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)
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.