The operation of sorting fractions in ascending order:
4/19, 4/16, 13/20
Analyze the fractions to be compared and ordered, by category:
positive proper fractions: 4/19, 4/16, 13/20;
Reduce (simplify) fractions to their lowest terms equivalents:
4/19 already reduced to the lowest terms;
the numerator and the denominator have no common prime factors:
4 = 22;
19 is a prime number;
4/16 = 22/24 = (22 ÷ 22)/(24 ÷ 22) = 1/4;
13/20 already reduced to the lowest terms;
the numerator and the denominator have no common prime factors:
13 is a prime number;
20 = 22 × 5;
To sort fractions, build them up to the same numerator.
Calculate LCM, the least common multiple of the numerators of the fractions
LCM will be the common numerator of the compared fractions.
The prime factorization of the numerators:
4 = 22;
13 is a prime number;
Multiply all the unique prime factors, by the largest exponents:
LCM (4, 13) = 22 × 13 = 52
Calculate the expanding number of each fraction
Divide LCM by the numerator of each fraction:
For fraction: 4/19 is 52 ÷ 4 = (22 × 13) ÷ 22 = 13;
For fraction: 1/4 is 52;
For fraction: 13/20 is 52 ÷ 13 = (22 × 13) ÷ 13 = 4;
Expand the fractions
Build up all the fractions to the same numerator (which is LCM).
Multiply the numerators and the denominators by their expanding number:
4/19 = (13 × 4)/(13 × 19) = 52/247;
1/4 = (52 × 1)/(52 × 4) = 52/208;
13/20 = (4 × 13)/(4 × 20) = 52/80;
The fractions have the same numerator, compare their denominators.
The larger the denominator the smaller the positive fraction.
::: Comparing operation :::
The final answer: