The operation of sorting fractions in ascending order:
34/10, 24/13, 20/14
Analyze the fractions to be compared and ordered, by category:
positive improper fractions: 34/10, 24/13, 20/14;
Reduce (simplify) fractions to their lowest terms equivalents:
34/10 = (2 × 17)/(2 × 5) = ((2 × 17) ÷ 2)/((2 × 5) ÷ 2) = 17/5
24/13 already reduced to the lowest terms;
the numerator and denominator have no common prime factors:
24 = 23 × 3;
13 is a prime number;
20/14 = (22 × 5)/(2 × 7) = ((22 × 5) ÷ 2)/((2 × 7) ÷ 2) = 10/7
To sort fractions in ascending order, build up their denominators the same.
Calculate LCM, the least common multiple of the denominators of the fractions.
LCM will be the common denominator of the compared fractions.
In this case, LCM is also called LCD, the least common denominator.
The prime factorization of the denominators:
5 is a prime number
13 is a prime number
7 is a prime number
Multiply all the unique prime factors, by the largest exponents:
LCM (5, 13, 7) = 5 × 7 × 13 = 455
Calculate the expanding number of each fraction
Divide LCM by the denominator of each fraction:
For fraction: 17/5 is 455 ÷ 5 = (5 × 7 × 13) ÷ 5 = 91
For fraction: 24/13 is 455 ÷ 13 = (5 × 7 × 13) ÷ 13 = 35
For fraction: 10/7 is 455 ÷ 7 = (5 × 7 × 13) ÷ 7 = 65
Expand the fractions
Build up all the fractions to the same denominator (which is LCM).
Multiply the numerators and denominators by their expanding number:
17/5 = (91 × 17)/(91 × 5) = 1,547/455
24/13 = (35 × 24)/(35 × 13) = 840/455
10/7 = (65 × 10)/(65 × 7) = 650/455
The fractions have the same denominator, compare their numerators.
The larger the numerator the larger the positive fraction.
::: Comparing operation :::
The final answer: