The operation of comparing fractions:
^{- 44}/_{137} and ^{- 52}/_{142}
Reduce (simplify) fractions to their lowest terms equivalents:
- ^{44}/_{137} already reduced to the lowest terms;
the numerator and denominator have no common prime factors:
44 = 2^{2} × 11;
137 is a prime number;
- ^{52}/_{142} = - ^{(22 × 13)}/_{(2 × 71)} = - ^{((22 × 13) ÷ 2)}/_{((2 × 71) ÷ 2)} = - ^{26}/_{71}
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:
44 = 2^{2} × 11
26 = 2 × 13
Multiply all the unique prime factors, by the largest exponents:
LCM (44, 26) = 2^{2} × 11 × 13 = 572
Calculate the expanding number of each fraction
Divide LCM by the numerator of each fraction:
For fraction: - ^{44}/_{137} is 572 ÷ 44 = (2^{2} × 11 × 13) ÷ (2^{2} × 11) = 13
For fraction: - ^{26}/_{71} is 572 ÷ 26 = (2^{2} × 11 × 13) ÷ (2 × 13) = 22
Expand the fractions
Build up all the fractions to the same numerator (which is LCM).
Multiply the numerators and denominators by their expanding number:
- ^{44}/_{137} = - ^{(13 × 44)}/_{(13 × 137)} = - ^{572}/_{1,781}
- ^{26}/_{71} = - ^{(22 × 26)}/_{(22 × 71)} = - ^{572}/_{1,562}
The fractions have the same numerator, compare their denominators.
The larger the denominator the larger the negative fraction.
::: Comparing operation :::
The final answer: