Fractions got nothin' on me

Took the fractions quiz at the learning centre on Tuesday night and aced it!

Fractions turn out to be really quite simple when you know how to add, subtract, multiply, and divide. I now know what is a proper fraction (eg. 1/4, when the numerator – the number on top – is smaller than the denominator – the number on the bottom), an improper fraction (eg. 4/1, when the numerator is bigger than the denominator, which means the fraction represents a number bigger than 1), and a mixed number (eg. 9/4 = 2 1/4, when the improper fraction is converted to a whole number plus the leftover fraction), and how to combine each of these and take them apart. After a week of self-paced practice at 1 hour per day, I mastered this section of the course and took the quiz without a problem. 

Here's how to add and subtract fractions:

And here's how to multiply and divide fractions:

If you want to test yourself, here's a fun little exercise to see if you remember Grade 8 math: http://www.thegreatmartinicompany.com/fractions/fraction-problems-home.html


Yesterday I took the day off from math practice (well-deserved, I'd say!) and started today with the "ratio and rate" section of the course. They gave me a booklet to take home to work through... and I got stuck on page one. Here's an example of a word problem I'm supposed to figure out:

The Miranda family purchased a 250-pound side of beef and had it packaged. They paid $365 for the side of beef. During the packaging, 75 pounds were discarded as waste. How many pounds of beef were packaged, and what was the cost per pound to the nearest penny for the packaged beef?

Okay, now I'm like, WTF? This is what I'm now calling a "purple pancake" type of math problem, which refers to the illogic of this meme: 

As soon as I see a word problem this is where my brain starts to hurt. But I know I need to just calm down and learn to methodically work out what the equation is that's being asked here. So, in this case, the first step is to subtract 75 from 250 (the amount of beef discarded), giving me 175. Next step is to divide 365 by 175 (written as 365/175) which is the cost ($365) divided by the total weight (175 lbs), which is 2.085 (I used my calculator for this, of course). In dollars this looks like $2.09, so the answer is $2.09 per pound for the beef. 

Okay, I think I've basically got a handle on this. The top number gets divided by the bottom number in a ratio. A ratio is how many parts of one thing to how many parts of another thing, and a rate is when those two things are different (as in time and distance). So far, so good. My aim is to master this and take the quiz next week. Fingers crossed, it'll work out as well as it did for fractions...