Mathematics is divided into two branches: arithmetic and algebra. So many people have confusion with the difference between algebra vs arithmetic. Arithmetic is the most fundamental field of mathematics. It concerns the calculation of numbers using operations such as adding, multiplying, dividing, and subtraction. Algebra, on the other hand, solves problems using numbers and variables. It depends on the use of universal principles to solve problems.
Arithmetic is a phrase derived from a Greek word that means “number.” It is the most fundamental aspect of mathematics. It’s all about numbers, thus it’s something that everyone uses in their daily lives. Higher Arithmetic also regards as number theory. It is involved with characteristics of rational numbers, integers, real numbers, and irrational numbers.
Algebra, on the other hand, is one more branch of mathematics. The name comes from the Arabic word al-jabr, which means “reunion of shattered pieces” and is an old medical term. After the basis of arithmetic, it might regard as the next level of mathematics.
Let us try to understand both the terms through their differences. So let us start with their definitions…
Algebra vs Arithmetic: Definitions
What is arithmetic?
The word “arithmetic” comes from a Greek word that means “number.” It is the most fundamental field of mathematics, including everything to do with numbers. And thus uses by individuals in their daily lives.
Moreover, the 4 major operations of traditional arithmetic are adding, subtraction, multiplying, and division. It also simply uses numbers to make various sorts of computations.
Number theory is another name for upper arithmetic. The features of whole numbers, rational numbers, irrational numbers, and real numbers are discussed.
The 4 major properties of operations are:
- Associative Property
- Additive Identity
- Commutative Property
- Distributive Property
The BODMAS and PEMDAS rules are followed for operation order involved +, −,×, and ÷. The order of operation is:
- B Brackets
- O Order
- D Division
- M Multiplication
- An Addition
- S Subtraction
Types of basic Operations in Arithmetic
The four fundamental arithmetic operations that is addition, subtraction, multiplication, and division are discussed below:
Addition (+)
For instance, if you add 1 and 4 the outcome will be 5.
1 + 4 = 5
If you add the opposite value.
For instance, if you do the addition of 4 with its opposite value -4, then the outcome will be
4 + (-4) = 0
Subtraction (-)
3 – 1 = 2
When you subtract lower value from higher
1 – 3 = -2
Multiplication (×)
The two values included in the multiplication operation are known as the multiplier. It also incorporates two values that multiplicand to provide a single product.
The outcome of two values apparently x and y are expressed in x.b or x * y form.
3 × 4 = 12
Division (÷)
The division is the operation that calculates the quotient of two values.
4/2 = 2
What is Algebra?
Algebra, on the other hand, is a separate discipline of mathematics. The phrase comes from al-Jabr, an antique medical term. It also means “reunion of fractured fragments” in Arabic (the Arabs were the ones who contributed the most to this branch). After Arithmetic, Algebra is considered the second level of mathematics. It also works with unknown values that are coupled with numbers, unlike the former.
Let’s take…
10x + 40
This refers to as an algebraic expression since x has a range of values. Also is hence a variable, whereas 50 is constant. The words are 10x and 40, and they can separate by the marker +. In place of variables, we may write anything a, b, c….z.
Algebra also includes different techniques of solving a couple of linear equations:
- Elimination method
- Cross multiplication method
- Substitution method
Algebra vs Arithmetic: Difference Table
The Difference between algebra vs arithmetic will make algebra and arithmetic clear.
| Parameter | Arithmetic | Algebra |
| Basic difference | The phrase comes from al-Jabr, an antique medical term that means “reunion of fractured fragments” in Arabic | The word “arithmetic” comes from a Greek word that means “number.” |
| Level | Normally, associated with the math of elementary school | Normally, associated with the math of high school |
| Problem-solving | Based on the details given in the problem (memorized outcomes for short values of numbers) | Based on the classic moves of elementary algebra |
| Computation Method | Computation with exact numbers | Familiarizes abstraction related concepts |
| Relation | Number related | Variable related |
| Primary focus | Addition, subtraction, multiplication, and division are its four main operations. | Algebra utilizes variables and numbers for problem-solving. It is based on the generalized application rules for problem-solving. |
Let’s wrap it up!
In the final discussion of algebra vs arithmetic, it is quite clear to say which is better. The most basic kind of mathematics is arithmetic. It is the cornerstone of contemporary mathematics. Everything is founded on it. Arithmetic is the math of finding unknown values in an equation using variables.
On the other hand, algebra is the math of finding unknown values in an equation using variables. The variables are symbols that represent an unknown value.