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

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.

hello :

70y^8 + 30y^6 = 2 ( 35 y^8 + 15y^6)

the lenght is : 35 y^8

the width is : 15y^6