Thinking back, a significant part of my middle school math education was spent converting "improper fractions" such as 9/8 into "mixed numbers such as 1 1/8. This went beyond understanding that a fraction is just like any other number: we were told that you should never write fractions with a greater numerator than denominator. Since then, I have not used a "mixed number" once in any sort of serious math. I am around 2 years in to a math heavy college degree and every single time some number of the form a/b where a>b showed up, it was written as a/b or as a decimal. Maybe it has some use in higher mathematics, but I am wondering what the Chicago Math people were thinking when they spent so much tie on this weird way to think about fractions. What use is there for teaching "improper fractions" as a core part of a middle school math curriculum?
[Math] Why was I taught to convert “improper fractions” into mixed numbers
educationfractions
Related Solutions
Please lead me through it step by step. \begin{align*} -100+\frac{1}{2} &= \frac{-200}{2}+\frac{1}{2}\\ &= \frac{-200+1}{2} \\ &=\frac{-199}{2}\\ &=-\frac{199}{2}\\ &= -\frac{198+1}{2}\\ &= -\left(\frac{198}{2}+\frac 12\right)\\ &= -\left(99+\frac{1}{2}\right)\\ &= -99\frac12 \end{align*}
I'm not sure whether people on this site (myself included) can give you better advice than people at school who know more about you than you have been able to summarize in your Question. So here are some things to think about. Perhaps take some as advice. Perhaps ignore others.
(1) I'm not sure whether starting to learn calculus at 15 is the best choice. Calculus may go better when you know some trigonometry and analytic geometry--and maybe patch a few gaps in your algebra.
(2) As you encounter things in math classes or independent reading that you don't understand, try to figure out if there are gaps in your background that may account for the difficulty and how you can go back and fill in the gaps.
(3) Because you're interested in uses of math in addition to theory, maybe look into aspects of physics, computation, statistics, and probability where math that interests you is used for various purposes.
(4) Think about the mechanics of solving problems: Here are a couple of suggestions to get you started. (a) Given the equation of a line and the coordinates of a point that is not on the line, can you compute the shortest distance from the point to the line? (b) Can you figure out the sum of this series? $1 + 1/2 + 1/4 + 1/8 + \cdots .$ (c) Given the equation of a parabola, can you figure out whether it crosses the x-axis? (d) What points in the plane satisfy $|x|+|y| \le 1?$ You might look on this site for other problems and solutions.
(5) When you run into an interesting math problem you can't solve, consider posting it on this site. Say what you have tried and what is puzzling you. Explain that it's for self-study, not a homework assignment. Maybe someone will give you an interesting and helpful answer.
(6) If there is a library at your school or in your town with some math books, consider browsing around to see if you can find interesting topics at your math level. I think books are more reliable sources of worthwhile math ideas than most stuff on the Internet.
(7) There are some books available online for free that are written by very good mathematicians who write well. One of them is Grinstead and Snell: Intro to Probability, which has interesting historical notes and doesn't require calculus. The PDF of the whole book is available free on the Dartmouth website. Maybe other people on this site can suggest other free (or inexpensive) books that might worth looking at.
(8) If you keep finding new math topics that interest you and keep patching gaps in the old ones, I think one day you may be advising others how to excel in math.
Best Answer
It's useful in everyday life. Most people will only ever come across fractions when dividing objects between groups, and then it is useful. For example, if you have to split 16 things between 5 people you do $\frac{16}{5} = 3\frac{1}{5}$ and you know you'll have three each plus one left over. This is much easier (and practically more useful) than actually doing the division to find the decimal expansion of $\frac{16}{5} = 3.2$.