Fraction Word Problems: "Kathy had $10 and gave half of it to her brother. She then gave a third of the remaining amount to a friend. How much money will Kathy have left?"
Apparently, you have to multiply the second part first then you subtract and it makes no sense to me when the whole sentence is using subtraction terminology. It sounds so simple and logical to just only subtract. I have heard if the word "of" is put in there it usually means multiply. I just can't make that connection and am struggling to catch it in time and then I'm already solving it the wrong way. Would anyone be so kind and write a few examples of these type of word problems with a brief explanation? Please explain it to me like a little kid. Much appreciated!
 A: Half of $10$ is $5$, so she gives $5$ dollars to her brother. She now has $5$ dollars left. Now she gives a third of the $5$ dollars she still has $\left(\text{which is }\dfrac{5}{3}\right)$. So now she has $\frac{2}{3}*5$ dollars remaining, or $3.33$ dollars.
A: 
Kathy had $10 and gave half of it to her brother. She then gave a third of the remaining amount to a friend. How much money will Kathy have left?

To solve these types of word problems, it is important to read the sentence one line at a time. This will help you solve the problem more easily.
The first sentence states that Cathy had $10$ initially. We are also given that she give $\frac{1}{2}$ of her total amount to her friend. Let us pause here. What can we do with this information?
When you give money to a person—perhaps your friend, what happens to your initial amount? A reasonable answer would be that it would decrease. That is exactly what this information is communicating.
Now, if we divide $10$ by $2$ (same as multiplying by $\frac{1}{2}$), we will get the amount that Cathy give to her brother. If we subtract this amount by the result, we will get how much money Cathy had left.
We get $10-10(\frac{1}{2})=5$, which is equal to Cathy's money after the exchange.
Therefore, Cathy had $5$ left.
This is the first sentence. Let us read on.

She then give a third of the remaining to her friend.

We just figured out the remain right? As you have suggested, the word "of" indicates multiplication. So we can multiply $\frac{1}{3}$ by $5$. Doing so, we would get how much she give to her friend. $\frac{1}{3}(5)=\frac{5}{3}$
Therefore, she give $\frac{5}{3}$ dollars to her friend. Now, let us read the last line.

How much will Cathy have left?

This sentence tells us to subtract her initial amount by the amount she give to her brother and to her friend. That is what the word "remaining" implies. We have already figured how much she give to her friend and her money amount after the exchange between her and her brother, we just need to subtract $5$ by $\frac{5}{3}$
Doing so, we will get $\frac{10}{3}$. So, she had $\frac{10}{3}$ left.
Since you want some similar examples, here are some made up problems which you can practice:

Bob used $\frac{3}{4}$ gallons of his total truck gas. If he had $27$ gallons left, how much can his truck hold?


There are $180$ people attended the meeting. If this is only $\frac{1}{3}$ of the original attendence, what was the original attendence?


I have $24$ dollars. I want to divide this amount evenly into six groups so that my six friends can have the same amount. However, I realized if I did this, I would have no money for myself. So I decided to keep $12$ dollars. How much will each of six friends receive?

I hope these three questions give you a better understanding how fractions work. The important thing you should remember is that always read the questions line by line and try to gather as much information about the problem as possible. Then form an algebraic equation concerning the relationship. Feel free to let me know any questions you might have.
