I'll Hold Your Breath

Dear Sensei,

The other day, I tried to just multiply my fractions by multiplying the big numbers, then multiplying the fractions the way I learned, but I got the answers wrong! Can you please explain what happened, because I have no idea. 

BNW

With this, I have some bad news, and some even worse news. The bad news is that yeah, that's not going to work. The worse news is that this is a very time-consuming thing to have to do.

Most math isn't hard, but it is time-consuming. In problems like this, you also get many times to make a simple mistake and throw the whole thing off. Let's look at an example.

To start, you have to make your mixed numbers into top-heavy fractions. We do this by multiplying the denominator by the whole number. Then we add that to the numerator.

So in this case, 3 * 3 + 2 = 11, and for the second one, 11 * 5 + 2 = 57. 

Now, we can multiply across the top and multiply across the bottom, but first, I see some cross-simplifying we can do. 11 and 11 can simplify down to 1 over 1, going diagonally. Also, 57 over 3 can simplify down to 19 over 3.

This one was really handy, because all you're left with is a 19 and some 1s.

 Now, let's look at another problem. You're going to follow the same steps...

Then when you get your answer this time, you have a 33 over 2. So turn it into a division problem...

And your answer is 16 1/2.

Don't worry, later on I'm going to go into more about fractions, simplifying, and some of those things that you could be excused for not knowing already when I went through this.

The bottom line, though, is that these problems will take a little while. They're not fun. They're not even all that rewarding, other than the fact that you're finished with them. I love Math, but man, these can be a slog; I get it. But hopefully even thought hey are time-consuming, you will find that they're not hard to do.

More later.