Laura Laing, author of Math for Grownups (the book + the blog!), loves to share easy tips and reminders to help adults use math effectively in every day situations. Sewing is chock-full of math, of course; Laura joined us on the blog before to talk about Spatial Skills and Patterns. Today she’s back to share a little about fractions. Learn about Laura in her introduction, and stop by the Math for Grownups blog for more!
If it weren’t for fractions, sewing would be a heck of a lot easier. Am I right?
But here’s the good news: almost all of the fractions used in sewing follow very predictable patterns. That means you don’t have to depend on the math you learned in elementary school— You know, finding a common denominator or converting improper fractions into mixed numbers. If you haven’t used those skills in a while, you’re probably pretty rusty.
And here’s another neat thing to notice. If you read music, the fractions are exactly the same. Cool, eh?
The key to understanding sewing and music fractions is to think of them as parts of one another. Take a look:
½ + ½ = 1
¼ + ¼ = ½
⅛ + ⅛ = ¼
So it’s probably pretty easy to remember that ½ plus ½ is 1. If you think of that same pattern for ½, you come up with ¼ plus ¼, right? You could create a list of these sums that goes on forever.
But the gist of it is this: two ½s is the same thing as one; two ¼s is the same thing as ½ and two ⅛s is the same thing as ¼, right?
Now, take a look at how this works out on a ruler or an adjustable seam gauge.
Count the space to the left of the ½ mark and the space to the right of the ½ mark. You’ll get two ½s , which is the same as 1. Easy-peasy.
Now do the same with the ¼s above. There are four of them, right? Two of them make ½, and four of them make 1. Now for the ⅛s.
There are eight ⅛s in the 1 inch, four ⅛s in each ½ inch and two ⅛s in each ¼ inch.
Make sense? Now you can use this information to help you deal with seam allowances. For this, let’s look at an example.
Suppose you’re making a pillow, like this Criss-Cross Cushion. To find out how much material you’ll need, you have to consider your seam allowances. In fact, you’ll need to add the total seam allowances to each dimension of the pillow.
But what is that total? If you’re using a ⅝-inch seam allowance, you’ll need to double it for the width of the pillow and double it for the height. That’s because you’ll have two seams that equal the width of the pillow and two seams that equal the height of the pillow.
But doubling ⅝-inch is a real pain. I’m here to tell you that you don’t need to multiply or find a common denominator or change an improper fraction to a mixed number. (Thank goodness!) Instead use the fraction facts above to help.
(Disclaimer: If you want to multiply or find a common denominator or change an improper fraction to a mixed number—go right ahead! The beauty of math is that there are often many different ways to come to a correct answer. Use the process that works for you.)
First off, it’s important to know that ⅝ is ⅛ more than ½. How do you know that? Take a look at the picture below. If you count to ⅝, you’ll see that you’re ⅛ above the ½ mark, right?
In other words:
½ + ⅛ = ⅝
Now remember what you already know.
½ + ½ = 1
⅛ + ⅛ = ¼
That means that when you add ⅝ and ⅝, you’ll get 1¼. Here’s how that’s done, mathematically:
⅝ + ⅝ = ?
Substitute what you know about ⅝:
(½ + ⅛) + (½ + ⅛) = ?
Now rearrange the addition, so that’s it’s easier. This is possible because you can add numbers in any order you’d like:
(½ + ½) + (⅛ + ⅛) = ?
Finally, it’s time to add:
1 + ¼ = 1¼
So every time you need to double your seam allowance, you’re adding 1¼.
Experienced sewers already know this. But the process that we just went through can be really useful when you’re adding any sewing fractions. Try it with ¾ + ¾:
¾ + ¾ = ?
(½ + ¼) + (½ + ¼) = ?
(½ + ½) + (¼ + ¼) = ?
1 + ½ = 1½