Answer:
13/18 < 11/14.
Step-by-step explanation:
Reduce (simplify) fractions to their lowest terms equivalents:
13/18 already reduced to lowest terms, numerator and denominator have no common prime factors, their prime factorization:
13 is a prime number and 18 = 2 * 32;
11/14 already reduced to lowest terms, numerator and denominator have no common prime factors, their prime factorization:
11 is a prime number and 14 = 2 * 7;
To sort fractions, buld up their denominators the same.
Calculate LCM, the lowest common multiple of the reduced fractions' denominators, this will be the common denominator, also called LCD, the lowest common denominator of the compared fractions:
Denominators' prime factorization:
18 = 2 * 32;
14 = 2 * 7;
For LCM, take all the unique prime factors, by the largest exponents:
LCM (18, 14) = 2 * 32 * 7 = 126
Each fraction's expanding number (divide LCM by each fraction's denominator):
For fraction: 13/18 is: 126 ÷ 18 = (2 * 32 * 7) ÷ (2 * 32) = 7;
For fraction: 11/14 is: 126 ÷ 14 = (2 * 32 * 7) ÷ (2 * 7) = 9;
Expand the fractions, build up each fraction by multiplying its numerator and denominator by its expanding number, so all the denominators are built up to their LCM, the lowest common multiple:
13/18 = (7 * 13)/(7 * 18) = 91/126;
11/14 = (9 * 11)/(9 * 14) = 99/126;
Fractions have equal denominators, simply compare their numerators.
The larger the numerator the larger the positive fraction.
