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Comparing fractions operation: 5/6 vs. 14/15
Reduce (simplify) fractions to their lowest terms equivalents:
5/6 already reduced to lowest terms, numerator and denominator have no common prime factors, so their prime factorization is: 5 is a prime number and 6=2•3;
14/15 already reduced to lowest terms, numerator and denominator have no common prime factors, their prime factorization is: 14=2•7 and 15=3•5;
To sort fractions, build their denominators the same.
Calculate LCM (Least Common Multiple) of the reduced fractions' denominators, this will be the common denominator, also called LCD (Least Common Denominator) of the compared fractions:
6=2•3;
15=3•5;
For LCM, take all the unique prime factors, by the largest exponents: LCM (6,15)=2•3•5=30
Each fraction's expanding number (divide LCM by each fraction's denominator): For fraction: 5/6 is 30 divided by 6=(2•3•5) divided by (3•5)=2;
Expand the fractions, build each fraction up by multiplying its numerator and denominator by its expanding number, so all the denominators are built up to their LCM, the least common mutiple:
5/6=(5•5)/(5•6)=25/30;
14/15=(2•14)/(2•15)=28/30;
Fractions have equal denominators, simply compare their numerators.
The larger the numerator the larger the positive fraction.
Sorry for such a long explanation. Hope this helps you though! If not, please let me know!!!!
~Karleif Westsson
