how many times does one ninth go into four and one ninth

(4 1/9) ÷ (1/9)

First, write 4 1/9 as a common fraction  =  37/9:

(37/9) ÷ (1/9)

When dividing by a fraction multiply by the reciprocal:

(37/9) x (9/1)  =  37    (the nines cancel)

Another way to think of this problem:  How man ninths are there in 4 and 1/9?

There are 9 ninths in each 1, so there are 4 x 9 ninths in 4 (which is 36),

so in 4 1/9 there are 36 + 1 ninths.