#2**+1 **

\(\text{Couple ways to do this}\\ 1)~\text{convert both to proper fractions and multiply}\\ 19\dfrac 3 4 = \dfrac{79}{4}\\ 1\dfrac 2 5 = \dfrac 7 5\\ \dfrac{79}{4}\dfrac{7}{5} = \dfrac{553}{20}\)

\(2) \text{distribute }\\ \left(19+\dfrac 3 4\right)\left(1+\dfrac 2 5\right) = \\ 19 + \dfrac 3 4 + \dfrac{38}{5} + \dfrac{6}{20} = \dfrac{553}{20}\)

.Rom Mar 30, 2019

#4**+1 **

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.

Guest Mar 30, 2019

#5**+1 **

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

Melody Mar 30, 2019