Compare the given fractions :
9/20,13/25
Answers
The operation of comparing fractions:
9/20 and 13/25
Reduce (simplify) fractions to their lowest terms equivalents:
9/20 already reduced to the lowest terms;
the numerator and denominator have no common prime factors:
9 = 32;
20 = 22 × 5;
13/25 already reduced to the lowest terms;
the numerator and denominator have no common prime factors:
13 is a prime number;
25 = 52;
>> Reduce (simplify) fractions to their simplest form, online calculator
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:
20 = 22 × 5
25 = 52
Multiply all the unique prime factors, by the largest exponents:
LCM (20, 25) = 22 × 52 = 100
Calculate LCM, the least common multiple, online calculator
Calculate the expanding number of each fraction
Divide LCM by the denominator of each fraction:
For fraction: 9/20 is 100 ÷ 20 = (22 × 52) ÷ (22 × 5) = 5
For fraction: 13/25 is 100 ÷ 25 = (22 × 52) ÷ 52 = 4
Expand the fractions
Build up all the fractions to the same denominator (which is LCM).
Multiply the numerators and denominators by their expanding number:
9/20 = (5 × 9)/(5 × 20) = 45/100
13/25 = (4 × 13)/(4 × 25) = 52/100
The fractions have the same denominator, compare their numerators.
The larger the numerator the larger the positive fraction.
::: Comparing operation :::
The final answer:
The fractions sorted in ascending order:
45/100 < 52/100
The initial fractions in ascending order:
9/20 < 13/25
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