Please help me!When two Fractions refer to the same whole and have the same denominators, explain why you can compare only the numerators

Think about it in terms of division

Step-by-step explanation:

if comparing 1/5 with 3/5 both are divided by like terms if you add them you have a total of 4/5 or four parts of a whole, if you were to compare the denominator, you would end up with 4/10. Thinking in terms of a pie for instance: adding 1 slice to your other 3 slices on your plate leaves one slice behind so you took 4 out of the five, the size of the pie doesn't change (the denominator)

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).