Fractions and bases

So, we’ve been enjoying Hard Math for Elementary School (for somewhat complex definitions of “enjoying” that involve both frustration and eventual pride).

Today DC1 said, “Different bases is just like fractions.”  Explaining a little more, ze noted that when you’re doing fractions with a denominator of 8, the numerator works just like when you’re counting in base 8.

By golly, I thought, ze’s right!

In base 8 you count, 1, 2, 3, 4, 5, 6, 7, 10, 11..

When you’re counting eighths, it’s 1/8, 2/8…7/8, 1, 1 and 1/8.

Adding works the same way too… 2 + 7 in base 8 is 11.  2/8 + 7/8 is 1 and 1/8.

Multiplying won’t be the same because we tend to cancel things out on the bottom, but in a world where we didn’t do that and we didn’t allow improper fractions, I think it would be the same.  So it could be the same.

Anyhow, that’s super cool.  Yay DC1!  And yay math!

18 Responses to “Fractions and bases”

  1. Comradde PhysioProffe Says:

    I was sitting at dinner last night between an algebraic geometrist and a topologist. It was interesting having them try to explain to me what their respective fields are all about. I think I kind of got the gist of both, although the algebraic geometrist made more sense to me.

  2. Moom Says:

    Only at the beginning of the series is this true:

    1/2, 1, 1 1/2 matches 1, 10, 11…

    But the next in the series is 2 which does not match the format of 100 (4 in base 10)…

    So, it works until you reach the number the base is based on.

  3. Liz Says:

    I had to look this up… I have lots more respect for “Are You Smarter Than a 5th Grader?” contestants now! *humbled*
    Come to think of it, I don’t think I was ever exposed to anything other than Base 10, and (briefly) Base 2. But I’m glad I know something new to introduce to my future imaginary children to expand their horizons. These non-Base 10 systems seem very useful for programming and coding.

  4. Leah Says:

    I’m impressed! Despite being an intelligent person who enjoys math, bases have always been really difficult for me. I read, learn, and then immediately forget. Go DC1 and math learning!

    Also, sounds like DC1 might be conceptually ready for algebra soon. I learned that pretty darn early, and it’s always been my favorite math.

    • nicoleandmaggie Says:

      I keep getting reminded that ze needs negative numbers first. There’s a lot of mental math that we have to do complicated gyrations around to avoid negative numbers.

      • Leah Says:

        Oh, yes, negative numbers are key. My brother taught negative numbers to me using two different colors of poker chips. I can’t remember exactly how it worked, but it was awesome.

      • Debbie M Says:

        Fortunately, I got to learn about negative numbers in the second grade because of a special project. I remember we all had number lines from -6 to +6 taped to our desks. I don’t remember if other people had trouble, but it worked for me.

      • Rosa Says:

        negative numbers are pretty easy to teach on either a line or a grid – a life size one is fun but a balance with numbers on it so you can have a tag hanging at +1 or -2 or whatever.

        Also for us our city and many towns we visit are on a grid, so we could do “if you think of East as positive and West as negative and Federal Avenue is zero…” and then find things on a map & a graph. I think he was 5 or 6 for that, though.

      • nicoleandmaggie Says:

        Yeah, we’ll get to it one of these days.

  5. monsterzero Says:

    Sounds like it’s time to learn the modulo operation and then…Python!

  6. Cloud Says:

    Hooray, DC1!

    Maybe I should look at that to see if I can finally really “get” bases- it always makes my head hurt to try to do anything in anything but base 10. It would probably help my comp sci confidence levels if I was comfortable in base 2, even though I have never run into a situation in my work where I really need it (beyond keeping up with the geeky jokes, that is).

    • nicoleandmaggie Says:

      I learned them in 4th grade because my teacher taught the old “new math”. WONDERFUL class. Probably my favorite year ever. (Then we touched on the same stuff in Number Theory but with proofs. :) )

  7. plantingourpennies Says:

    haha, at my last office birthday I was reminded by the engineers that as we age it’s much more comforting to start tracking our age in HEX. Next year I’ll be 20… in HEX. =)

  8. Laura Vanderkam (@lvanderkam) Says:

    It was the base 8 thing that convinced me to buy Hard Math for Elementary School. My 6-year-old and I were figuring out what various numbers would be in different bases. Then I saw on the Amazon write-up that the whole bases concept was covered in the book. Score! We’re taking a hiatus to do Bedtime Math, though, as book number 2 just came out this week.

    • nicoleandmaggie Says:

      Us too! It was probably someone commenting on your website that pointed us to the books initially. I had been trying to find a book that covered bases for AGES. I had them in 4th grade under the old “new math” and then made up my own teaching materials for it when I was doing pull-out math for fourth graders, but those materials are long-gone. Nothing is more fun than seeing a fourth grader’s eyes get big when you do something like 2 + 6 = 10 (base 8) (It looks better vertically than horizontally.)

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