Question

Why can you compare two fractions with the same denominator by only comparing the numerators

Answer 1

Think about it like this: You have two pizzas that are cut in 8 pieces. You ate 5 and your friend ate 7. Who ate more? Obviously your friend did since 7 is greater than 5.  BUT, you can only do that if both pizzas were cut in 8 pieces. If your pizza was cut in 7 and his was cut in 12, you can't just look at the numerator and say your friend ate more. You have to find a common denominator. That's why when you have a common denominator you can compare fractions because the "things" are cut into equal pieces.