+6251 \(\text{Couple ways to do this}\\ 1)~\text{convert both to proper fractions and multiply}\\ 19\dfrac 3 4 = \dfrac{79}{4}\\ 1\dfrac 2 5 = \dfrac 7 5\\ \dfrac{79}{4}\dfrac{7}{5} = \dfrac{553}{20}\)
\(2) \text{distribute }\\ \left(19+\dfrac 3 4\right)\left(1+\dfrac 2 5\right) = \\ 19 + \dfrac 3 4 + \dfrac{38}{5} + \dfrac{6}{20} = \dfrac{553}{20}\)
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Nickolas, I could understand your answer. Rom's... well, I'm sure it's accurate, but I have no idea where those numbers came from.
+118667 I am sure you are grateful to both oRom and Nickolas for their time and effort,
but I am equally sure they would both like to hear that from you.
Fractions are very difficult to learn. Much more difficult than most mathematicians realize and it is difficult to teach it on the internet.
But i will give it a go.
\(19\frac{3}{4}\times 1\frac{2}{5}\)
You cannot multiply mixed numerals. You have to turn them into improper fractions first.
So how many quarters are there in 19+3/4
there are 4 quarters in 1
4*2 = 8 quarters in 2
4*3= 12 quarters in 3 etc
so
there are 4*19 = 76 quarters in 19 and the other 3 and you have 79 quarters in 19 and 3/4
so
\(19\frac{3}{4}= \frac{4*19+3}{4}=\frac{79}{4}\)
Using the same idea
\(1\frac{2}{5}=\frac{5*1+2}{5}=\frac{7}{5}\)
so
\(19\frac{3}{4}\times 1\frac{2}{5}\\=\frac{79}{4}\times \frac{7}{5}\\ =\frac{79\times 7}{4\times 5}\\ =\frac{553}{20}\\\)
I used a calculator to help me get 553 but you could do it on paper.
Now how many whole numbers is that and how much is left over?
there are 5 twenties in 100
so there are 5*5=25 twenties in 500
then 2 more in 40
so that is 27 lots of 20 in 540
\(\frac{553}{20}=\frac{540}{20}+\frac{13}{20}=27+\frac{13}{20} = 27\frac{13}{20}\)
Think about it and then you can let me know if that helps 
