Rational Numbers and Yarn

I have a few little problems I'd like to work out. Remember my muffler problem from a previous post? I probably should finish it before winter is over so I need to figure out if I have enough yarn, and what type of striping design or pattern I can create.

About the amounts noted above, I basically eye-balled these amounts, so there isn't 100% accuracy. That would entail unwinding all the yarn and then measuring it by the yard, which is of course, something I'm not willing to do.

I do know that according to the label there is 108 yards in every skein. So to get my approximate yardage for each skein I simply have to multiply the numbers and fractions above. I'll give a visual representation of solving for the moss green amount first. By the way I got lazy and wrote out the problem on paper and scanned it as an image rather than using PowerPoint or a graphics program.

Of course, I could have just divided 108 by 4. That would have been easiest, but for the sake of reinforcing knowledge I regained last week, I wanted to solve using fractions.

Now I want to make a muffler which is shorter than a scarf so I'm going to make it 5 feet in length. I want the wearer to be able to tie the scarf at least once. FYI - a normal length for a scarf is the height of the person who is going to wear it. From my estimation below it will take 40 inches of yarn to make a foot. Therefore, it will take 200 inches or 5.555 yards per row (actually 5.5555 with the decimal repeating).

I suddenly realized that .1111 with decimal repeating equals the fraction 1/9. (Mr. Grant's, my sixth grade teacher, efforts to drill the fraction decimal amounts into us didn't fail me). So this number is actually 5 5/9 yards or in fraction form 50/9.

Back to my calculations, as I noted in the graphic each row of striping in a Garter stitch pattern takes 4 rows of knitting. So I'm going to take my 5 5/9 or 50/9 yard number and multiply that by 4. I get 200/9 or 22 2/9 yards. So considering that I only have 27 yards of yarn I now know that I can only make 1 stripe of moss green on my muffler. Maybe it's enough for just the edging.

Gosh this is a lot more work that I thought, and of course, I'm an experienced enough knitter to be able to visually estimate what I can do, but now I can the problem thinking I employed here in the future to analyze more complicated problems when it comes to yarn estimation for patterns. I'm pretty stoked!