An Introduction to Algebra for Knitting

This is sort of a side-step to the design theory posts. I was plotting out my next post, about figuring out the numbers for your own design projects, and realized maybe a little tutorial about how using very basic algebra is incredibly important to all aspects of knitting. If you feel pretty comfortable with solving for various parts of an equation, feel free to skip ahead, though I would love some feedback on this, both from knitters with mathy skills and those who have more trouble with numbers.

I know for many knitters, “math” is one of the bad four-letter words. And that’s okay. You don’t have to be good at math in order to knit or crochet. If you’re going to start modifying or designing patterns, though, you’re going to need to buck up a smidge and accept that math is an important part of that side of crafting. Plus, in this instance, you get to “cheat” and use a calculator whenever you want, without having to show your work.

In my opinion, math for designing is a bit easier, because you’re starting with a completely blank slate. If you’re going to modify an established pattern, you have more parameters in which to work, which can get a bit dicey. For a design, however, everything is wide open and you are working within your own comfort level, at your own gauge, with your own ideas.

So, a basic tutorial on introductory algebra before we get into the nitty-gritty about finding numbers for the sweater dress. I’m rather certain that many of the math-phobic among us actually use this sort of basic algebra in day-to-day life and just don’t think about it. For instance, if you’re at a yarn store, and you have a budget of $100, you can probably figure out how much of what kinds of yarn you can buy. If you need 5 skeins of Cascade 220 and it’s $5 a skein, you know you will need to use $25, so how much of your original budget is left over?

That looks a lot like a word problem, so I’m going to break it out a bit.

5 skeins of yarn * $5 per skein of yarn = $25 for all the yarn.

$100 budget for yarn – $25 spent on Cascade = $75 remaining in the budget.

Lo and behold, that was basic algebra, much along the lines of what we’ll be doing. You’re taking information that you already have and using it to solve for information that you don’t have. Most of us probably remember equations involving letters,

y = x + z

and those letters can trip people up. “Why are there letters in my numerical equations?” When we don’t have all the information we need, we need place holders. Think of the letters of stitch holders—you have these stitches that you’re going to need later, but you need to set them aside for a moment until you get to that point. So in our previous example, where we’re solving to find the remaining money in our yarn budget, you could write it this way:

y = x – (z * a)

BREATHE.

In that equation, y = the really big important information, how much money we have left over, or the information we’re missing; x = our original budget, or $100; z = the number of skeins of yarn we’re buying, or 5; a = the cost of each skein, or $5. Following the order of operations, we work the numbers inside the parentheses first:

(z * a); or (5 * $5) = $25

Now our equation looks like this.

y = x – $25

I simply replaced the original unknowns z and a with our known information, 5 skeins and $5. Five times five equals 25, and because we’re working with money, we place the dollar sign in front.

But we do have more information than this. We also know that x, or the original budget, is $100. So we can fill in our equation a little bit more.

y = $100 – $25

This entire example has been about solving for y, finding that missing piece of information, and now we have enough information that we can easily see that $100 minus $25 equals $75. The information has been worked through and now that we know we have $75 left to spend, we can totally begin this process over again to figure out just how many skeins of Malabrigo we can buy.

Don’t tell me you’ve never done that.

Questions? PLEASE ASK THEM. This is an important step in the designing process, and I’d hate for people to get frustrated and give up because of such a silly thing as math.

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15 thoughts on “An Introduction to Algebra for Knitting

  1. Panda, I think I love you. No one has ever managed to explain algebra to me, in a way where I can make sense of it in any way, shape, or form. You just did. Thank you! I’ll never be a wizz at it, but hopefully I can do a little better at it now 😉

    (and if all else fails, I at least know who to go to to ask now, when I get stumped ;-))

    • Oh good! I’m so glad this helped. And really, you don’t have to be a whiz at algebra to be able to design or modify knits, you just have to know what information you have and what information you’re looking for, and how to work with those things. 🙂

      • It did, though it still intimidates me a little lol. I wouldn’t mind having a go at making something from scratch and stuff…. I’ve always winged it, with varying results. Not that I have any spiffy designs in my head at the moment… just a dream right now 😉 I’ll know who to go to for handholding, if it comes to that, though… right? 😉

  2. excellent real life yarny example! I’m excited to see what you will do for the oh so scary fractions/ratios! (but of course, I have no fear of such things because I’m Asian. Naturally. 😉 )

    (actually, in high school I had an old school hard ass for an algebra teacher, so it was learn the essentials, sans calculator, or die.)

    • I figured if I kept it related to knitting, it might make more sense. 🙂 I think that’s part of the problem with trying to teach math, coming up with examples that relate to everyone you’re trying to teach. That’s hard!

      And I don’t know that we’ll really get into fractions or ratios, at least not in the way that I’m thinking of them, but maybe another time. 😉

      I did learn how to do all of the essentials without a calculator, and I’ve retained a good bit of my math knowledge, but I know a lot of knitters who start throwing things at me when I say “math is easy,” so I figured a little refresher wouldn’t hurt. 😉

  3. Why? Why use algebra for something that doesn’t need it? I know how to subtract 5 times $5 from $100. In my head even. It’s not rocket surgery.

    Also, if you don’t understand why there are letters in math, maybe you need to go back to high school. I suck at math but I still figured that one out.

    • yeah, thanks for that one… I suck at math, but damn if it wasn’t for lack of trying! My math teacher literally ended up telling me he wouldn’t teach me because he claimed I didn’t want to learn. Mind, this was AFTER I’d gone to him, begging him to explain it in a different way because I wasn’t getting it. Not all math-fail is deliberate.

    • Nope, it doesn’t need it, but it is still an algebraic equation, and I was trying to use an easy example to show people who hear the word “algebra” and freak out that they’re already doing algebra and just haven’t realized it.

      I’ll be using different numbers in another post to show how knitters can use algebra when they’re designing a knitting pattern, but I wanted to lay down a refresher course for some people who were always intimidated by math or who have been out of high school for a while.

      I do welcome all comments to my blog, and I’m very happy that you’re a whiz-bang at math, but if you feel the need to leave a comment in the future, I would appreciate some civility. Just because something is easy for you doesn’t mean it’s easy for everyone else; that’s why we write blogs, to disseminate information to people who want or need it.

      • No, it wasn’t easy. And I suck at math. Which I said.
        I don’t think I was uncivil, but apparently some of you have been assaulted by math in the past, and I apologize for bringing up bad memories.
        I guess the other commenters who do algebra in their head are just not as uncouth as me.

        • The tone of the original post came across as mean-spirited. Maybe that’s not what was intended, but that was the impression left on me and quite a few other people.

  4. Six!!! 6.8 skeins of Malabrigo!

    I secretly love doing algebra in my head. This habit began as a young girl shopping the sales with my granny, when she taught me to calculate percentage discounts quickly. I think it’s why I took to knitting. Now if only I liked checking gauge…

    • Made for each other, babe. I am such a nerd, I love doing math in my head. and sweet, six skeins of Malabrigo is a good deal! 😉

  5. I do this ALL THE TIME. I even do it for my friends when sizing patters up past a 48″ bust (oh when you only need 2 more inches!). Great post 🙂

    • Yay! I’m glad to know I’m making sense. And I hope people read your comment about sizing up or down—really, math is so crucial to being able to knit for yourself.

  6. Pingback: Design Theory Part 2: Measuring and Mathematics « Threadpanda

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