 # Basic Arithmetic Operations in Mathematics

Which basic arithmetic operations in mathematics do you know? In this article, we would like to summarize the basic arithmetic operations. These are addition, subtraction, multiplication, division, powers, roots, exponents, and logarithms. You can apply all these basic arithmetic operations in all fields of study (mathematics, economics, business administration …, etc.) and everyday life.

## Introduction to the Basic Arithmetic Operations of Mathematics

Without the basic arithmetic operations of mathematics, there is no logic and no foundation to abstract everyday life using numbers. What we perceive every day, we can summarize with numbers. But how can we review everyday phenomena in numbers? The basic arithmetic operations provide us with the means and possibilities to do exactly that. In the following subsections, we will introduce the basic arithmetic operations in pairs. By doing that, you will understand how the sets influence each other by dealing with both arithmetic operations simultaneously.

## Summation and Subtraction

The first two pairs of basic arithmetic operations are summation (adding) and subtraction. According to the basic rules of summing numbers, subtraction is the inverse element of addition. In addition, the symbol $(+)$ means adding, while subtraction uses the symbol $(-)$ as deducting.

3+4=7 \\ \text{"The addition of three with four is seven."} \\ 5-2=3 \\ \text{"The subtraction of three from five is two."}

## Multiplication and Division

The next two pairs of basic arithmetic operations are multiplication and division. According to the basic rules of multiplication, division is the inverse element of multiplication. Multiplication uses the symbol $(\cdot)$, while division uses the symbol $(:)$.

3\cdot 4=12 \\ \text{"The multiplication of three by four is twelve."} \\ 6:2=3= \\ \text{"The division of six by two is three."}

## Powers and Roots

Now let’s look at powers and roots as another basic arithmetic for special terms in mathematics. For the powers we use the term $(a^n=b)$, while the roots use the term $(\sqrt[n]{b}=b^{\frac{1}{n}}=a)$.

2^3=8 \\ \text{"The third power of two is eight."} \\ \sqrt{8}=8^{\frac{1}{2}}=3 \\ \text{"The square root of eight to the base of two is three."}

## Exponents and Logarithms

As the latter, we look at the exponents and logarithms as another basic arithmetic for special terms in mathematics. For the exponents, we use the term $(\exp_a (n)=a^n=b)$, while the logarithms use the term $(\log_{a}(b)=n)$.

\exp_2 (3)=2^3=8 \\ \text{"The exponent of three to the base two is eight"} \\ \log_{2}(8)=3 \\ \text{"The logarithm of eight to the base of two is three."}

## References

Auer, B., & Seitz, F. (2013). Grundkurs Wirtschaftsmathematik. Springer Fachmedien Wiesbaden. https://doi.org/10.1007/978-3-658-02734-6 Cite
Sydsæter, K., Hammond, P. J., Strøm, A., Carvajal, A., & Böker, F. (2018). Mathematik für Wirtschaftswissenschaftler: Basiswissen mit Praxisbezug (5., aktualisierte Auflage). Pearson. Cite
Tietze, J. (2013). Einführung in die angewandte Wirtschaftsmathematik. Springer Fachmedien Wiesbaden. https://doi.org/10.1007/978-3-658-02361-4 Cite
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