Fractions, theory: how to compare two fractions with both unlike (different) nominators and denominators?
Tutoring: Comparing ordinary fractions
How to compare two fractions?
To compare two fractions with equal denominators (like denominators), but different numerators (unlike numerators), the larger (bigger, greater) fraction is the one with the larger numerator.
To compare two fractions with equal numerators (like numerators), but different denominators (unlike denominators), the larger (bigger, greater) fraction is the one with the smaller denominator.
To compare two fractions with different denominators and numerators (unlike denominators, unlike numerators), fractions should be first brought to the same denominator (or if it's easier, to the same numerators):
Multiplying number of each fraction's both numerator and denominator must be calculated: divide the lowest common multiple LCM calculated above, by the denominator of each fraction, obtaining the corresponding multiplying number for each fraction
Multiply each fraction's both numerator and denominator by the corresponding multiplying number calculated above.
At this point, fractions are brought to the same denominator, so it's now only a simple task of comparing fractions' numerators.
The larger (bigger, greater) fraction will be the one with the larger numerator.
An example of comparing two fractions with different denominators and numerators (unlike denominators and numerators)
Let's compare these fractions: 16/24 and 45/75.
Reduce each fraction to lowest terms (simplify it):
Factorize into prime factors both the numerator and denominator of each fraction
Divide each fraction's both the numerator and denominator by the number containing only their common factors, at lowest powers - this is the greatest common factor GCF (greatest common divisor GCD) of each fraction's numerator and denominator