Category: Arithmetic

  • 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!

  • How to Check if a Number is Divisible by 3 or 9

    How to Check if a Number is Divisible by 3 or 9

    This is a trick that everyone should learn in the 3rd grade. If not, then at least by the 9th grade.

    If you’re in the dark on this one, no big deal. Now’s the time to learn. If you’re a parent – this trick will win you points like crazy. Especially if you get to it before the teacher does.

    So here’s how it works. For both 3 and 9, start by adding up the digits in the number. If the result is divisible by 3, then so’s the original number. If the result’s divisible also by 9, then… you guessed it… so’s the original number.

    If your result is way to big to tell, do it again. Check out the videos for both:

    Questions or comments? Leave them in the comment section below.

  • 2 Ways to Multiply Mixed Numbers

    2 Ways to Multiply Mixed Numbers

    Multiplying fractions provides an interesting challenge. Put some mixed number into the situation and you could be facing a real bear.

    Here’s one way to work the problem 234×8172 \frac{3}{4} \times 8 \frac{1}{7} by converting it to mixed numbers:

    Or you can use the handing dandy distributive property (or as some might recognize it – FOIL):

    Here’s one more for fun:

    Thanks to NapNinja4 on MyMathForum for this question.

  • How to Convert Mixed Numbers to “Improper” Fractions

    How to Convert Mixed Numbers to “Improper” Fractions

    This isn’t something you do everyday. Therefore it would be helpful to know how to remember it long term.

    The mixed number 2342 \frac{3}{4} really means 2+342 + \frac{3}{4}.

    Notice the PLUS sign? That’s the big key to doing this.

    This video shows the long expanded way that most people won’t show you. You wouldn’t really convert this way, but it helps to see it in the long form. This way you know what your teacher is showing you isn’t some pixie dust magic:

    Now that you can do that, you can probably go the other way too:

    And how about checking your work? Nevermind the devil box (aka the calculator), the more you check your own work by hand, the more your confidence in your own math abilities will be. Try doing this:

    What do you think? Will this help you remember? Do you have another way to remember? Share it in the comments.

  • How to Multiply By Hand Without Hurting Your Brain

    How to Multiply By Hand Without Hurting Your Brain

    There’s an amazingly fancy tool that I began discussing in the last post. This D-word probably has been a close friend of yours for a while. It’s likely you’ve used it before and just didn’t realize it.

    Well, now you can give it a name and give it some practice. It’s the Distributive Property.

    Fancy name. Fabulous friend.

    Check out what’s really going on with  87 x 48 here…

    That one you can do quickly with pencil and paper. Here’s an easier one that you are more likely to do in your head (after practice with P&P of course)…

    Have you done this before? Share your stories in the comments.

  • How to Subtract Using Reverse Addition

    How to Subtract Using Reverse Addition

    This was requested by Jake’s Mom. Since she was taught to borrow, she was dumfounded at what Jake brought home. Happily, Jake is young enough and unscathed enough to not balk at a “different” method than what his mom was taught. He got it right away.

    But Jake’s mom, on the other hand, is struggling.

    If your kiddo is being taught this, here’s a way to look at it that might help you understand what’s going on.

    First, a brief review on the relationship of subtraction to addition:

    Here’s what “reverse addition” looks like in relation to our old friend “borrowing,” using the same example:

    And here’s an example:

    Another example (along with a special tip for you):

    And a final example, just to help you get the hang of it.

    Still have questions? Post them in the comments.

    Thanks, Jake’s Mom, for the question!