Arithmetic and Algebra

Arithmetic

Arithmetic is the study of numbers and the basic rules of calculation, also called arithmetic operations. For example addition, subtraction, multiplication and division, as well as the order of operations.

 

Arithmetic is also called calculation.

 

Arithmetic has developed over thousands of years, starting with simple whole numbers and today including roots, fractions, complex numbers etc.

As numbers develop, the rules of calculation must also develop. Among other things, the order of operations.

 

 

Order of operations

If you need to calculate an expression with several operations, it is important to do things in the right order. Otherwise you will not get the correct result.

 

For example:

 

$$ \large 3 + 3 \cdot 7 $$

 

Here you must always multiply before you add. So it becomes:

 

$$ \large 3 + 21 = 24 $$

 

The order of operations is as follows:

 

1. Roots and powers
2. Multiplication and division
3. Addition and subtraction

 

If you want a different order in a particular calculation, you can use parentheses. Parentheses must always be calculated first!

Inside parentheses the order also applies.

 

We know that:

 

$$ \large 3 + 3 \cdot 7 = 24 $$

 

Here the parentheses must be calculated first, so the result is different:

 

$$ \large (3 + 3) \cdot 7 = 42 $$

 

 

Algebra

Algebra is also called symbolic calculation and is an extension of arithmetic. Algebra makes it possible to set up equations, formulas and functions without knowing the numbers.

 

It could be the expression:

 

$$ \large a + x = b $$

 

where the solution is:

 

$$ \large x = b - a $$

 

It can also be used to describe a development, for example:

 

$$ \large f(x) = x + 2 $$

 

When performing the calculations, ordinary arithmetic is used.