numbers being written on our website: comma ',' is used as a thousands separator; point '.' used as a decimal separator; numbers rounded off to max. 12 decimals (if the case). The set of the used symbols on our website: '/' the fraction bar; ÷ dividing; × multiplying; + plus (adding); - minus (subtracting); = equal; ≈ approximately equal.