Question

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

Answer 1

When comparing fractions with the same denominator, you can compare the numerators because the equal parts are the same.

Step-by-step explanation:

When comparing two fractions with the same denominator, you can simplify the comparison by only comparing the numerators. This is because the denominator represents the number of equal parts into which the whole has been divided, and if the denominators are the same, then the equal parts are also the same. So, by comparing the numerators, you are essentially comparing the quantities of the equal parts.

Answer 2

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.