Tag: prime factorization

  • How to Use Prime Factors to Cancel Fractions

    How to Use Prime Factors to Cancel Fractions

    I previously posted about prime factors and about using them in multiplication. Now we’ve got fractions to handle.

    Before we get in too deep, first let me note the main reason why we do this with arithmetic. In algebra, students will be asked to take a rational expression, factor it and reduce it like this:

    If they are familiar with how factoring works with numbers, this will be normal to them.

    I also find that reducing factors in this neat and clean way helps a lot. In this video I showed the first few steps of reducing the fraction a sloppier way after I did it the “neat” way:

    Here’s one that’s a little more complex:

    Will be helpful to show your kids? Is there something I’m missing? Share with us in the comments.

  • How to Use Prime Factoring to Win Friends and Influence People

    How to Use Prime Factoring to Win Friends and Influence People

    Alright, you might not win friends with this, but the more you can do arithmetic in your head… well… okay, you can’t influence people with it either. Regardless, it’s handy to know and helps with multiplication.

    Yesterday I posted a couple of videos about factoring numbers into primes. Now it’s time to put those to work.

    How about a rather simple one to get us started:

    Here’s one that’s a little more challenging. The key is that you can combine the bits to something you’re more comfortable doing. I don’t like multiplying nines, so I avoid those.

    Can you use this? Why or why not? Ha ha, just kidding – no essay questions here! – but if you do find a use for this, or if this annoys you, let me know in the comments.

  • 2 Ways to Factor Numbers into Primes

    2 Ways to Factor Numbers into Primes

    Factoring is traditionally considered an “f-word” for students of math. But it sometimes has its good sides (which I’ll show over the next couple of days).

    In the meantime, I’ll show the two ways (that I know) to factor numbers.

    This method’s called a factor tree:

    You don’t have to put the primes in order for it to be “right.” But it helps for later things.

    Here’s another tree:

    Here’s another way to factor using an upside division bar-type thing:

    Remember, we don’t factor for the sake of factoring. This is only a tool to use when we do other stuff. You’ll see some of this in tomorrow’s post. Here’s one last example:

    The way you factor is personal preference. Pick the one you like, or flip-flop. There’re no rules!

    Share your preference (or a different way) in the comments!