In this article we will explain how to know how to differentiate algebra from arithmetic, since it is common to find that people confuse them, many times even thinking that it is the same and it really is not.
Both terms refer to branches of mathematics; while arithmetic works only with numbers, algebra does so by combining these with signs and letters; in the first we work with real values, which we already know, such as 8, 34, 85.45678, 8/9, among others, where there is a more obvious and simple way to write some value, (4+8-3+8-9×5) would be an operation arithmetic; while in the second we work with values that are unknown, such as X,Y,Z, A,B,C, among others; in 2 + X =6, we would have to look for the value of X that would be 4; We can say that with algebra we work with operations that are abstract and generalized within the world of mathematics, that is, we must find values for the variables that are represented by some letter or symbol. Below we will explain in more detail the differences between the two to make it much clearer.
Instructions to know how to differentiate algebra from arithmetic
- Arithmetic: it really is something that you are using every day without realizing it, since it includes everything related to numbers. The word arithmetic descends from a Greek term (ariqmo) which means number. It is a basic branch of mathematics and with it you traditionally work with the 4 basic operations that we usually use, which are: subtraction, addition, division and multiplication. In other words, we can say that with this branch we can do calculations and operations using numbers. We can also talk about advanced or superior arithmetic, which is also known as number theory, where not only integers and their characteristics are seen, but also irrational, real, and rational numbers.
- Algebra: it is also a branch belonging to mathematics; the word is derived from an Arabic term (al-Jabr), since they themselves were the ones who contributed the most to the formation of this branch; al-Jabr was actually a medical term meaning something like putting the broken pieces back together; the Arabs invented algebra in order to be able to reason logically, where the important thing was reasoning and not values, due to this it had letters and not numbers, since what they wanted was to be able to reason regardless of the figures; within mathematics we can put algebra as a second level followed by arithmetic. What mainly differs from arithmetic is that it does not work only with numbers, but mixes these with other values that are unknown. When you find symbols of a mathematical operation, such as Y, X, B, or A, you will know that it is algebra; within it, operations that are arithmetic are also manipulated, as well as complex numbers, algorithms, quadratic binomials, formal theorems, among others. As you can see, algebra is much more complex and is used to solve different equations.
- Let’s look at the difference between the two in simple examples:
9X9 = 81 (it is an arithmetic statement).
X = 5 (it is an algebraic statement). - With arithmetic we can do different calculation procedures with amounts that are fixed and explicit, which are indicated in numbers, likewise when we carry out the operations we have specific results that will also be given in numbers; while with algebra we can do more advanced operations, in a certain way we go further, we can create solutions for different types of problems and not only for those with certain and known values, but for those that are generalized; In other words, with this is the way to leave embodied solutions for any form of value that could be in different types of problems, that is, that the solutions can be applicable in other similar operations proposed, which is done through the variables that are generally indicated in letters such as X,A,Y. Let’s go back to an example with a simple sum 5 + 9 = 14, as you can see we have expressed all the quantities and we use arithmetic to determine that five plus nine equals fourteen.
A + B = 14, in this case you can see that there is a sum that has more possibilities, since you can make different combinations that would give 14, perfectly A could be 10 and B 4, or A could be 9 and B=5, etc., that is, each symbol could take several different values to be able to solve the operation or problem, as long as the result is 14, for this reason the letters are called variables and that is how we use algebra. - Arithmetic works with numbers and looks for concrete results after a calculation, while algebra is in charge of studying the properties of the different main abstract entities such as numbers, functions, sets, vectors, etc.
- Arithmetic works with results that are concrete and also with the calculation of numbers, while algebra is in charge of generalizing (some due to ignorance call this working and calculating with letters) also with conditions that must be true for numbers whole.
- Basic arithmetic only uses numbers unlike algebra, but there is a higher arithmetic that uses letters, that is why it is also said that algebra has among its purposes to facilitate arithmetic.
- We can say that in conclusion, arithmetic is the most basic branch of mathematics and for this reason it is responsible for analyzing numbers through basic operations such as division, multiplication, subtraction and addition, while algebra is already a branch of mathematics. that it is at the second level, which is why it uses numbers accompanied by variables for the solutions of mathematical problems; It is an application that is generalized for finding the solution of the problem.
- Now let’s see it with a daily example to understand their difference even more, if for example they tell you Marcela is 15 years old, you will get a specific number and you know that they are talking about Marcela’s age and not someone else’s, or be arithmetic, but if, on the contrary, they want to represent the age of a student at the school by means of an “y” you already know that this does not indicate Marcela’s age but that “y” could be the age of any other student, like this that we can know that “y” is 15, only when it is known exactly that the student is Marcela, this is the way of reasoning and applying variables in algebra.
Tips to know how to differentiate algebra from arithmetic
- We can say that arithmetic is a much easier branch, that almost everyone can do it and that we even use it on a daily basis, when, for example, we go to make a purchase and add the cost of what we take and calculate the change (returned). ), while the algebra is a bit more complex and complicated.
- The concept of quantities in algebra is much more complex and extensive than in arithmetic.
- The algebra is generalized and is expressed by means of letter values, which can be any value.