Reasonable is a fancy way of saying fair or balance. When you are talking about math, reasonable means fair or balance in math.
Reasonable is a term that describes what is fair or not in math. When you are talking about math, reasonable also refers to what is not too much or not too little in math.
The word reasonable was added to the language of mathematics to describe what was once called impossible. When this word was added to the language of mathematics, it became impossible for someone to say something was reasonable that did not sound like it involved a lot of effort.
The term impossible was kept as an alternative term for unreasonable because no one wants to hear that something is too much when there should be only enough effort involved.
This article will talk about possible changes to the way we think about and talk about reasonable in math.
Contents:
Understanding reasonable math
In order to understand reasonable math, it is important to understand what math is not.
A number is not a measure of something. Numbers do not mean anything. A number does not describe a thing, it merely represents a thing. For example, a dollar amount represents a buy box, but the dollar amount does not describe the buy box.
A measure of something is what that thing is valued at or how many of that thing there are. For example, in the buy box example, one would likely consider two $5 buys boxes reasonable, whereas one might consider one $10 buy box insufficiently large of a purchase box.
In order for an average student to be able to understand unreasonable math such as equations with multiple variables or complex operations, they must be able to recognize when two steps in an equation or two pieces of data in an equation or operation are reasonable enough.
Reasonable math examples
Some examples of reasonable math examples are: “If the tire size on your car is 25 millimeters in diameter, then a car that is the same size but has a larger tire is reasonable math.”, “If you put five apples and five oranges in your bag, what is the probability that you will end up with four apples and one orange?”
Some examples of reasonable math include: “If the odds of winning $1,000 are one in six, then how much money do you think you would win if you played against that odds?”; “If the probability of a given event happening twice in a row is half, how many ways can an example of reasonable math be repeated?”; and last but not least, “What is the probability that if we draw two black cats it will be consecutive times when one is black and one isn’t?”.
These types of examples can help students learn more about different probabilities and how to reason with them.
What is reasonable math used for?
In math, we talk about reasonable and unreasonable numbers. Both terms have different meanings, so it is important to know which one you are talking about when discussing numbers.
Reasonable numbers are numbers that are close to what is expected. For example, if you were to tell someone that their pay raise was five dollars and your pay raise was six dollars, you would probably think that your pay raise was reasonable.
Unreasonable numbers are different from reasonable numbers in that they are different amounts of something. For example, a salary of $50,000 is unreasonable against the fact that at this salary, you can buy a car and a house!
When it comes to math problems, if the answer has two parts to it, the first part is reasonable and the second part is unreasonable, the problem is going to be asking for an unreasonable answer.
Where can I find reasonable math?
In college, you learn a lot of abstract concepts. You also learn when people use them, how they’re applied, and what they mean.
In college, you also learn a lot of abstract concepts. You also learn how people apply things to life in academia and everyday life.
Some ideas about reasonable in math that make sense to me include: 1) It’s not enough to say something is reasonable; we have to believe it is; 2) We can’t always assume things are reasonable; we have to find out they aren’t; and 3) It doesn’t mean I can’t tell if someone is on a reasonable budget or not.It just means that they don’t have a hard-and-fast rule for spending.
Who invented reasonable math?
In 1923, Thomas R. Allen, a professor of mathematics at Carnegie Mellon University in Pittsburgh, Pennsylvania, invented reasonable math to help students compare and contrast quantities.
Reasonable math was originally developed as an aid in algebraic equations and numerical problems. In algebraic equations, if we replaced one variable with a certain value, we could change the quantity being compared and changed the difficulty of the problem.
For instance, if we had an equation that said one thing and a second thing, we could make the first thing reasonable because it is very easy to compare differences. For instance, if the second thing was easy to compare but difficult to determine exactly what it was, then the first thing would be reasonable.
Is there an easy way to do reasonable math?
Sometimes, the answer is no. Sometimes, the answer is yes.
Generally, reasonable math means doing simple math problems without too many assumptions or doubt about the solutions.
So, for example, determining the size in inches of a book using a length of fabric as your solution. You might assume that a fabric of 12 inches will measure half an inch around, so a solution would be to carve 12 inches into the fabric and then add another half an inch for hemming.
Reasonable math comes down to what are the most elementary solutions you can find. When looking for solutions to basic algebra and trig functions, for example, there is no point in spending too much time trying to find more complicated answers that do not apply to you.
How do I know if something is reasonable?
There are a few things that you can look at to tell if a math solution is reasonable or not. These include the following:
Is the problem tractable? If so, a reasonable solution would be one that can be solved in an hour or so.
Does the solution work for all cases? If not, it may be too difficult or complex.
Is the cost of the solution acceptable? Many times when a student asks for help in class, the cost is too high. For example, someone may pay $50 for an online tutoring session and get little help from the student due to the quality of the material.
Do other solutions not fit the situation fit better? In case of emergency, using some basic math problems may be reasonable. For example, if someone spent money to go to town and buy toilet paper because they needed it urgently, then yes, Academic solutions would be reasonable.
What does “X is Y% of Z” mean in mathematics?
When we look at things on a scale, we call them “values.” We have positive, negative, and abstract values.
When we calculate something like a cost or an investment return, we use a value as the basis for the calculation. This value is what you want, or what you cannot live without.
In our lives, we have values that go from small things like money to things that are much bigger like life. For example, how much time you want to spend on your next step in life might be a big “value” you have.
When we calculate something like an investment return or cost/return on an investment, we use a value as the basis for the calculation. This value is what you want, or what you cannot live without.