Why are variables useful in algebra?
I feel the use of variables make it difficult for many people to understand because it is subconcious that math is numbers, not letters....
Thank you!
By using a variable, one may make use of a formula which is good for hundreds of situations where only the variable changes. If not for variables we would br forced to memorize each of those hundreds of situations rather than just the one.
I'm not sure I agree with you about why the use of variables makes it difficult for many people. I agree that it does make it difficult for many people; however, not for the reason you cite. I think it makes it difficult because using variables makes us think in the abstract whereas many people do better thinking in terms of the finite. If your "theory" is correct, then people would not have any trouble at all with fraction (all numbers) but I am told that fractions cause more trouble for more students than any other arithmetical operation, except, perhaps word problems.
Variables are actually extremely useful in algebra because they provide a way to represent unknown values or quantities. Instead of working with specific numbers, we can use variables to represent any number or value that fits into a given situation.
Here's an example to illustrate this. Let's say you have to solve the problem "Find the length of a rectangle whose width is 5 units and the perimeter is 24 units." Instead of using specific numbers to represent the length, we can use a variable, let's say "L". So, we can write an equation:
2L + 2(5) = 24
By using a variable, we can now solve this equation to find the value of L, which represents the length of the rectangle. In this case, L would equal 7.
Now, imagine if we didn't have variables and only worked with specific numbers. We would have to solve this problem anew every time the width or perimeter changes. Variables allow us to generalize the problem and solve it once for multiple scenarios.
While it is true that some people find it challenging to work with variables because they associate math with numbers rather than letters, understanding and using variables is a fundamental concept in algebra. It allows us to describe mathematical relationships and solve problems more efficiently by creating formulas and equations that can be applied to various situations. With practice and understanding, the use of variables in algebra becomes second nature and a powerful tool in problem-solving.