Adding and Multiplying two fractions mean intuitively? I want to get the intuition of multiplying and adding fractions.
For example, If a man can do 1/8 work in one day and another man can do 1/4 work in one day.
If we add 1/8 and 1/4, then What is the meaning of the resultant answer intuitively?
Also If we multiply 1/8 and 1/4, then What is the meaning of the resultant answer intuitively?
The Question may be small but I really need to understand what happens when we do these things. It would really be helpful if you add your own examples to demonstrate adding and multiplying fractions.
 A: It's important to note that when we are using fractions instead of whole numbers, nothing too drastic has changed. Fractions are more abstract than whole numbers, but they obey roughly the same properties when you add and multiply them.
For starters, let's think about what whole numbers communicate. The way we are first introduced to whole numbers is through the notion of counting:

Here are $10$ dots. And, well, that's it. You can't go much further than this if you don't allow yourself to start adding and multiplying whole numbers. Unfortunately, though, some of the ways in which we conceptualise adding and multiplying whole numbers don't work for fractions. You can't 'count' $9.5$ dots, or half a pizza. In fact, the only way in which these two concepts make sense is if we instead think about size:

This pizza is half a big as a pizza normally is. This is about as close as we can get to visualising what me mean by $\frac{1}{2}$. Now that we have got that out of way, let's consider your question:

If a man can do $1/8$ work in one day and another man can do $1/4$ work in one day, then what is the meaning of the resultant answer intuitively?

Again, remember to think about size. There is $1$ piece of work to be done, and we can split that piece of work up into more manageable chunks. We call these chunks fractions.
If two men work together, then the combined result of their labour is the result of adding two of these chunks up. Therefore, we have:
$$
\frac{1}{8} + \frac{1}{4} = \frac{1}{8} + \frac{2}{8} = \frac{3}{8}
$$
Therefore, $\frac{3}{8}$ of the work has been done. Unfortunately, there isn't a nice geometric interpretation of this like there is for pizza. We can't pick up 'work' like we can pick up a pizza from the store. But we can talk about work using the same mathematical ideas. The most intuitive explanation I have is that if these two men worked for $8$ days, doing the same amount of labour each day, then after $8$ days, these two men would have done $3$ pieces of work.
Multiplying fractions is trickier to conceptualise, but I like to think of it as taking a fraction of a fraction. Take a look at the pizza that I showed you above. If I eat half of what's left, then only a quarter of the original pizza remains. That is
$$
\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}
$$
Unfortunately, mathematics could be described as an inherently abstract discipline. The method that I used to multiply those two fractions doesn't really resemble anything in the real world. However, this method is logical, coherent, and originally rooted in real-world ideas. With this in mind, it is no surprise that mathematics has so many real-world applications. If you have any more questions, feel free to ask.
