I haven’t done any new idioms recently, so here we go…

I think the best way to do this is to give some examples first and then explain them.

As the other runners tired, they all fell behind the leader.

After I lost my job, I fell behind in my rent.

If you party too much, you will fall behind in your studies.

As you can see from these examples, fall behind means to do something less than is required or expected.

The other runners could not keep up with the leader.

You should not use a credit card unless you can keep up with the payments.

If you study every day, you will easily keep up with the class.

As you can see from these examples, keep up means to stay at the same level by doing what is required or expected.

Eventually, one runner was able to catch up to the leader.

Once I get a new job, I will be able to catch up on my rent.

If you don’t study regularly, you will have to catch up at the end of the semester.

As you can see from these examples, catch up is the opposite of fall behind. In fact, you can only catch up after you have fallen behind. If you catch up it means that you work hard to do what is required or necessary to reach an expected level.

Here’s one last example using all of these idioms together:

It is easier to keep up with your homework than it is to catch up after you have fallen behind.