Question

When two fractions, refer to the same whole and have the same denominators, explain why you can compare only the numrators ?

Answer 1

Ok, suppose that we have two fractions with the same denominator but different numerator, let's write them as:

a/b and c/b

We can write these two as:

a*(1/b) and c*(1/b)

Now if we want to add these, we get:

a*(1/b) + c*(1/b)

Now we can take the common factor (1/b), and write the sum as:

(a + c)*(1/b)

now we can rewrite this as:

(a + c)/b

then we got:

a/b + c/b = (a + c)/b

We can directly compare the numerators because we can think on the same denominator as a common factor.