when two fractions refer to the same whole and have the same denominators, explain why you can compare only the numerators

When two fractions with the same denominators are used to refer the same whole numbers have have the same denominator, you compare only the numerator because the denominators are already equal and the only sufficient part to confirm that the fractions are equal is if the denominators are equal. This is because the only way two fractions with the same denominator can be equal to each other is if they both have equal numerators.