Question

6:11 and 7:12 solve this question this is cross product question

Answer 1

Reduce (simplify) fractions to their lowest terms equivalents:

7/12 already reduced to lowest terms, numerator and denominator have no common prime factors, their prime factorization:  

7 is a prime number and 12 = 22 * 3;

6/11 already reduced to lowest terms, numerator and denominator have no common prime factors, their prime factorization:  

6 = 2 * 3 and 11 is a prime number;

To sort fractions, build up their numerators the same.

Calculate fractions' numerators LCM (lowest common multiple), it will be the common numerator of the compared fractions:

Numerators' prime factorization:

7 is a prime number;

6 = 2 * 3;

For LCM, take all the unique prime factors, by the largest exponents:  

LCM (7, 6) = 2 * 3 * 7 = 42

Calculate each fraction's expanding number (LCM divided by each fraction's numerator):

For fraction: 7/12 is: 42 ÷ 7 = (2 * 3 * 7) ÷ 7 = 6;

For fraction: 6/11 is: 42 ÷ 6 = (2 * 3 * 7) ÷ (2 * 3) = 7;

Expand the fractions, build up each fraction by multiplying its numerator and denominator by its expanding number, so all the numerators are built up to their LCM, the lowest common multiple:

7/12 = (6 * 7)/(6 * 12) = 42/72;

6/11 = (7 * 6)/(7 * 11) = 42/77;

Fractions have equal numerators, simply compare their denominators.

The larger the denominator the smaller the positive fraction.

::: Comparing operation :::  

Final answer:

 

Fractions sorted in ascending order:  

42/77 < 42/72  

Initial fractions in ascending order:  

6/11 < 7/12